library, ,

MAR 1 5 i

NBS MONOGRAPH 39

Calibration Procedures for

Direct-Current Resistance Apparatus

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
THE NATIONAL BUREAU OF STANDARDS

Functions and Activities

The functions of the National Bureau of Standards are set forth in the Act of Congress,

March 3, 1901, as amended by Congress in Public Law 619, 1950. These include the development

and maintenance of the national standards of measurement and the provision of means and methods

for making measurements consistent with these standards ; the determination of physical constants

and properties of materials ; the development of methods and instruments for testing materials,

devices, and structures; advisory services to government agencies on scientific and technical problems; invention and development of devices to serve special needs of the Government; and the

development of standard practices, codes, and specifications. The work includes basic and apphed

research, development, engineering, instrumentation, testing, evaluation, calibration services, and

various consultation and information services. Research projects are also performed for other

government agencies when the work relates to and supplements the basic program of the Bm"eau

or when the Bureau's unique competence is required. The scope of activities is suggested by the

listing of divisions and sections on the inside of the back cover. Publications

The results of the Bm-eau's research are pubHshed either in the Bureau's own series of publications or in the journals of professional and scientific societies. The Bm-eau itself publishes three

periodicals available from the Government Printing Office : The Jomaial of Research, published in

four separate sections, presents complete scientific and technical papers; the Technical News

Bulletin presents summary and preliminary reports on work in progress; and Basic Radio Propagation Predictions provides data for determining the best frequencies to use for radio communications throughout the world. There are also five series of nonperiodical pubhcations: Monographs,

AppUed Mathematics Series, Handbooks, Miscellaneous Publications, and Technical Notes.

A complete listing of the Bureau's pubhcations can be found in National Bureau of Standards

Circular 460, Publications of the National Bureau of Standards, 1901 to Jime 1947 ($1.25), and

the Supplement to National Bureau of Standards Circular 460, July 1947 to Jime 1957 ($1.50),

and Miscellaneous Publication 240, July 1957 to June 1960 (Includes Titles of Papers Pubhshed

in Outside Journals 1950 to 1959) ($2.25) ; available from the Superintendent of Documents,

Government Printing Office, Washington, D.C.
UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Calibration Procedures for

Direct-Current Resistance Apparatus

Paul P. B. Brooks

National Bureau of Standards Monograph 39

Issued March 1, 1962

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 40 Cents

Preface

The summer of 1960 at the University of CaUfornia, Los Angeles, I gave

a series of lectm^es on the precise measurement of d-c resistance. These

lectures were part of a course on basic measurements and standards in a summer program for industry entitled "The 1960 Statistical Methods in

Industry Course." For use in this course, I asked Paul P. B. Brooks of the

NBS staff to prepare a detailed description of the procedm-es used at the

National Bureau of Standards for the accurate measurement of d-c resistance.

In view of the current urgent needs of industry and the military services for

information on precision measurement techniques, it was decided to expand

and publish this material in the present Monogi-aph.

Because of the recent tremendous growth in standardizing laboratories,

and the lack of personnel with training in measurements, it seemed desu'able

to present this material on d-c measurements in as nontechnical a way as

possible. It should then be helpful to the largest number of people, although

admittedly containing much detail that is unnecessary for those with scientific training.

James L. Thomas, Chiej,

Resistance and Reactance Section,

Electricity Division.

iii

Contents

Page

Preface--. iii Part 1. General Outline of Equipment and

Procedures 1

1. Object and scope of this paper 1 2. Errors, corrections, and tolerances 1 3. Basic circuit for d-c measurements 2

4. Resistance standai'ds 3

4.1. Design for precision measurements.- 3

4.2. Two-terminal versus four-terminal

resistance 3

4.3. Stability of resistors 4

4.4. Correction for temperature 4

5. Connections and supports for standards 5

5.1. The mercury stand 5

5.2. Amalgamating solution 5

6. The sensitive galvanometer and accessories- 6

6.1. The galvanometer 6

6.2. Damping 8

6.3. Some sources of trouble 8

6. 3. a. Temperature 8

6.3.b. Thermoelectromotive forces 8

6.3.C. Vibration of the galvanometer

support 9

6.3.d. Magnetic disturbances 9

6.3.e. Continuous small oscillations,- 9

6.3.f. "Zero drift" 9

6.3. g. Reactive "kick" 9

6.4. The reversing key 9

6. 4. a. Advantages 9

6.4.b. Design 9

6.4. c. A convenient battery box 10

7. Miscellaneous 10

7.1. Absolute ohm versus international ohm 10

7.2. Algebra of small quantities 10

7.3. "Rounding off" numbers 11

7.4. Interpolation 12

7.5. Extrapolation 12

7.6. Errors versus mistakes 12

7.6.a. Errors 12

7.6.b. Mistakes 13

8. The Direct Reading Ratio Set. Its use in resistance measurements with a 1:1 ratio - 13

8.1. Basic circuit, connections, and preci- sion 13

8.2. Resistance by substitution 14

8.3. Resistance by the interchange

method 15

8.4. Comparison of a four-terminal resistor with a two-terminal resistor.. 16

8.5. Approximate measurement of a small

resistance 16

8.6. Determination of the two-terminal

resistance of a 1-ohm resistor when

its four-terminal value is known- 17

9. Measurement of "odd-valued" resistors 18

9.1. "Odd values" distinguished from val- ues of conventional standards 18

9.2. Combinations of resistors 18

9. 2. a. Resistors of the same nominal

value in series 18

9.2.b. Resistors of the same nominal

values in parallel 19

9.2. C. Resistors of different nominal

values in series 20

! 9.2.d. Resistors of different nominal

i values in parallel 20

j 9.2.e. Resistors in series and in

\ parallel 20

i 9.3. Adaptation of the Direct Reading

1 Ratio Set for ratios of l:/i and «t:tt-- 21

! 9. 3. a. Typical adaptations 21

i 9.3.b. "Bridge zero" 21

9.3. C. Applications of above proce- dures to the measurement of

! odd values 22

Pago

9.3. (1. iJcti'rmination of "bridge zero" with two standards and th(!ir corrections . . . 24

9.4. Calibration of nicf^olim boxes and

0. ] -iiicgolini l)(j\cs for use as resistance slaiidacds 25

9. 4. a. Calibration of the box 25

9.4.b. Us<! of the calibrated box as a

resistance standard 26

10. The Universal Ratio Set (I'H.S) 26

10.1. The Universal Ratio Set compared

to a slide-wire 26

10.2. Application to four-terminal meas- urements 27

Part 2. Calibration of a Wheatstone Bridge-,. 28

11. Test equipment 28

12. The Wheatstone bridge circuit 28

12.1. Ratio arms, A and B 29

12.2. Rheostat arm, R 29

13. Outline of test procedures 29

13.1. Need for testing 29

13.2. Required measurements 29

13.3. The circuit diagram 30

13.4. Reducing contact resistance 30

13.5. Load tolerance 30

13.6. Applicability of general principles- - 31

14. Test of open dial bridge 31

14.1. Test 1: Zero and internal lead

resistance 31

14.2. Test 2: The rheostat arm 33

14.2.a. Calibration of X and Y 34

14.2. b. The 0.1-ohm-per-step decade. 36

14.3. Test 3: The ratio arms 36

14.3. a. The A arm 37

14.3.b. The B arm 38

14.3. C. Working test 39

15. The National Bureau of Standards certificate 39 Part 3. Testing General Purpose Potentiometers. 40

16. The Potentiometer—general description.. 40

16.1. The potentiometer circuit 40

17. Adaptability of the universal ratio set to testing potentiometers 41

17.1. Measurement of voltage ratios 41

17.2. Interpretation of URS readings 41

17.3. "Direct reading" versus "not direct reading" 42

17.4. General outline of test procedures. . 43

17.4. a. Dial tests 43

17.4.b. Factor tests 44

17.4. C. Standard cell dial 44

17.5. Some modifications of procedure 44

18. Details of procedure as applied to a specific

model. . 45

18.1. Description of potentiometer

Crompton type 45

18.2. Test equipment 45

18.3. Tests required 45

18.4. Points to remember 46

18.5. Testing procedures 46

18. 5. a. Connections and dial settings. 46

18.5.b. To make the URS "direct reading" 46

18.6. Measurements on the main dial 47

18.7. Measurements on the slide wire 48

18.8. Measurements on the standard cell dial 48

18.9. Finding corrections for the main dial. 48

18. 10. Finding corrections for the slide-wire. 49

18.11. Tabulation of data for the standard

cell dial 49

18.12. Factors 50

18.13. Application of corrections 50

18.14. Procedure when the URS is not

"direct reading" 51

18.15. A working test 51

19. Sample certificate for potentiotneter - 53

V

Calibration Procedures for Direct-Current Resistance Apparatus

Paul P. B. Brooks

The equipment and procedures used at NBS for the precise rrieasurerncnt of d-c resist- ance are explained in detail. Ttie specific, application of tliesc procedures to the calibration

of bridges and potentiometers is explained. It is expected Ili.i1 this [laper will be of considerable help to the many company and governmental standardizing laboratories now being

established.

Part 1. General Outline of Equipment and Procedures

1. Object and Scope of This Paper

This paper describes the apparatus and procedures used at the National Bureau of Standards

for the measurement of d-c resistance when an

j accuracy of a few parts in a million is required.

I The instruments usually used for this work are the

Direct Reading Ratio Set and the Universal Ratio

Set. These instruments, together with an assortj ment of standard resistors, special mercury stands,

1 and galvanometers, switches, and batteries, are

' used for the calibration of practically all types of

d-c measuring instruments.

I The object will be to explain procedures in detail

; and as simply as possible, with a minimum ref- erence to theory. For the reader who wishes to go into greater detail of design and theory. Circular 470 of this Bureau, "Precision Resistors and

I Their Measurement," or text books on electrical

i measurements shotild be consulted.

, 2. Errors, Corrections, and Tolerances

I These quantities may be expressed in units of

j| measurement, proportional parts, percentages, or

parts per million.

If the value of a resistor, as measured with a

bridge, is 99.7 ohms, whereas its correct value is 100.0 ohms, the error of the bridge measurement

is —0.3 ohm. The correction which must be added

to the bridge reading to obtain the true value is + 0.3 ohm. It is important to avoid confusion

between error and correction.

i If the bridge reading had been 100.3 ohms, the

I correction would have been —0.3 ohm.

I In precision measurement, we are concerned

with the correction which must be added algebraically to the reading of an instrument or to the

u nominal value of a resistor to obtain the true value.

I In the preceding example, the correction +0.3

ohm, expressed in proportional parts, is +0.003,

or +3/1,000, or +3 parts per 1,000 of the bridge

reading. The correction in proportional parts to the reading of an instrument is equal to the cor- rection divided by the reading. Likewise, the

I correction in proportional parts to the nominal

value of a resistor is equal to the correction in

ji ohms divided by its nominal value in ohms.

ij The correction in percent is 100 times the cor-

, rection in proportional parts. Hence, the correction in the above illustration is +0.3 percent

of the bridge reading. The correction in parts per

million (ppni) is 1,000,000 times tlie cori'cction in proportional parts. Tlie above correction is +3,000 parts per million ( +3,000 ppm).

Proportional parts X 100=percent

Proportional parts X 1,000, 000=parts per million

Percent X 10,000=parts per million

The correction of 3,000 ppm is many times

larger than the corrections for good laboratory

equipment. However, the difference between

3 000 ppm (0.3 percent) of 99.7 ohms and 3 000

ppm of 100.0 ohms is only 0.0009 ohm. Therefore, in laboratory measurements, it is usually

immaterial whether a correction to a resistance

is based on its nominal value or on its true value.

A tolerance is usually expressed as a percentage.

If the certified value of a resistor is 100.003 ohms

with a stated accuracy of 0.002 percent, the

tolerance is ±0.002 percent of 100.003 ohms,

or ±0.002 ohm. The true value is within the

range 100.003 ± 0.002 ohms (100.001 to 100.005

ohms).

Resistors are designated by their nominal

values. Due to limitations on the accm-acy of

manufacture and to inherent instabilities in resistance materials, some correction, positive or negative, generally must be added to the

nominal value of a resistor to obtain its true value. Since the correction is usually given in parts per

million by the special bridges used at the National

Bureau of Standards, it must be expressed in terms of the ohm before it can be used.

Example: What is the true value of a resistor

if its nominal value is 1 000 ohms and its cor- rection is +57 ppm?

Solution: The correction, +57 piJ'n, is +0.000057 proportional parts; 0.000057 of 1 000

ohms is 0.057 ohm. Since the correction is positive, the true or corrected value is 1 000.000 +

0.057 = 1,000.057 ohms.

A quick and simple solution is expressed in the following rule: Affix, enough zeros to the nominal value to make one million {or a small integral

multiple of one million). Underneath, write the correction with its algebraic sign. Add, and place

the decimal point consistent with its position m

the nominal value.
Examples:

1. The nominal value of a resistor is 1 000 ohms. Its correction is +57 ppm. What is its corrected value?

(See block at rig-ht).

Nominal value

Affix 3 zeros Add correction

Point ofi"

1 000.

1 000 00(

+5'-

1 000. 05'/ The corrected value is 1 000. 057 ohms. If the correction had been —57 ppm, the corrected valu(

would have been 999.943 ohms.

2. Find the corrected value of a 0.001 -ohm (nominal

value) resistor with a correction of —63 ppm.

The corrected value is 0.000999937 ohm.

3. Non)inal value, 50 ohms. Correction, +71 ppm.

Find the corrected value. The addition of five zeros makes j^i)e million. Hence, add 5X( +7l) = +355 parts

'per five million.

The corrected value is 50,00355 ohms.

Nominal value

Add 6 zeros Add correction

Point off

Nominal value

Affix 5 zeros Add correction

Point off

0. 001

1 000 ooq

-63'

0. 000 999 937

50. 50 00 000

+355

50. 00355

The notation, i?(l +c), is a short and con- venient metliod to express the true value of a

resistor in terms of its nominal value, R, in ohms

and its correction, c, in parts per million. For

example, 100(1+27 ppm) shows that 0.000027 of the nominal value must be added to the ICO ohms

nommal value to obtain the true value. Hence,

the true value is 100X1.000027 = 100.0027 ohms.

Likewise, 10(1-85 ppm) shows that a correction

of —85 ppm must be applied to the nominal

value of 10 ohms to give the true value of the

resistor. The true value is 10(1-0.000085) =

10X0.999915 =9.99915 ohms.

In any case, the true value may be found by

the method illustrated by the above examples.

3. Basic Circuit for D-C Resistance Measurements

Precise measurements of resistance with the

Direct Reading Ratio Set or the Universal Ratio

Set make use of a Wheatstone bridge circuit in which the ratio set forms the ratio arms.

(A) BA Figure 1A and B.(b) Wheatstone bridge circuit.

The Wheatstone bridge circuit is represented

schematically in figures lA and IB, where X, R,

A, and B represent the arms of the bridge and also their respective resistances. Resistors A and B

form the ratio arms. One of these arms, or both,

are variable. X is a resistor of unknown value,

and R is a known resistor. G is the galvanometer

and BA is a battery of suitable voltage. In

addition to the components shown in the diagram,

a key or switch is in the battery branch of the

circuit. A key, if present in the galvanometer

branch, is usually kept closed during measurements. A variable resistor or battery rheostat in the battery branch serves to adjust the voltage

across the bridge arms. A voltmeter across the

battery and the batterv rheostat will indicate the

applied voltage.

W^hen the battery and galvanonieter keys are

closed and the variable resistors in the bridge arms are adjusted to reduce the current through

the galvanometer to a minimum, the bridge is said

to be "balanced." When the bridge is balanced,

the value of X is given by the basic equation,

X=-RB

This equation applies regardless of the relative

locations of battery and galvanometer as shown in the above diagrams. The choice of arrangement

is determined mainly by the distribution of cuiTent

in the arms of the bridge. Current which produces excessive heat in any branch will impair the

accuracy of measurement.

The circuit arrangement generally used for measurements with a ratio set is shown in figure 2.
Figure 2. Ratio set in a Wheatstone bridge circuit.

In the diagram, S is a resistance standard, X an unknown resistor of the same nominal vahie, and

the ratio arms A and B are the arms of a Direct

Reading Ratio Set. G is the galvanometer and

V is a voltmeter across the battery, BA, and the

battery rheostat, Rh. The cm-rent divides at M

into parts which are nearly equal tlirough the

branches MPO and MNO, thus applying approximately equal loads on these two branches of the

network.

The advantage of the circuit of figure 2 is that,

j since the nominal resistance of each arm, A and B,

I of a Direct Reading Ratio Set is 100 ohms, the

j resistance of each branch, MPO, and MNO, for

i any value of S and X, is always more than 100

f ohms. With a sensitive galvanometer excessive

I heat in any part of the bridge circuit may be

I easily avoided.

j On the other hand, if the galvanometer is

' connected to M and O and the battery is connected

I to P and N, corresponding to figiu'e lA, and

j: S=X=1 ohm, the current through S and X will

: be 100 times the current through A and B.

[ Although the emf required across the bridge in

j' this case may be considerably less than the emf

required in the circuit of figure 2, the current through the one-ohm resistors, nevertheless, will be greater. Since the heat developed in a resistor

is proportional to the square of the current, there

1 is a chance of producing excessive heat. The emf

j may be usually increased in the circuit of figure 2

] to give adequate galvanometer deflections for large values of vS ancl X without overheating any

part of the circuit.

4. Resistance Standards

4.1. Design for Precision Measurements

A high degree of accuracy in resistance measure- ments is attained by comparison of an miknown

Figure 3. NBS standard resistor. resistance with one which is accuratelj' known.

For this purpose, resistance standards, accurate

to a few parts in a million, are available in a wide

range of values, usually in decimal multiples or submultiples of 1 ohm.

The resistance element of manganin wire is enclosed in a protective case and connected into a circuit by two copper arms, the terminals of

which (a, a', fig. 3) are plane, clean, free of corrosion, and amalgamated. The arms with amalgamated terminals are designed to support the

resistor with the terminals in mercury cups or on

a mercury stand. Contact resistance cannot be

ignored when precision is required. Mercury contact resistance may be kept to a few microhms,

while clamped contacts will probably oft'er a re- sistance of 100 to 1000 microhms. AJso, mercurycontact connection can be repeated without

significant change in contact resistance. Binding

posts (b, b') are usually provided at the top of the arms. The difference in resistance between

a and a' and the resistance between b and b' is insignificant in comparison with the resistance of a resistor of large denomination. For a resistor

of 1 ohm or less, the dift'erence is important.

4.2. Two-Terminal Versus Four-Terminal Resistance

This leads to consideration of the dift'erence between two-terminal and four-terminal resistance. In figure 4, if the resistance is measured twoterminally between c and d, it is equal to the

resistance of R plus the resistance cf tlie leads, ca and bd. Likewise, if the resistance is measured
CURRENT

LEAD

a b WWWWf

POT

"leads

CURRENT

LEAD

Figure 4. Four-terminal resistance.

two-terminallj^ between e and f, it includes the

resistance of the leads, ea and fb. However, if ciurent leads go through c and d and potential

leads go through e and f, the measurement gives

the resistance between the junction points a and

b, regardless of resistance of current leads or

potential leads. The four-terminal measurement

is based on the fall of potential across R compared

with the fall of potential across a resistance

standard in series with R, with a constant current through the two resistors. Fom-terminal measurement is necessary in testing laboratory instruments, such as Wheatstone bridges and potentiometers, in which connection to a given resistor can be made only through

other resistors. The resistance of the connecting arms of a re- sistance standard of small denomination is proportionally large compared with the resistance of

the element. Hence, standards of a nominal

value of 1 ohm or less are calibrated four-terminally. The current leads of 1-ohm standards

enter through the amalgamated terminals, a, a', and the potential leads are taken to the top

binding posts, b, b' (fig. 3). The potential leads

for standards of smaller denomination go to extra binding posts mounted on the insulating cap of the protective case with leads to the enclosed

resistance element.

The National Bureau of Standards usually

certifies the four-terminal values for standard re- sistors of 1 ohm or less, the two-terminal values

for all others. The two-terminal values for 1-ohm

standards are certified only if they are requested.

In some testing procedures, the two-terminal value

of a 1-ohm standard may be required. The twoterminal values of the NBS-type standards ofi recent manufacture are usually 40 to 50 microhms

greater than the four-terminal values. However,

in different makes the difference between the two

values may be considerable. If the two-terminal

value of 1-ohm resistor is not given, it may be

measured readily with a Direct Reading Ratio

Set. The method will be explained in section 8.6.

4.3. Stability of Resistors

The value of a resistor is not perfectly constant.

It changes with time and with temperature; and;

unsealed resistors, such as those in bridges,^

potentiometers, etc., are affected hj humidity.

A severe shock, such as a fall on the floor, may

change the value of a resistor and impair its stability. Overloading may result in permanent'!

damage. A load that does not exceed }io w is desirable. However, 1 watt is usually a safe load,

probably with a decrease of accuracy.

Modern resistance standards are quite stable. An annual change of more than 20 ppm is ex-|

cessive. The average yearly change of several

hundred standards calibrated at the National,

Bureau of Standards was less than 10 ppm

However, a standard that has not been calibrated

for several years cannot be relied on for precise

measurements.

The resistance standards maintained at thej

National Bureau of Standards are subject to only

small changes of temperature and are recalibrated

regularly at 25.0 °C to the nearest part per million.

Well aged standards submitted to the National

Bureau of Standards usually are certified to the nearest 20 ppm at 25.0 °C. New standards usuall,y are certified to 50 ppm.

4.4 Correction for Temperature

If a resistance standard is used at some temperature other than the temperature at which it was

calibrated (25.0 °C), a correction must be applied

to its certified value.

Components of 1-ohm standard resistor of type used at the National Bureau of Standards

to maintain the ohm.

Left to right: complete standard, top terminal assembly, outer wall, inner wall, annealed resistance coil. 4
I

TEMPERATURE, °C

|l Figure 5. Temperature-resistance curve of manganin wire. The resistance of manganin wire increases as the

temperature rises until it reaches a niaximum at some point between 20 and 50 °C (fig. 5). The

' resistance then decreases to a minimum as the

) temperature rises, and then increases again.

S "Within the range of usual room temperatures, tlie resistance may be accurately expressed by the

|| following equation:

/?,= /?25[l +a(^-25)+/3a-25)2].

9j In this equation, t is the temperature of the resistor

ij and 7?, is its resistance at < °C. /?25 is its resistance

El at 25 °C. Alpha (a) and beta (/3) are its tempera-

•I ture coefficients. The Bureau determines the

t! temperature coefficients if they are requested.

?j They do not need to be redetermined because

1 temperature coefficients do not change apprecij ably with age.

I The following example illustrates the application

I of the temperature coefficients. The resistance

J of a certain standard is fOO.006 ohms at 25.0 °C.

j Its temperature coefficients are alplui—

I +0.0000063 and beta= -0.00000051. When

1 these numbers are substituted in the above equa1 tion, the resistance at 20.0 °C, rounded oft' to the

Ij nearest thousandth ohm, is found to be 100.002

ohms.

L The need for the temperature correction is determined by the accuracy required and the temperature at which a test is made. In the above

' example the temperature correction for the resis- tor at any temperature between 24 °C and 26 °C

, is less than 10 ppm.

I

|i 5. Connections and Supports for Standards

il The binding posts on the lead arms of resistance

I standards of small denominations (1 ohm or less) are intended for potential leads in four-terminal

, measurement. The binding posts on the arm of

resistors of greater value may be used for conneci tions in two terminal measurements if high pre-

; cision is not required or if the value of the resistor

\ is large enough to make the contact resistance

Fi(;uRE (). Top of mercuri/ .stand.

negligible. For precision, standards should bo

supported on a mercui'V stand to reduce contact

resistance to a minimum and to permit repetition

of the measurements within a few parts in a million. Mercury cups, which are sometimes used, are difficult to cleaji. A pool of mercury is unnecessary. A fiat amalgamated surface is quite

satisfactory.

5.1. The Mercury Stand

Figure 6 illustrates the arrangement of tlie nickel-plated copper contact blocks and tlie binding posts of the NB8 jnercury stand. The blocks

are % in. square with a length of about Sji in. for the long pair and 1)^ in. for the short blocks. The

upper surfaces are plane, clean, and well amalgamated. The spacing and the height of the supporting posts permit resistors to hang freely

between the blocks. The blocks are effectively

insulated from the supporting posts which extend

upward from the base.

The mercury stand offers several advantages in addition to its low contact resistances. Standards

may be quickly connected into a circuit, removed,

or interchanged. A connecting or shorting link

is useful to fill a gap in a circuit when a standard

is to be shorted out or removed. Standards on

the stand may be connected into two arms of a bridge circuit. Two resistors may be placed in parallel on the stand, or as many as five may be

connected in series. Two or more stands may be

connected by short leads between their binding

posts, or by shorting links. A shorting link is a practical and essential acces- sory to the stand. Tlie link used at XBS is a

nickel-plated copper rod ji in. in diameter and

about 3/^ in. long with right angle bends which

space the ends 3 in. apart, center to center. The

ends are plane and amalgamated to make good

contact with the amalganiated surfaces of the

stand. A link of this description w'ill have a

resistance of about 40 microhms.

5.2. Amalgamating Solution

Contact surfaces occasionally need to be cleaiunl and re-amalgamated. A satisfactory amalgamating solution consists of:

1 oz water

oz mercm'ous nitrate

}i oz concentrated nitric acid.
Stir the mixture. If it does not become clear,

warm slightly. Some mercurous nitrate will precipitate when the solution cools. An added drop

of mercury will improve the keeping qualities.

The proportions in this solution may be varied

considerably. Caution should be observed in handling nitiic acid and poisonous compounds of mercury.

The surface to be amalgamated should be clean

and free of grease ancl corrosion. After the

solution is applied, the surface should be washed

free of corrosive chemicals with water and a small

drop of mercury applied.

6, The Sensitive Galvanometer and Accessories

6.1. The Galvanometer

Galvanometers used in direct current measure- ments usually employ the D'Arsonval movement,

which consists of a movable rectangular coil supported in the magnetic field between the pole

pieces of a permanent magnet. A current through

the coil will produce a "turning force" or torque

which will turn the coil about its vertical axis

until it is brought to rest by the opposing torque

due to the stiffness of the suspension.

Commercial galvanometers are of many types

and models with different sensitivities suited to

specific uses. However, at the National Bureau

of Standards, only one type is used for resistance

measurements in testing resistors, bridges, potentiometers, etc. Specifications for this type will be given after the following description.

The moving element of the galvanometer is a

flat rectangular coil suspended between the soft iron pole pieces, P, P', of a permanent magnet,

PM, figure 7. The plane of the coil, at rest, is parallel to the field of the magnet. A soft iron

core, C, \& fixed inside the coil. The sides of the

coil are free to rotate in the narrow gap between

the pole pieces and the core. This conditio]

necessitates careful leveling of the galvanometer'

A small mirror, M, is attached to the upper en(

of the coil and rotates with it. The upper suspension is a thin, narrow, coppe

ribbon between the supporting stud. A, and thi

coil. The upper suspension serves three purposes

(1) it supports the coil; (2) it serves as a curren

lead to the coil; and (3) it provides a restoring

torque in opposition to any rotation of the coil. The lower suspension is a loose coil of fin* copper wire from the lower end of the coil to the

stud, B. It offers negligible opposition to tlu rotation of the coil and serves only as a curreni

lead. The studs, A and B, are connected to tin binding posts.

A metal case encloses the instrument to shield' the coil from air currents. A window in the cast permits a light beam to be reflected from the mirror and affords a view of the coil, pole pieces'

and cor^. A lens of suitable focal length focuses

the light beam on a scale. Leveling screws on the

base can be adjusted so that the coil can rotate

freely in the narrow gap between the pole pieces

and the core. f The torque which causes the coil to rotate on^

its vertical axis is proportional to the current audi

is directed clockwise or counterclockwise, depend^'

ing on the direction of the current. The opposing

torque due to the twist of the suspension is pro-'

portional to the angle of rotation. The angle'

through which the coil rotates before it is broughtj

to rest hy the opposing torque is proportional to the current. Oscillations of the coil about the rest position can be controlled by suitable elamping.

When galvanometer deflections are read by the

use of a light beam reflected from a mirror to a

scale, small deflections on the scale are approximately proportional to the current. If the dis- tance from the mirror to the scale is 100 cm, the

limiting deflection on the scale is 15 to 20 cm,

depending on the accuracy requireel. However,

resistance measurements are rarely maele b^' galvanometer deflection. Resistance measurements

are usually made in a bridge circuit adjusted to obtain minimum deflection of the galvanometer.

A perfect zei'o deflection or "null" reading of the

galvanometer is frequently impossible.

The indicator is a narrow beam of light re- flected from the mirror to a ground glass scale (fig. 8). The light source used at NBS is a straight

filament lamp. These lamps are rated at about

10 v; hence the line voltage must be stepped

'LAMP FILAMENT

SCALE

MIRROR

~IMAGE OF LAMP FILAMENT

Figure 7. The D'' A rso rival galvonomeier movement. Figure 8. Arrangement of lamp, mirror, and scale of re- flecting galvanometer.
!

down by ii transronner. A shield iirouiid the

lamp allows the light to pass through a nari'ow

slit to the galvanometer mirror. A lens of suit- able focal length focuses the reflected light on

a ground-glass millimeter scale. By adjusting

the distance from the mirror to the scale, or the

light source, or both, a sliarp image of the lamp

filament niay be obtained on the scale. T\w

image of the lump filament is observed from the

opposite side of the scale. A standard distance

from mirror to scale is fOO cm. With a lens of greater focal length, a distance of 150 cm can be

used with satisfaction. In effect, the light beam

provides the rotating coil with a weightless pointer about 200 to 300 cm long.

The scale is of ground glass graduated in centimeters and millimeters. The zero on the scale may be at either end or in the middle. It is not necessary to set the "rest" position of the

indicator on the zero graduation of the scale. The deflection from any "rest" position is readily

obtained.

If the galvanometer is used only as an indicator, a very small deflection is sufficient. If however, an interpolation is to be made, or a measurement is to be made by galvanometer deflection, the deflection must be large enough to be read accurately.

The specifications for a sensitive galvanometer

usually include: (1) sensitivity, (2) CDRX, that

is "critical damping resistance external," (3) period, and (4) coil resistance.

The following specifications are from the maker's label on one galvanometer used at NBS for resistance measurements

(1) Sensitivity^: hmeter

(2) CDRX:

(3) Period:

(4) Resistance:

0.08 microvolt/i

(ytiv/mm)

50 ohms.

8.8 sec. 17.6 ohms.

The specifications will difl'er somewhat for each

galvanometer. A repair or replacement of a suspension will change its specifications somewhat.

If the sensitivity is adequate, variations of 10 to 20 percent in the other constants are usually

acceptable.

The sensitivity given above is the voltage sensitivity. Evidently the voltage across the galvanonieter branch which will produce a deflection of one division on the galvanometer scale (or the

number of scale divisions of deflection caused by

1 microvolt (mv)) will depend on the resistance of the circuit. Hence, the sensitivity can be specified only for a given resistance in the galvanometer

circuit. For sensitive galvanometers, American

manufacturers generally specify voltage sensitivity in microvolts per millimeter when the exter- nal resistance in the galvanometer circuit is equal

to the CDRX Avith the scale 100 cm from the galvanometer. The above specification of voltage

sensitivity means that with a resistance in the

galvanometer circuit of 67.6 ohms (CDRX plus

galvanometer resistance), 0.08 mv will produce a

deded ion of I iiini on a scale al a (Nslnncc of 100 cm IVoin I he galvanometer. Note (hnl I he sm.-dlci- the IVaction of a, microvoll, iIh' gi'cjilcr I he

sensitivity.

The sensitivities of the gaivaiiomel ers u.scd foi- resistance mcasurenK^its at the Bureau are usuall\'

expi'essed in millimeters pel' mici'ovolt at a seale distance of 150 cm. The inci'eased scale distance

gives larger deflections, and the reflected light spot on the ground-glass miUimetcr scale is. still bright

enough to be readable in adequate room lighting.

The above sensitivity would ])e 1/0.08, or 12.5 nun/

yixv at 100 cm and it would be al)0ut 18.8 mm/juv

at 150 cm. Note that, expressed in this \v:\y, the larger the numerical expression of snisUirUij, the greater the sensitivity. This seems like a logical

way of expressing sensitivity.

The term "sensitivity" is often used loosely

in the sense of "readability." The sensitivity depends upon certain characteristics of design. As

long as none of these characteristics are changed,

the specified sensitivity remains fixed. If a, ver\'

small current through the galvanometer does not

give an observable deflection, a larger current may

give a readable deflection. The sensitivity has

not changed.

The accuracy of resistance measurements may

be adversely affected by either too low or too high

a sensitivit}''. Suppose a galvanometer of low

sensitivity is used with the Direct Reading Ratio

Set to measure a resistance. To get enough cur- rent through the galvanometer to obtain an observable change in the deflection for a change of one

step on the lowest dial of the ratio set, it may be

necessary to increase the voltage across the test circuit until excessive current raises the temperature, resulting in incorrect results or even damage

to the equipment.

On the other hand, too high a sensitivity is ac- companied by a slow movement of the galvanometer coil, which makes reading tiresome. Of more

importance is the fact that the greater the sensitivity the more the galvanometer is aft'ected by

thermal emf's, which ma}' make accurate readings

difficult or, in extreme cases, impossible. A sensitivity between 10 and 30 ram//xv at 150 cm has

been found generally satisfactory for resistance

measurements.

The CDRX is the resistance in the galvanomelcr

circuit, in addition to the galvanometer resistance,

which will cause the galvanonu'ter to complete a

deflection and stop without oscillation. This

condition is known as critical damping, which

will be discussed in section 6.2. The CDRX is usually several times the galvanometer resistance.

The period is the time required for the un- damped coil to make one complete oscillation.

If a small current is sent monuMitarily through

the coil and the circuit imnu^diately opened, the

coil will oscillate freely until the oscillations die

out due to the damping action of the air ai\d the

molecular friction in the suspensions. The time

required for the coil to move iron; one extreme

7
position to the other, then back to the first, or,

tlie time from the rest position to one extreme,

then to the other extreme, and back to the rest position is the period. About 5 to 10 sec is generality a satisfactory period for a sensitive

galvanometer.

The galvanometer resistance is the resistance

of the coil and its suspensions. It is generallv

less than the CDRX.

As has been stated, galvanometers of the same

type will vary in their specifications. The

following table gives the range of specifications

for different sensitive galvanometers used in the

resistance and reactance laboratory at the Bureau.

Sensitivity: 10 to 30 mm/fiv at 150 cm. CDRX: ' 40 to 80 ohms.

Period: 5 to 10 sec. Resistance: About 15 or 20 ohms.

6.2. Damping

If a momentary emf is applied to a galvanometer

and the circuit immediately opened, the coil will oscillate freely as a torsion pendulum. The

period for a sensitive galvanometer will probably

be between 5 and 10 sec. The oscillations

will be "damped," that is, they will gradually

decrease, due to friction with the air and molecular

friction in the suspension, until, after several

oscillations, the coil will come to rest. If the coil

is part of a closed circuit, the oscillations will die out more quickly due to the damphig effect caused by the rotation of the coil in a magnetic

field. The degree of damping will depend upon

the resistance of the circuit, including the galvanometer resistance and the resistance of the

external circuit. For each galvanometer, there

is a Critical external damping resistance (CDRX).

With critical damping, the coil swings to its steady

position and stops without oscillation. With

under-damping, the coil may oscillate before it settles to a steady position. With o-ver-damping

,

Figure 9. Connection of dam-ping resistor in galvanometer

circuit.

the coil is sluggish a]\d the reading time is pro

longed, until the coil completes its deflection.

For a damping resistor, a dial box with a rang(

of 100 ohms in 10-ohm steps is usually adequate

This may be connected into the circuit with a double-pole double-throw switch as shown in figure 9. With the blades of the switch in tht upper position, the variable resistor is in parallel

with the gahanometer and, with the blades in the lower position., the resistor is in series in the

circuit. Practically, the best damping is little less than

critical. The galvanometer "overshoots" slightly

and settles back to its final position. The reading

time is not excessively long, while the overshoot

and return of the galvanometer to its final value

assures the observer that the coil swings freely.

Usually, the experimenter will find the damping

best suited to his work by trial and error. However, a knowledge of the critical external dampint:

resistance of the galvanometer and of the resist- ance of the apparatus in the circuit may save some needless trials. For example, the CDRX of a certain galvanometer is 50 ohms. If the circuit external to the

galvanometer has a resistance of 50 ohms, the

galvanometer is critically damped. If the external

resistance is less than 50 ohms, the galvanometer]

is over-damped. Additional resistance in series in the circuit is needed. If the external resistance is more than 50 ohms, a parallel resistance is required. In either case, the eft'ective sensitivity

is reduced.

During use, it is preferable that the galvanometer circuit remain closed. That will, to some

extent, damp oscillations due to vibration or to other extraneous sources, and will eliminate thermal emf's introduced by closing a switch in the

galvanometer circuit.

6.3. Some Sources of Trouble

6.,?. a. Temperature

Variations of temperature affect not onl}- the

galvanometer, but every branch of the circint of which it is a part. The laboratorj" should be at a constant uniform temperature, free from drafts. When the battery key is closed, heat is produced

in the circuit in proportion to the square of the

current, the resistance of the circuit, and the time

of current flow. Hence, the emf of the battery

should be only large enough and the key should be

depressed only long enough to get a definite

reading on the galvanometer scale. When measurements are made with a potentiometer, a constant current is required in the instrument. In

that case, the current should flow long enough to establish a stable heating condition in the potentiometer circuit.

5.3.b. Thermoelectromotive Forces If two conductors in a circuit are of different

composition and the temperature at their junction

is different from the temperature at other points

i

8
n the circuit an electromotive force will be

produced. To minimize these thermoelectromotive forces, only copper lead wires should be used,

and precautions should be taken to maintain

imiform temperature throughout the circuit. The

heat from a hand resting on an instrument panel

will sometimes produce an erroneous deflection of the galvanometer.

6.3.C. Vibration of the Galvanometer Support

The sensitive galvanometer is quite susceptive

to vibration. Rimning machinery in the building,

a heavy truck on the pavement near the laboratory, strong wind gusts against a wall on which

the galvanometer is moimted, or even an earthquake some thousands of miles away, may distm-b

the sensitive movement. The instrument should

be mounted on the steadiest support possible.

6.3.d. Magnetic Disturbances The galvanometer is sensitive to the magnetic

fields of nearby motors, generators, etc.

6.3. e. Continuous SmalJ Oscillations

After major disturbances have been reduced to a minimum there may still persist oscillations of

small amplitude of miltnowm cause. They make

it difficult to determme the "zero" or rest position on the galvanometer scale, and also, to obtain an

accurate reading of a deflection.

6.3.f. "Zero Drift"

After a deflection, the galvanometer may not

return to its initial rest position. This shift of zero may be negligible if the deflection is small.

Another type of zero shift is a continuous slow

drift in one direction or the other.

6.3.g. Reactive "Kick" When a circuit which contains one or more

coils of wire is closed or opened, an instantaneous

emf, which either aids or opposes the impressed

emf, is produced in the coil. The residting surge

of current gives the galvanometer a temporary deflection different from the deflection produced by

a steach'^ current. The effect will be especiall}"

noticeable in resistance coils of large denomination. It is important to recognize the "Idck" and

to allow the galvanometer to settle to a steady

state before taking a reading.

6.4. The Reversing Key

6.4.a. Advantages

Use of a reversing key reduces some of the errors arising from disturbances listed above, eliminates

others. After a deflection has been read, the cm-rent through the bridge is immediately reversed and

and the deflection in the opposite dii"ection is read.

The "spread" between the two deflections is double a single deflection. Ajiy error in reading is

propoi-tionately reduced. The (h'llcclioii is doubled, but errors due to th(u-mal cmf's, zero drift,

etc., are not increased. If thcic is a steady drift of galvanometer zero, it is in the diiwtioji of one

deflection, opposite to the otlier. The same is probably true for deflections due to thermoelecti'omotive forces. The effect of persistent oscil- lations of the galvanometer ma\' be reduced by

maldng several reversals wliich are not coincident

with the oscillations and using the average of the

double deflections.

6.4.b. Design

Figure 10 represents, in a somewhat simplified

form, the essential elements of a reversing key.

Tw^o keys of spring brass or phosphor bronze. A, A,

are fastened to an insulating base at B, B. The

spring strips or keys pass under a yoke, C. Adjusting screws pass through the yoke to make contact with the springs. At the free ends of the

springs are buttons of insulating material, D, D,

for depressing the keA's with the finger tips. Wlien

the keys are depressed, they make electrical contact with the studs, E, E, in the base. Binding

BATTERY

-o .o

BRIDGE

X) O

BAT. LEADS

Figure 10. Reversing key.
VARIABLE SPST TOGGLE REVERSING

TO BRIDGE

CIRCUIT

Figure 11 A. Panel of battery box.

Figure IIB. Wiring diagram of battery box.

posts for battery and bridge connections are provided as shown. The conducting wires beneath

or within the base are shown by broken hnes.

Wires from one pair of binding posts go to the

spring strips. One binding post of the other pair

is connected to the yoke, the other is connected to both contact studs in the base.

If the battery is connected to one pair of binding

posts and a bridge or other appaz-atus is connected

to the other pair, there will be no current as long- as both keys are up in contact with the yoke, nor when both keys are depressed. If one key is depressed, current will flow through the apparatus.

If the first key is released and the other key is depressed, current in the apparatus will reverse.

It does not take a great deal of mechanical sldll to build a key similar to the one described. It has the decided advantage that it may be tapped

lightly to check on the proper functioning of the

apparatus with which it is being used.

6.4.C. A Convenient Battery Box The battery box illustrated in figures 11 A and

llB combines the reversing key, battery, variable

resistor, and voltmeter in one compact unit. The

unit illustrated uses a lever-action, 2-pole, 3-

position, spring-return switch wired to make a reversing key which will fit into the limited space on a 4 in. x 10 in. panel. By increasmg the length

of the panel and box, a tapping key of the type described above may be used mstead of the lever

action switch. The battery consists of two 6-v dry

batteries in series. The battery switch is a singlepole, single-throw, toggle switch. The variable

resistor of about 2 000 ohms is the rotary type

commonly listed among radio parts as a "potentiometer." It serves as a "voltage divider" to reg- ulate the voltage at the binding posts. The meter

is a high-resistance voltmeter.

7. Miscellaneous

7.1. Absolute Ohm Versus International Ohm

Electrical units are defined in terms of the

fundamental units of length, mass, tune, and the i permeability of free space. Since the "absolute" i electrical units originally chosen, were not of a magnitude suitable for practical measurements, a

set of practical units related to the absolute units

by a simple factor was required. Prior to 1948,

the practical unit of resistance was the International Ohm, which was defined in terms of a "reproducible standard" as the resistance at 0 °C , of a column or thread of mercury of uniform

circular cross-section and specified length and

mass. In 1948 the International Ohm was dis- carded by the national standardizing laboratories ; and was replaced by a unit very accurately deter- ; mined in terms of the defining units of length, j time, and permeability. Such a unit is main- j tained by groups of wire-woimd resistors the i stability of which is checked by repeating measure- men ts in terms of the defining units. National

laboratories use essentially the same unit which

they check against one another through the Inter- national Bureau of Weights and Measures.

The absolute determination of the ohm requires

highly skilled techniques and months of tedious

work with very special apparatus. Hence, the

determination is made at rather rare mtervals. In this country the ohm is determined by the : average value of the resistance of ten Thomas-type

1-ohni resistance standards at the National Bureau

of Standards, specially constructed and main- | tained to insure a very high degree of stability.

This value is compared with the absolute determination as often as required.

Resistance measuring equipment which was made before 1948, and calibrated in International

Ohms, when recalibrated in Absolute Ohms, will have corrections about 0.05 percent larger.

7.2. Algebra of Small Quantities

There are no exact measurements. Though a measurement may be accurate to better than one

part per million, it is, nevertheless, approximate.

Some mathematical operations may be approximate, yet accurate, if the results are as close to the exact value as can be expected from the measure- ments on which they are based.

Consider the product,

(1+a) il +b) = l+a+b+ab.

If a and b are each less than. 0.001, the product,

ab, is less than 0.000001. Hence, for small values

10
of a and h, the appx'oxhiiation,

(l+a)(l +6) = l+a+6,

is accurate to better than one part per miJlion.

The same principle applies to the following:

etc.

If c is very small, the terms c^, etc., that is, all tenns above the first degree in c, are negligible.

A.n accurate approximation is then

Lilcewise,

1+c= l-c.

1+a

and

j-q;j^=l+o— 6, approximately,

f Suppose that A and B are the nominal values of

I the ratio arms of a Wheatstone bridge and that

\ a and h are their respective corrections in proj portional parts. Let .4=1000, 5=100, a= +

Ii 0.00003, and 6= +0.00002. Then,

^(l+g) ^ 1000(1+0.00003)

j 5(1 +6) 100(1+0.00002)

: =10(1 +0.00003-0.00002)

j =10X1.00001 =10.0001.

Compare this result with the following result

|: obtained by long division:

A{l^a) ^

l 000.03

5(1 +6) 100.002^ a0.0000999 + .

Since the values of the ratio arms are certified

to the nearest part per hmidred thousand, the

result is rounded ofl" to 10.0001.

The preceding method of approximation may

be used to find the correction in parts per million

to the nominal value of n resistors in parallel.

For simplicity, the problem will be limited to three resistors each with a nominal value, r and small corrections Ci, C2, and C3, respectively.

Then,

1 1 R r(l +c,) ' /(I +C2) r(l +c3) =\ (I-C1 + I-C2+I-C3) =- [3-(ci +C2 +C3)]

approximate!}^

Let

Then,

3 =c.

i=;Ul^.),a„d«4.-fi-=-;(l+c).

The correction to tlie nominal value, r/3, of the

three i-esistors in parallel is

c=

C1 +C2+C3

3

Extension of this method to n resistors gives

C1 +C2 +C3H \-c„ c=-

7.3. "Rounding Off" Numbers

The result of a measurement usually will include one or more uncertain digits. The doubtful digits are partly the result of probable errors in calibration, partly the result of limitations to the accuracy

of the calibrated instrument in use. Hence, one

or more digits are dropped from the results of the

measurement.

The following rules for "rounding off" numbers

are suggested. The five-digit examples are rounded oft' to four digits. No decimal point is shown

in the examples. If the decimal follows the digit to be dropped, then the dropped digit is replaced

by zero.

Apparatus for evaluating a l-ohm resistor in terms of a computable capacitor and frequency.

This gives its value in terms of length, time and an assumed value for the permeability of free space, in accordance with the definition of the ohm.

616969—62 3 11
1. If the digit to be dropped is less than 5, leave the digit to its left unchanged.

Example: 87 643 is rounded off to 8 764.

2. If the digit to be dropped is greater than 5, increase the digit to its left by 1

.

Exainple: 38 927 is rounded off to 3 893.

47 698 is rounded off to 4 770.

3. If the digit to be dropped is exactly 5, make

the digit to its left the nearest even number.

Example: 52 525 is rounded off to 5 252.

52 535 is rounded off to 5 254.

"Odd" may be substituted for "even" m rule 3, but one or the other usage should be followed

consistently.

7.4. Interpolation

The use of a three-dial Direct Readmg Ratio

Set or a five-dial Universal Ratio Set requires

interpolation of the last digit of a readmg when

that accuracy of measurement is required. For

example, the dials of the DRRS in figure 12 show

only three digits of the reading, hence the last digit is zero, if readings are expressed as parts per

million. The reading is 5 370. Suppose that at

this setting of the DRRS, the galvanometer

deflection is 8.3 scale divisions and that the direction of the deflection shows that the readuag is too small. Also suppose that when the third dial

is advanced to 8 (reading 5 380), the deflection is 11.8 divisions in the reverse direction, showing

that 5 380 is too large. One step on the third dial

corresponds to 8.3 + 11.8 =20.1 scale divisions

of galvanometer deflection. Also one step on the

third dial is equivalent to 10 units in the fourth

place.

A reading of 5 370 corresponds to a deflection

8.3 scale divisions too small. Therefore, it is necessary to add to the fourth place of that reading

8.3/20.1X10 =4 DRRS units; 5 370 +4 = 5 374,

the correct DRRS reading.

The interpolated digit equals

Deflection at lower setting of dial

Deflection at lower setting + Reverse deflection at

higher setting

multipled by 10, the number of units in the interpolated place equivalent to one step on the lowest

dial. opA' A oCDo ooB B'

P'iGURE 12. Three-dial DRRS.

Interpolation is necessary to give the fourth place.

12

7.5. Extrapolation

Extrapolation differs from interpolation in that

it is used to determine a value outside the range i of an instrument scale instead of a value between j two scale readings. It may be used to extend the i scale at either end, either below zero or beyond | the highest reading, by a small amount. Extrapo- i lation is rareh^ necessary. It is as simple as interpolation, but, nevertheless, may be somewhat,!

puzzling.

The zero of a Mueller bridge may be negative. "I Suppose that a trial shows that the galvanometer i deflections increase to the right as the dial settings ' of the bridge are increased; that is, the galvanom- ; eter is connected to the bridge so that a deflec-

!

tion to the right indicates too much resistance in j the bridge circuit. Also, suppose that with all! dials on zero, the deflection is 10.5 scale divisions,] to the right. The lowest dial is then advanced/

one step, to a reading of 0.0001 ohm. Suppose

that the deflection now is 15.7 scale divisions to i the right. Then, 15.7 — 10.5 =5.2 scale divisions]

correspond to one step on the lowest dial. Hence,

the deflection of 10.5 scale divisions when the

bridge reads 0.0000 corresponds to 10.5/5.2 =2

»

steps on the lowest dial. Since the bridge resist-

,

ance was too large with all dials on zero, the zero' for the bridge is -0.00020. , (Note: The Mueller bridge has an N circuit,

and an R circuit. The zero may be negative on

either or both.)

It is rarely necessary to extrapolate beyond the , top reading of an instrument scale. It may be

desirable to extrapolate to avoid resetting all

'

dials to give a higher reading which would involve:

changes in dial corrections. This situation is not:

likely to occur with modern precision equipment.

Suppose the galvanometer deflection for the

' top setting of the dials of an instrument is Si and

that the deflection when the lowest dial is setj

back one step is S2. Then S2 —Si is the deflection

which corresponds to one step on the lowest

dial, and

Si

S2 Si

is the fraction of a step in excess of the highest

reading on the dials. Therefore,

is the extrapolated digit.

7.6. Errors Versus Mistakes

7.6. a. Errors An error is a deviation of measurement from

the exact value of the quantity measured. Errors

are unavoidable, but are reducible by improvements in equipment and measuring techniques.

Mistakes are due to carelessness (that is, lack 01
sufficient care). They can and should be ehmi

nated by adequate checks.

For this discussion, it is convenient to classify orrors as of instrumental origin ov of personal

origin.

For illustration of an instrumental error, assume

that a certain steel tape is 1 percent too long. No

matter how many measurements are made with

it, there is always an instrumental error of +1

percent. The error is also cumulative. If the

tape is used (without correction) to lay off a line

100 ft long, the true length of the line is 101 ft,

I and the error is 1 ft. If it is used to laj^ off a

| line 1 000 ft long, the actual length of the line is

1 010 ft and the error is 10 ft. Personal errors (not mistakes) are largely due

!j to limited powers of observation, as for example,

'l visual acuity. Say an experienced observer must

:lj make an accurate measurement of the diameter

^ of a circle using a steel scale with decimal graduj ations. He will probably estimate a fraction of

the smallest division on the scale and determine

a value to 0.001 in. Since the resolvmg power of

\ the human eye is about 0.003 hi. (a hair's breadth),

his measurement maj^ be in error by that much.

If he makes several unprejudiced measurements,

usually some ol his errors will be positive, some

negative. The average result of several trials,

I then, may be accepted as probably more reliable

I than a single measurement.

' "Miiltiplying'' devices have been designed to extend the pov/ers of observation. In the field

'j of visual observation, there are vernier scales,

I micrometers, measming microscopes, etc. Abeam

]' of light reflected from a mu-ror of a galvanometer

magnifies an almost imperceptible rotation of the

' coil hito an easHy readable deflection on the scale,

i; Although refinements in equipment and measm-mg

'I techniques have reduced tolerances m some cases

i almost mibelievably, the result of a measurement

|| is still limited by the accmacy of observation.

7.6. b. Mistakes Mistakes may be made in takmg a reading, in

, recording a reading, in copying data, or in making

jl computations.

i' A mistake may result from "prejudice." An

inexperienced observer, especially, may report the

length of a line as 10.00 cm because he expected

it to be 10.00 cm. However, the length of the

line may have been slightly short of 10.00 cm,

which he shoifld have observed and reported the

length as 9.99 cm. Instead, he read on the scale

j a preconceived notion rather than an accurate obserI vation. Accuracy in reading scales depends on

. unprejudiced judgment as well as visual acuity.

Wlien an instrument is calibrated, at least two

i trials should be made, preferably by different

observers. Say the instrumeiit is a potentiometer to be calibrated with a Universal Ratio

Set. After the first trial, the connections of the

potentiometer to the Universal Ratio Set should

j be reversed for the second trial so that the readings

for the second test will not duplicate those for

the first. The results of tlu; two tests should

agree withm reasonable toha-ances. Aii3'^ ('xccssivo

disagreement between two results for the same

dial setthig on the potentiometer indicates a mistake. If the mistake is not found in the computation, measiu-emont should l)e i-cpcated.

If a bridge is calibrated, a different set of

resistance standards should be used for eacfi of the two trials. As in the preceduig case, disci-epancies in the results of the two tests, m excess of

reasonable tolerances, indicate mistakes. However, unsatisfactory results for every step on the same dial of the bridge may indicate a faulty

standard resistor.

If interpolation is necessary, great care is neces- sary to avoid mistakes. If corrections to dial

readmgs on the ratio set are required, attention

must be given to the algebraic sign of each correction and the correction must be added algebraically

to the dial reading. Corrections should not be

confused with errors. They are of opposite algebraic sign. A mistake in an algebraic sign is a WO percent mistake.

Observations should be entered directly in the

laboratory notebook, not made on a scratch pad

to be copied later. Another mistake to be avoided is misplacing

the decimal pomt. An engmeer, when he saw the

collapse of a bridge that he hacl designed, is said

to have exclaimed, "There goes my decimal point!"

Figuratively, many bridges have failed because

of a misplaced decimal point. Computations need

to be checked and rechecked, preferably by

different persons. After mistakes have been ehmmated, there

remam the indetermmate errors. The last digit

of a resistance measm^ement is usually uncertain.

In some cases, additional digits are meaningless.

Therefore, the measurement is romided off to the

last significant figure.

8. The Direct Reading Ratio Set. Its Use in

Resistance Measurements With a 1:1 Ratio

8.1. Basic Circuit, Connections, and Precision

As was stated at the begmning, the Direct

Reading Ratio Set is used at the National Bureau of Standards for a large part of the measure- ments of d-c resistance. The Direct Reading

Ratio Set (or DRRS) is designed to measure, with

great accuracy, a dift'erence of not more than 0.5 percent in the resistance between two resistors. The essential panel features of the set are shown in figure 13. A schematic representation of the cirFiGURE 13. Four-dial Direct Reading Ratio Set.

13
a' a 100 U ± % C 100 B B'

Figure 14. Ratio arms of DRRS.

cuit is given in figure 14. The binding posts, A

and A', are at the left end of the variable resistor,

AC. They are in duplicate so that two connections

need not be made to the same binding post. Also,

duplicate binding posts are at the right end of the

fixed resistor, CB. The end binding posts may be

marked as battery posts. Connected to the junction between the variable resistor and the fixed

resistor is the binding post, C. It may be labeled

G for galvanometer. The AC and the CB arms

of the set are used as the ratio arms of a bridge

circuit with a ratio of approxunately 100 : 100 which

is the same as 1:1. Siiace, in a Wheatstone bridge,

the connections of the galvanometer may be interchanged with those of the battery, C may be used

for a battery connection and the galvanometer

may be connected to the end posts. In some

cases the choice of connections is optional. In

others, it is determined by the need to avoid

excessive current in some branch of the circuit. The fixed arm, CB, has a resistance of 100 ohms.

The variable arm, AB, has a range from about

99.5 ohms to about 100.5 ohms.

An additional bindmg post, D in figure 13, if mcluded on the panel, is connected into the CB

arm to provide a resistance between C and D of

10 ohms. The use of this binding post instead of

a' A C B B'

^ © '

Figure 15A. Connection of DRRS for resistance by

substitution.

B provides a ratio of approxunately 100:10, that

is 10:1.

The panels of commercial ratio sets may have

switches and additional bindmg posts. The manufacturer's instructions will identify the different

elements of the set. In the absence of instructions, the circuit may be traced with a simple

tester (volt-ohm-meter) . The discussion to follow

will be based on the above diagrams.

The resistance of the variable arm is adjusted

by four dial switches (three dial switches for three

decades in older sets) . The first dial, left, changes

the resistance of the arm 0.1 ohm per step. The

changes per step of the other dials are, in order,

0.01 ohm, 0.001 ohm, and 0.0001 ohm. Accordingly, the dials on some sets are marked in terms

of the change in resistance per step, that is, XO.l,

XO.Ol, etc. On other sets, the dials are labeled

XI 000, XlOO, XIO, and XI. The latter marking conforms to the use of the set to measure the

difference in resistance of two resistors in parts per

million of their nominal value. With the older

three-dial sets, it is necessary to interpolate the

fourth place for the same precision.

The contact resistance of a dial switch may be

of the order of 0.001 ohm. However, any error

in measurement with a high-grade Direct Reading

Ratio Set due to switch-contact resistance is negligible, due to an ingenious arrangement of the

circuit as explained in NBS Circular 470. The

circuit arrangement also minimizes effects of er- rors in the resistance of the coils in the set. The

result is that the mstrumental error for any reading of the dials need not exceed 5 ppm and the

error m the difference of two readings, if the

XI 000 dial has not been changed in taking the

readings, need not exceed 2 ppm, when comparing

nominally equal resistances.

8.2. Resistance by Substitution

Let X be a resistor of unknown value, and S a

calibrated resistance standard of the same nominal value as X.

I 0 1

c Figure 15B. Schematic diagram of figure 15A.

14
In figure 15A, the letters A'A, C, BB' represent

the bniding posts of a Dh^ect Reading Ratio Set

as in the preceding diagrams. S is the standard

mounted on the mercury stand. The "dummy,"

D is a standard resistor of the same noniinal

value as S, also moimted on the stand. The

dmnm}'' is necessary to balance the circuit, but

its exact value does not enter into the measurement. The schematic diagram of figure 15B

shows that the circuit is a Wheatstone bridge

network. With the battery key closed, the

bridge is balanced by adjusting the dials on the

DRRS imtil there is no deflection (or minmium

deflection) of the sensitive galvanometer. When

the bridge is balanced, the reading of the dials of

the DRRS is recorded as Rdgi. The standard

is then replaced by the unknown resistor, the

bridge is again balanced and the reading of the

dials is recorded as Rdg2.

If Cs is the correction in parts per million to the

nominal value of the standard and Cx is the cor- rection to the nominal value of X,

c^=Rdg2— Rdgi+^-s.

All quantities in equations and formulas are used algebraically; hence, attention must be given

to algebraic signs.

Note that the resistance of the unlmown is not directly measured.

Rdg2— Rdgi =C:,— Cs.

This result is the dift'erence in parts per million

between the resistance of the unknown and the

resistance of the standard.

The method of "resistance by substitution" was used in the following example: X was a "100-ohm" resistor, the exact value of which was unlmowi. Hence, the nominal values of

the dmnmy and the resistance standard were

each 100 olmis. The exact value of the dmnmy

was not needed. The value of the standard was

certified as 99.997 oluns, with a probable accuracy

of 0.002 percent. Then the correction, Cs, for the standard was —0.003 ohm, or, in proportional

parts, —0.000030 of its nominal value

or —30 ppm, accurate to 20 ppm.

Reading for X, Rdg2 5396

Reading for S, Rdgi 5347

Rdg2—Rdgi

Correction for S, Cs +49 ppm —30 ppm

Correction for X, +19 ppm

Resistance of X 100.0019 ohms ± 20 ppm.

The resistance of X was reported as 100.002 ohms.

An error of 2 percent in the difi^erence of the

DRRS readings in the above example would

amount to an error of only one part per million

Figure 16. DRRS connections for resistance hy the inter- change method.

in the measured value of X. The accmacy of

the method lies in the measurement of small

differences of ratios instead of direct measm'ement

of ratios.

8.3. Resistance by the Interchange Method

In figure 16, X is a resistor of unlmown value,

and S is a standard of the same nominal value.

Both are mounted on a mercury stand with connections to a DRRS as sho^vn. Let Rdgi be the reading of the dials of the ratio set when S is on the

left. After the positions of S and X are interchanged, Rdg2 is taken. If Cs and Cx are the cor- rections in parts per million for the standard and

the unknown, respectiveh'', _Rdg2-Rdgi

This method is satisfactory^ if the standard and the

unknown do not differ by more than 0.1 percent.

Example: X is an milcnown of approximately

1 000 olinis resistance; S is a 1 000-olun standard

with a correction of +87 ppm. Rdgi = 5 476;

Rdg3 =4 898.

Cr=-

4 898-5 476

-87 = —202 ppm.

202 ppm of 1 000 ohms=0.000202X 1 000 =0.202

ohm.

X=l 000.000-0.202 =999.798 ohms.

The result is rounded oft' to X=999.80 ohms.

15
P H

Figure 17. Four-terminal measurement with the DRRS.

8.4. Comparison of a Four-Terminal Resistor with a Two-Terminal Resistor

This method is important in testing laboratory

apparatus in which two of the connections to a

four-terminal resistor can be made only through

other resistors. In Figure 17, let X be a resistor, the terminals

H and K of which are not available for external

connections. The available terminals are the

binding posts P, Q, M, and N. Hence, X is a

four-terminal resistor. Current leads are taken to the binding posts P and Q, potential leads go to the binding posts M and N. The potential leads

may pass tlu-ough considerable resistance. The

termmals H and K of the resistor X, are the jimction points of current leads and potential leads. The resistance is measured between these

j mictions.

S and L, on a mercury staiad, are respectively a standard resistor of the same nonimal value as X

and a Imk.

With S on the left of the stand, L on the right,

and the battery lead clipped to the potential point,

M, Rdgi is taken on the DRRS. After exchanging

places between the standard and the link and clipping the battery lead to N, Rdga is taken. If Cs and Cx are the respective corrections to the nominal

values of the standard and the unknown, and L is

the resistance of the link expressed in parts pei

million of the same nominal value,

^_Rdg.-Rdg,

Unless the resistance of the link is quite large (100

microhms or more), the last term in the preceding

equation is usually negligible for nominal values

of X in excess of 10 ohms.

Example: Nominal value of imknown 100 ohms

Nominal value of standard 100 ohms

Correction, for standard —35 ppni

DRRS, Rdgi 5485

Rdg2 • 5453

In this case, the correction for the link is neglinble.

5 453-5 485 , , — 51 ppm

51 ppm of 100 ohms =0.000051X 100 =0.0051 ohm

X= 100.0000-0.0051 =99.9949 ohms.

in general, the last digit ma.y be considered uncertain, hence the reported value is 99.995 ohms.

As noted above, the correction for the link, L

in the above equation, is in parts per million of the

resistor with which it is used. If the resistance of

of the link is 40 microhms, it is 40 ppm of 1 ohm,!

4 ppm of 10 ohms, and a negligible 0.4 ppm of

100 ohms.

8.5. Approximate Measurement of a Small Resistance

A resistance element of very small value may be

measured approximately with the Direct Reading

Ratio Set in the circuit of figure 18. Two standards, S, S, of the same nominal value, are mounted

on the stand, one on each side of the unknown, X.

If X is a resistor that can not be mounted on the

middle blocks of the stand, it is connected to the

binding posts by the shortest possible leads. Potential points are taken at a and b as shown in the diagram, and current leads from the ratio set go to the outer terminals of the standards. Readings are taken on the DRRS with the potential

lead first at a, then at b.

-^^^ Rdg2—Rdgi

(Rdg2— Rdgi)/2 is in parts per million.

The least value of the standards is limited by

the resistance of X, which should not greatly

exceed 0.25 percent of the value of the standards.

The method is approximate but sufficiently accurate for the small resistances for which it is usually

16
J

Figure 18. Measurement of a small resistance with the DRRS.

used. S in the above equation is the nominal

value of the standards.

The following examples will illustrate some

applications of the method:

(1) To find the resistance of a shorting link. The resistance of the link described in section 5

is less than 0.25 percent of 1 ohm (less than 0.0025

ohm). Hence, 1-ohm standards should be used.

Readings taken with a similar link were:

1st reading, Rdgi

2d reading, Ildg2

5 438

5 514

5 514-5 438

=38

38 ppin= 0.000038 XI ohm=0.000038 ohin=

38 microhms.

(2) To find the lead and contact resistance of

the rheostat arm of a Wlieatstone bridge.

This resistance will probably exceed 0.005 ohm,

which is greater than 0.25 percent of 1 ohm, but

but less than 0.25 percent of 10 ohms. Ten-ohm

standards were used to obtain the following readings on a DRRS for the lead and contact resistance

of the rheostat arm of a Wlieatstone bridge:

Rdgi

Rdg2

5 617-4 224

4 224

5 617

=696 ppm

0.000696X10 ohms=0.00696 ohm

FiGUEB 19A. Four-terminal one-ohm standard.

8.6. Determination of the Two-Terminal Resistance of a 1-Ohm Standard When Its Four-Terminal Value

Is Known

The NBS certificate usually gives only the fourterminal value of a 1-ohm standard. In some

resistances measurements, the two-terminal value

is required. When the four-terminal resistance

is known, the two-terminal value can be determined readily with the Direct Reading Ratio Set. In figure 19A, the plane contact surfaces of the

resistor arms which rest on the mercury stand are designated a, a', and the bindmg posts at the top

of the arms, b, b'. The standard which is to be

tested is mounted on the middle blocks of the

stand with another 1-ohm standard (a dummy) on

the left and a link on the right, figure 19B. Short

tabs of bare copper wire are connected to the

binding posts of the stand as shown at a, a . Similar tabs are connected to the binding posts of

the standard at b, b'. These are the potential

points for connection of an alligator clip at the end

of the battery lead. Current leads extend froni

the end posts, A, B, of the ratio set to the end

posts of the stand. The galvanometer leads also are connected to the end posts of the ratio set. With the battery clip at a, then at b, readings

taken on the DRRS are designated Rdg,, and

Rdgb. Then, with the dunuuy transferred to the

right of the stand and the link to the loft, reatlings

Rdga and Rdgb' are taken with the clip at a',

17
LINK

Figure 19B. Measurement of two-terminal value of one-ohm

standard.

then at b'. The amount to be added to the fourterminal resistance to get the two-terrninal vahae is Rdgb—Rdga I Rdga'—Rdgb' ppm.

The resistance of the diunmy and the resistance

of the link do not enter into the computation.

And, of course, either standard resistor may be

used for comparison to find the two-terminal

value of the other.

Example: The four-terminal correction for a 1-ohm standard was —54 ppm, hence, its fourterminal resistance was 0.999946 ohm. The

DRRS readmgs obtained by the preceding procedure were: Dummy on the left a 5 772

b 5 814

Dummy on the right

' a' 5 847

b' 5 801

Substitution of the readings in the above equation

gives

5 814-5 772 , 5 847-5 801

=21 +23= +44 ppm.

2

' 2 Hence, the two-temainal value of the resistor was

0.999946+0.000044 =0.999990 ohm,

and the two-terminal correction was —54+44 =

— 10 ppm.

18

9. Measurement of "Odd-Valued" Resistors

9.1. "Odd Values" Distinguished From

Conventional Standards

Values of

The term "odd-valued," as used here, includes

those resistors which are not decimal multiples or submultiples of 1 olmi. Some examples are resis- tors with denominations of 2 ohms, 5 ohms, 20

ohms, 50 olims, etc. A similar set of resistance;

values is found in some types of resistance boxes.

Other denominations occur, either separately, or

as components of laboratory apparatus.

Most of these odd values can be measured at a one-to-one ratio on the Direct Reading Ratio Set

by use of combination standards consisting of two

or more conventional standards connected to produce the required resistance. The correction

in parts per million of the nominal value of any

combination standard may be derived readUy

from the corrections of its components.

9.2. Combinations of Resistors

Resistors may be connected in series, in parallel, or in combination of series and parallel. The

notation i?(l +c) which was explained in section 2, will be used in the following discussion to express

the true value of a resistor in terms of its nominal

value, R, and its correction, c in parts per million

of its nominal value.

9. 2. a. Resistors of the Same Nominal Value in Series If n resistors, ri, r2, rs, . . . r„ are in series, the

total resistance is i?=ri+r2+r3+ . . . +r„.

If these resistors have exactly the same value, r, the series resistance isR—nr.

In general, no two resistors have exactly the same

value. Suppose n resistors have the same nommal

value, r, with corrections in parts per million of

the nominal value, Ci, C2, Cg, ... c„, respectively.

Then the equation for the series resistance is B=r(l +cO +ra +C2) +r(l +C3) + +r(l+cj

=wr^ C1+C2+C3+ +c„

In the equation, nr is the nominal value of the

series resistance, and (C1 +C2 +C3 + . . .-^c„)/n is the

correction to that nominal value.

Hence, if resistors of the same noyninal value are in series, the nominal value of the series resistance

is equal to the nominal value of one component

resistor multiplied by the number of resistors in

series,

and

the correction in parts per million of the series

resistance is the arithmetical mean of the corrections of the components in the series.
Example: Three resistors, each of 100 olmis.

nominal value, are in series. Their corrections

in parts per million of the nominal value are +45, —7, and —10 respectively. Find the series resist- ance. The nominal value of the series resistance is ^r=3X100 =300 ohms.

The correction in part's per million of the nominal value is the arithmetical mean of the corrections of the components of the series, which is

(+45) + (-7) + (-10) , ,

Hence, the series resistance is 300(1 +9 ppm) =300X1.000009 =300.0027 olmis.

To illustrate the application of the correction

to a series resistance in the measurement of an unlmown, the above resistors in series were used as

a combination standard for measurement of a 300-ohm resistance coil in a Kelvin Ratio Box.

A bridge circuit was set up with a Direct Reading

Ratio Set as ratio arms as explained for resistance

by the interchange method in section 8.3. The

three standards in series formed one upper arm of

the bridge, and the 300-ohm coil, connected

through binding posts of the box, formed the

other upper arm. After the bridge was balanced

and a reading taken on the DRRS, the positions

of the standards and the unknown were interchanged, the bridge was balanced and a second

reading taken. The readings were:

Standard on the left, Rdgi 5 315

Standard on the right, Rdg2 5 437

Correction for the standard, Cj +9 ppm

Substituting these values in the equation for resist- ance by the interchange method gives

Rdg2-Rdg, , 5437-5315 , _„ c,= — ^+c, = h9=+70 ppm.

Then,

X=300 (1+70 ppm) =300X1.000070 =300.0210 ohms.

The result was rounded off to report X=300.021

ohms.

If the measurement had been made by simple

substitution, (sec. 8.2), a dummy would have

been necessary requiring another 300-ohm resistor

(three 100-ohm resistors in series).

9.2.b. Resistors of the Same Nominal Value in Parallel The equation for n resistors in parallel is

1 +:

If the resistance of each component is exactly r,

the equation becomes

In 1 r -T,—- ) and k=— K r n

Since the components with the same nominal value

will liave different corrections, the corrected equation for parallel resistance is

1 R r(l+ci) ' r(l+c,) ' rd +Ca)

1 1

r(l +c„)

An expression of the form jq^^. when expanded,

becomes

1 l+c :1— c +c^ —c^ + etc.

If G is less than 0.001, the second-order term,

is less than 0.000001, the third-order term, c', is less than 0.000000001, etc. If c is small, the

higher the order, the less significant the term.

If terms of the second and higher orders are

negligible, the above equation may be reduced to the followmg approximate form which is generally

accurate for application to standard resistors and

their corrections:

+c„^

n\ n

(See sec. 7.2.) In the equation for R, - is the

nominal value of the parallel combination,

C1+C2 +C3+ . . . +C„ . ^. .1 . IS the correction to that

71 nominal value.

If resistors of the same nominal value are con nected

in parallel, the nominal value of the parallel re- sistance is equal to the nominal value of one

resistor divided by the number of resistors in

parallel, and (assuming that second order terms

are negligible) the correction in parts per million

of the nominal value of the parallel resistance is equal to the arithmetical mean of the corrections

to the components in parallel.

It follows that n resistors of the same nominal

value have the same proportional correction,

whether they are connected in series or in parallel

if, as stated above, the second-order terms are

negligible. The nominal value with the resistors

in series is tunes the nominal value with the

resistors in parallel.

Example: The preceding principles may be illus- trated by application to the measurement of a

resistor which has a nominal value of 250 ohms.

Four 1 ,000-ohm standards may be used in parallel as a 250-ohm standard. If these standards have

corrections, respectively, of +76, —125, —16, and

+29 ppm, the correction to the 250-ohm parallel

combination is the arithmetical mean of the four

individual corrections, which is — 9 ppm. Assume

19

616969—62-

w
that the following data are obtained by use of the

above combination of resistors as a 250-ohni

standard for the measurement of the unknown by

the interchange method:

Correction for standard, Cs —9 ppm

Standard on the left, Rdgi 5 398

Standard on the right, Rdg2 5 220

5 220-5 398 —9=—98 ppm

.Y= 250 (1-98 ppm) =250X0.999902 =249.976 ohms.

9.2.C. Resistors of Different Nominal Values in Series For illustration, consider a 100-ohm resistor

and two 10-ohm resistors in series to produce

a nominal resistance of 120 ohms (fig. 20). Suppose that the corrections to the nominal values

of these resistors are +35, +27, and —65 ppm

respectively. The 100-ohm resistor may be considered equivalent to ten 10-ohm resistors in

series, each with the same correction, +35 ppm.

The complete series is equivalent to twelve 10-

ohm resistors. The simi of the twelve corre- sponding corrections is:

(10X35)+27-65 = +312.

This sum divided by 12 (niunber of equivalent

10-ohm resistors) gives +26 ppm, the correction

to the nominal value of the series. Hence,

J?= 120(1 +26 ppm) = 120 X 1.000026 = 120.0031

ohms.

The correction (+26 ppm) in the above ex- ample is the "weighted mean" of the corrections

of the three resistors in the series. Since the

resistors are not of the same nominal value, the

average of the three corrections would not be

correct. Evidently, the 100-ohm resistor has ten times the "weight" of each of the other resistors. To find the weighted mean of the corrections to several resistors, divide the nommal value of each

by the least nominal value in the group. These

quotients are the "relative weights" of the corre- sponding corrections. Multiply each correction

by its relative weight. Divide the algebraic sum

of the products by the sum of the relative weights.

The correction in parts per million of the nominal resistance of any number of resistors of

different nominal values in series is the weighted

mean of the several resistor corrections.

AAAAA

100 4- AAAV

10 10

9.2.d. Resistors of Different Nominal Values in Parallel Although this case rarely, if ever, occurs in practical testing, a complete discussion requires

its inclusion. There is no simple expression for the resistance of a combination of this type. If the resistors of the preceding example are con- nected in parallel, the resistance of the group

must be found from the following relation: 11,1,1

R 100.0035 ' 10.00028 ' 9.99935

This equation gives l/i?=0.210003, and

i?=4.76183 ohms.

This result can not be satisfactorily expressed

in terms of a nominal value and its correction.

9.2.e. Resistors in Series and in Parallel A nominal resistance of 125 ohms may be produced by connecting eight 1 000-ohm resistors

in parallel. The same result is obtained with

five resistors in series-parallel as shown in figure

21. The inclusion of the last two 10-ohm resistors between vertical bars in the equation in- dicates that they are in parallel, equivalent to one 5-ohm resistor. The parallel group is in

series with the other resistors, so that the entire

combination amounts to 100 + 10 + 10 +5 = 125

ohms nominal, and it is equivalent to 20X5+2X5+2X5+1X5,

or twenty-five 5-ohm resistors in series. Suppose

that the corrections, in the order in which the

resistors are listed, are +20, +30, +40, and

+50

ppm. Since the last two resistors are in

el, equivalent to one 5-ohm resistor, the cor- rection m parts per million of 5 ohms is (50 +70)/ 2 = +60. The next step is to find the weighted mean. (+20)X20=+400

( +30) X 2=+ 60

(+40)X 2=+ 80

( +60) X 1-+ 60

+70

paral

25 J+600

+ 24

Hence, the correction for this combination of

resistors is +24 ppm of its nominal value, 125

ohms. The total resistance is

125(1 +24 ppm) = 125X1.000024 = 125.0030 ohms.

-AAAA120 Figure 20. Resistois in series.

100 + 10 + 10 + = 125 Figure 21. Resistors in series and in parallel.

20
9.3. Adaptation of the Direct Reading Ratio Set for Ratios of l:n and m:n

In using the Direct Reading Ratio Set it is usually best to set up the bridge to use a substitution method. For example, to measure a

300-olmi resistor the 100:100 arms of the ratio

set would be used, and a Wheatstone bridge

would be set up and balanced using a 300-ohm auxiliary on the right and the unknown

300-ohm resistor on tlie left. After balance, the

unknown would be replaced by three 100-ohm

standards connected in series on the mercury

stand, and a second balance obtained. The

difference in readings would then be the difference

in parts per million between the unknown and

the sum of the resistances of the three 100-ohm

standard resistors. However, if three calibrated

100-ohm standards are not available, the ratio set

circuit may be modified to give a 1:3 ratio and

the 300-ohm unknown measured against a single

calibrated 100-ohm standard. It is also possible

to adapt the circuit to measure the 300-ohm

unknown against two 100-ohm standards, or by

setting up a 3 : 5 ratio, in terms of two 1 000-ohm

standards in parallel.

9.,S.a. Typical Adaptations

Some commercial ratio sets have a connection

for a fixed arm of 10 ohms, affording a ratio of

10:1. A variety of other DRRS ratios may be

formed, as 1:2, 1:3, . . . 1:10, or 2:3, 3:4, etc. Figure 22 illustrates an adaptation for a ratio

of 1:2. A 100-ohm standard is connected to binding post, B'. The right hand terminal of the

set becomes F, the fixed arm CF, and the ratio of

AC to CF is 100:200.

A ratio of 1:10 may be formed as in figure 23. A 1 000-ohm standard connected to the middle post,

C, of the DRRS forms the fixed arm, CF, of the

set and the ratio of AC to CF is 100: 1 000.

A ratio of 1:1.5, or 2:3, can be formed as in

figure 24. Two 100-ohm standards in parallel

provide a supplementary resistance of 50 ohms,

which added to the CB arm of the DRRS, makes

the fixed arm, CF, of the modified set equal to 150 ohms and the ratio of AC to CF 100:150.

A ratio of m:n, in which m and n are both

integers, may be provided by using supplementary

standards to make the right arm of the set equal

to 100 times n/m.

The resistance of leads used in making connections should be insignificantly small.

9.3.b. Bridge Zero One arm of the ratio set is adjustable so that

the ratio of the arms is variable from about 0.5 percent below to about 0.5 percent above the

ratio, m:n. At some setting of the dials, the ratio

is exactly m:n. Call this setting "bridge zero" and designate it by "Rdgo."

If a DRRS has been adapted to a ratio of m:n

by addition of resistors to the fixed arm (or to the middle binding post), a bridge is set up by

Figure 22. Adaplalion of DRRS for 1:2 ratio.

Figure 2.3. Adaptation, of DRRS for 1:10 ratio. © © CD 0

100 n

-50 n -

Figure 24. Adaptation of DRRS for 2:3 ratio.

using m+"' standards each of the same nomina

value, in the upper arms, m standards on the left and n standards on the right. The value of these

should be large enough to make lead and contact

resistance negligible. With the standards in a

definite pattern, the}^ may be rotated step by

step, until each resistor has occupied each position

in the pattern. At each step, a reading is taken on the dials, from Rdgi to 'Rdgm+n- Bridge zero

is the arithmetical mean of the m-fn readings

taken.

Rdgi-fRdg24-Rdg3+ . . +Rd

±tago= 1

This number is independent of the corrections

to the nominal values of the standards used if each is less than 1 000 ppm. It applies equally

well to standards in series or in parallel.

Unless the resistances of the leads to the upper arms of the bridge are negligible, the resistances

of the leads must also be in the ratio m:n. The

leads may be adjusted to the correct ratio by

shorting each arm and balancing the bridge by

adjusting the leads. It is not always necessary to use m+n standards

to form a ratio of m:n. B}^ a combination of

series and parallel connections, the number of required standards may be reduced. A ratio

of 2:3 may be obtained with four standards

instead of five. A ratio of 1 :10 may be obtained

with seven standards instead of eleven.

21
Figure 25A. Assembly to find Ro/or a 1:2 ratio.

9.3.C. Application of Above Procedures to Measurement of Odd

Values The following examples are intended to clarify

the preceding explanations.

Example 1 : It is required to find the true value

of a resistor which has a nominal value of 20 000

ohms.

With the ratio set adapted to a ratio of 1:2, a Wheatstone bridge is completed by using three

1 000-ohm standards (or 100-ohm standards) in

the upper arms, one on the left and two in series on the right.

To reduce the number of binding post connections, the standard resistors can be mounted

on a mercury stand. In figure 25A, the 100-ohm

resistor on the right-hand end of the stand is in series with the 100-ohm resistor, CB. The

resistance from. C to F (200 ohms) constitutes the

fixed arm of the DRRS, giving a ratio of 1:2. Note that the lead to the galvanometer is taken

from F, not from B'. The standard resistors a, b, and c form the upper arms of the bridge with a in the left upper arm

and b plus c in the right upper arm, also in a ratio

of 1:2. Compare figure 25A with figure 25B.

After Rdgi is taken on the DRRS with the

resistors in the position shown, the resistors

a, b, and c are rotated as follows: Resistor b is moved to position a, c to position b, a to position

c, and Rdg2 is taken. (The same result will be

obtained by interchanging a and b. However,

if several resistors are involved mistakes may be

avoided by following a definite plan of rotation.)

Then resistor c is moved to position a, a to position

bj b to position c, and Rdg3 is taken.

The rotation of the resistors and the corresponding readings are shown in condensed form in the

0

c L 0 1

Figure 25B. Schematic representation of figure 25A.

following table:

a:(b +c) Rdgi= 5 387

b: (c+a) Rdg2= 5 491

c:(a+b) Rdg3= 5 421

3 )16 299

Rdgo= 5 433

The reading 5 433 designated above as bridge

zero is the reading of the dials of the DRRS which

makes the resistance ratio AC:CF exactly 1:2.

Unless the resistances of the leads are negligible,

they should be adjusted to a ratio of 1 :2 (approximately) before determining the bridge zero. The standards in the upper arms of the bridge

are now replaced by a 10 000-ohm standard on the

left and the unknown (20 000 ohms, nominal) on

the right. After the bridge is balanced the dials are read giving (say) Rdg3;=5 425. If the correction for the 10 000-ohm standard is Cs=— 83 ppm,

the correction, Cx, for the unknown is found by

substituting the numerical values in the following

equation

:

Cj=Rdgo— Rdgi+Cj.

Hence,

Cx=5 433-5 425-83 = -75 ppm

and X=20 000(1-75 ppm) =20 000X0.999925 =

19 998.5 ohms. The value of Cx is negative, hence,

is used with its algebraic sign in the equation for X.

Example 2: To calibrate a resistor with a nominal value of 100 000 ohms. The ratio set is adapted to a ratio of 1 : 10. Instead of using eleven

standards in the upper arms of the bridge to obtain

a ratio of 1:10 to find Rdgo, seven standards are connected to form the same ratio (50:500), as is shown in the simplified diagram of figure 26A.

22
Figure 26A. Schematic diagram for 1:10 ratio with seven standards. Note that, instead of the 100-ohm standards shown

in the diagram, 1 000-ohm standards could be

used, forming the ratio 500:5 000. The arrangement of the seven standards on two mercury

stands, connected by a link (Z) to form the upper arms of a bridge, is shown in figure 26B. Resistors a and b, in parallel, form the left upper arm

of 50 ohms. Resistors c, d, e, f, and g, in series,

form the right upper arm of 500 ohms.

The fixed arm of the DRRS is replaced by the

1 000-ohm standard connected to C and mounted

on the right end of the stand to give the DRRS a

ratio of 1 :10. The galvanometer leads (g, g') are taken from A' and F. By comparison with the schematic diagram, fig- ure 26C, it is clear that the circuit is a Wheatstone

bridge circuit with arms in a ratio of 1 :10. To find bridge zero, Rdgo, readings on the

DRRS are taken for each sequence as the standards are rotated in the pattern.

:(c+d+e+f+g). (d+e+f+g+a),

^1 : (e+f+g+a+b), |^|

: (f +g+a+b+c),

^j:(g+a+b + c+d),

:(b +c+d +e+f).

:(a+b +c+d +e).

Rdgo is the arithmetical mean of the seven readings.

The measurement of the unlaiown follows the

procedure described in the preceding example.

Rdgi is taken with a 10 000-ohm standard in the

left upper arm of the bridge and the unknown

100 000-ohm in the right arm. As in example 1, Cj=Rdgo— Rdg3;+c,.

Example 3: To measure a 250-ohm (nominal

value) resistor with a 1:4 ratio. The measure- ment of this resistor at a 1:1 ratio using four 1, 000-

ohm resistors in parallel as a combination standard was explained in section 9.2b. The addition of

three 100-ohm resistors in series to the fixed arm

of a DRRS changes the set to a ratio of 100:400.

"With the modified ratio in the lower arms of a

bridge, bridge zero may be determined hj use of

four 100-ohm standards in the upper arms, two

in parallel on the left, two in series on the right, to form a ratio of 50:200.

Figure 26B. DRRS connected to seven standards on

stands for 1:10 ratio.

Figure 26C. Simplified representation of figure 26A.

Figure 27A shows how the standards may be

moimted on two mercury stands connected by a

link, L. The arrangement of the stands permits

reasonably short leads from the A and B binding

posts of the DRRS to the stands. The three 100-

ohm resistors on the right hand stand are in series with the 100-ohm fixed resistor, CB, of the DRRS,

making the fixed-resistance arm, CF, 400 ohms

and the ratio, 100:400 or 1:4. The galvanometer

leads (g, g') are connected to A' and F. On the left hand stand, the 100-ohm resistors, a and b, are in parallel to make the left upper arm

of the bridge 50 ohms. The resistors, c and d, are

in series to pi'oduce a resistance of 200 ohms in the

right upper arm of the bridge. The ratio of the

upper arms is 50:200 or 1:4. After Rdgo has been fomid, as previously ex- plained, the standards a, b, c, and d are removed

from the stand and a 1 000-ohm standard is mounted between H and D. If the 250-ohm

unknown cannot be mounted on the stand betwi>eu

23
Figure 27 A. Arrangement of standards to determine

"bridge zero" with a ratio of 1:4. D and K, it is connected by short leads to the

binding posts of the respective bars of the stand.

A schematic diagram of the A^heatstone bridge

circuit with the 100-ohm standards on the left- hand stand replaced by the unknown and the

1 000-ohm standard is shown in figure 27B.

After the bridge is balanced, Rdgx is taken on

the DRRS. Note that in the preceding examples,

the standard was in the left upper arm of the

bridge, the unkno^ra in the right arm. Since, in this case the positions of S and X in the upper arms has been interchanged, there will be a cor- responding interchange of the algebraic signs of

Rdgo and Rdg^ in the equation for c^. The equation is

C;r =Rdg:, —Rdgo +c,. From the following data:

S= 1 000 ohms

Cs= +75 ppm

Rdgo=5 520

Rdg^=5 347

c^=5 347 —5 520 +75= -98 ppm

and

X=250(l-98 ppm) =250X0.999902 =249.976

ohms.

0

c

I -q) 1

Figure 27B. Schematic circuit with the unknown, X, and

the standard, S.

C

I 0 1

Figure 28. Schematic diagram, ratio l:n.

It is important to avoid confusing the two equations

or Cj;. If the standard is on the left c^=Rdgo— Rdg^+Cj.

If the standard is on the right

Ca;=Rdg^— Rdgo+Cs.

9.3. d. Determination of Bridge Zero With Two Standards and Their

Corrections Figure 28 shows schematically a bridge with the

ratio set adapted to a ratio of 1 :n. In the upper arms of the bridge are two standard resistors with

nominal values of A and B, also in the ratio 1 :n. Cl is the correction to the nominal value of A, the

24
D R R S

Figure 29 A. Rq with two standards, ratio 1:10.

standard on the left, and Cr is the correction to the nominal value of B, the standard on the

right, both in parts per miUion. If Rdg is the

reading on the dials with the bridge balanced,

bridge zero equals the reading of the ratio set minus the correction to the resistor on the left plus

the correction to the resistor on the right. Rdgo =Rdg—Ci+Cft. The next step is to replace the

standards used to find the zero reading on the

bridge by the unknown, X, and a standard resistor,

S. The value of the standard selected must be

such that with S on the left and X on the right, or

vice versa, the ratio of the upper arms is the same

as the ratio of the lower arms of the bridge. The

bridge is balanced and read. If the unknown is on the left, by transposing the above equation, its correction is Ci=Rdg— Rdgo+Cfl.

If the unknown is on the right, by transposing the

equation, its correction is Cs=Rdgo— Rdg+Ci.

Example: To measure a resistor with a nominal

value of 150 000 ohms. The Ratio Set is adapted

to a ratio of 1:10 by connecting a 1 000-ohm

standard to the middle post, C, of the DRRS,

figures 29A and B.

The galvanometer leads (g, g') are connected to A' and F. To calibrate a resistor of this value, a 1 000-ohm standard with a correction of +421

ppm was used in the left upper arm of the bridge

and a 10 000-ohm standard with a correction —18

ppm in the right upper arm, figure 29A. The

bridge reading was 6 173. Hence, bridge zero: Rdgo=6 173-421-18 = 5 734.

Measurement of X: The 150 000-ohm unknown

was connected into the right upper arm of the

bridge, figure 29B. For a 15 000-ohm standard

Figure 29B. Application to calibrat ion 150,000 ohms

nominal value.l

in the left arm, to make the ratio of the upper arms 1:10, three 10 000-ohm standards in the

series-parallel connection shown in the figure were

used. With the bridge set up in this way the

reading was 6 321.

Using the corrections to the standards, as shown

in the diagram, the "correction on the left" was

c^=^(^2X432+ ~^^^~^^^= +277ppm. (sec.9.2.e)

Then the correction for the unknown, "correction on the right," was Cr=5 734-6 321 +277=-310 ppm.

And X equals 150 000(1 —310 ppm) = 150 000

X0.999690 = 149 954 ohms.

9.4. Calibration of Megohm Boxes and 0.1-Megohm

Boxes for Use as Resistance Standards

9.4.a. Calibration of the Box The boxes considered here consist of ten nominally equal resistance coils which may be con- nected on the panel either m series or in parallel.

The components of the 0.1 -megohm box are

10 000-ohm coils. With the coils in parallel, the

resistance of the box is nominally 1 000 olmis.

Its resistance may be compared with that of a

1 000-ohm standard by the usual substitution

procedure. Say, the correction found is +250

ppm. With this correction, the resistance of the

box is 1 000(1+250 ppm) ohms.

The same correction applies to the nominal resist- ance of the box when its components are in series. Hence, the resistance of the box with its components in series is 100 000(1 +250 ppm).

A 1-megohm box may be calibrated the same

way. With its 100 000-ohm components in parallel, the resistance of the box may be compared

with the resistance of a 10 000-olun standard.

The proportional correction found is also tlie proportional correction to the 1 000 000-ohm

25
nomiBal value of the box when its components are

in series. The method is not Hmited to megohm and 0.1- megohm boxes, but is apphcable to any resistance

box having 10 nominally equal stable components

which may be used in parallel or in series, per- mitting a step-up of 100:1. If each component

is within 0.1 percent of their average the 100:1

ratio is accurate within one part per million,

provided that the insulation resistance is large

enough to avoid any appreciable effect on the

ratio. The method is very useful for measuring

high resistances.

9.4.b. Use of the Calibrated Box as a Resistance Standard After a box has been calibrated, it may be used

in a Wheatstone bridge circuit to measm-e the

resistance of an unknown in the same way that

any other standard resistor would be used.

For illustration, consider the use of the 0.1- megohm box as a standard to calibrate a resistor

of 150 000 ohms nominal value. After a bridge

has been set up with a ratio set adapted to a ratio

of 1 :1.5 the next step is to find bridge zero. In figure 30 two 100-ohm standards in parallel

have been added to the fixed arm of a DRRS to make the ratio of AC to CF equal to 100:150.

Four 1 000-ohm standards in the upper arms of

the bridge arranged as shown in the diagram

make the ratio of those arms 1 000:1 500. The

readings on the bridge corresponding to the

different sequences of the standards in the pattern

are given in the following table:

a:(b+

b:(c+

c:(d+

d:(a +

Rdgi=5 435

Rdg2=5 412

Rdg3=5 400

Rdg4 = 5 433

4) 21 680

Rdgo=5 420

Figure 30. Ratio 100:150, to find Rq.

The standards are removed from the upper arm^

of the bridge and replaced by the 0.1-megohm box

on the left and the unknown on the right. Suppose the reading of the bridge is now 5 580. The

correction found for the box was +250 ppm.

This is Cl, correction on the left. The correction

for the unknown is Cr, correction on the right.

Making the relevant substitutions in the equation.

Cfl=Rdgo— Rdg+cz,,

the correction for the unknown is

Cfl=5 420-5 580 +250 = + 90 ppm.

Hence, the value of the unknown is

150 000(1 +90 ppm) = 150 000X1.000090 =

150 014 ohms.

The 1-megohm box may be used in the same way to measure resistances of the order of 1 megohm. Readings to the fourth place on the

ratio set may be impossible due to insufficient

galvanometer sensitivity. Excessive battery voltage to increase the galvanometer deflection will heat the resistance coils and decrease the accm-acy

of measurement.

The use of the Direct Reading Ratio Set in the

calibration of a Wheatstone bridge is given in

detail in sections 11-15.

The examples which have been given illustrate the usefulness and adaptability of the Direct

Reading Ratio Set. Theoretically, the set can

be adapted to any ratio. However, the nimiber

of practicable ratios is limited.

Another ratio set with arms as finely adjustable

as those of a slide wire is desci'ibed in the next

section.

10. The Universal Ratio Set

In the preceding sections the Direct Reading

Ratio Set and its uses have been discussed. It is usually used for the determination of the differ- ence in resistance between standards and unknown

resistors of nominally the same value. Where

they differ by more than about 0.5 percent the

Direct Reading Ratio Set is not usually suitable

and a I'atio set with a larger range is required.

In this case the Universal Ratio Set may be used.

It is also very useful where only the ratio of re- sistances is requifed, as in the calibration of a potentiometer. This requires the determination

of the ratio of the main resistance to the standardcell resistance for the many settings of the in- strument.

10.1. The Universal Ratio Set (URS) Compared to a

Slide Wire

Figure 31 shows the arrangem.ent of dials and

binding posts on the panel of a recent model of a

six-dial Universal Ratio Set. The first dial (left)

is divided into twenty divisions corresponding to a resistance of twenty steps of 100 ohms each

26
o o o o o

BA A G B BA'

lOOJl lOA in .1/1 Oin. .OOlJl

BA A B BA

Figure 31. Universal Ratio Set. Each of the other dials is divided into ten steps of

resistance vahies which range from 10 ohm.s per

step on the second dial to 0.001 ohm per step on

the sixth dial. The URS is used to form the ratio arms of a

bridge. It is equivalent to a slide wire (fig. 32)

with a slider, C (connected to binding post, G),

which may move along a wire with a resistance of

2111.110 ohms between the binding posts A and B.

Adjustment is made by an arrangement of coils and dial switches such that as one or more dials are advanced, additional resistance is introduced

into the AC arm and equivalent resistance is rem.oved from the CB arm of the set. The

reading of the dials is the resistance of the AC arm. The binding post, G, is marked for a galvanometer connection. The binding posts BA and BA'

(battery connections) are convenient extra binding

posts at the ends of the slide wire. As in Wheatstone bridge circuits, generally, the battery connections are interchangeable with the galvanometer connections. Frequently, the galvanometer

s connected to the BA and BA' (or A and B)

binding posts and the battery is connected to G.

10.2. Application to Four-Terminal Measurements

The URS is especially suited to the comparison

of four-terminal resistors. In figure 33, S and X

are a standard resistor and an unknown, in series,

connected to the end terminals of a URS. Let X

be the value of the unknown and S the nominal

value of the standard which has a correction, Cg. The leads, AD and BF, are connecting leads. At

the potential terminals of each resistor are short

wire tabs, Si, $2, x^, a*2, for convenient connection of a clip on a battery or galvanometer lead. Also

let Si, $2, Xi, X2, be the readings of the URS when

the battery clip is connected to corresponding

potential points and the circuit is balanced.

With a constant current in the circuit, the dif- ference between two readings on the URS is proportional to the difference of potential between

the resistor terminals.

Hence,

_The potential drop across X

S2—S1 The potential drop across S

However, the potential difference across any

segment of the circuit is proportional to the

resistance of the circuit. So,

X2—X1 The resistance of X

S2—S1 The resistance of S

Figure 32. Slide-wire representation of f'fiS. OS X F O—^yww^-—•—

^vvw\/|-—

Figure 33. Four-terminal measurement with URS.

Since a reading on the URS depends only on the

ratio of two resistances, the equation is true even though the current in the URS is not constant. Using the corrected value of the standard,

»S'(1 +Cs)) the last equation becomes,

X X2 —Xi S (l+Cs)~S2—s/

and

XExample:

«i= 0.310

S2= 913.445

Xi= 918.132

X2=l 703.027

»S'= 10 ohms

Cs= —12 ppm

Sil +Cs) = 10(1 -0.000012) =9.99988 ohms

-^=f:7T7^X9.999S8 =8. 595.50 ohms.

Note that in figure 33 the galvanometer is connected to the URS binding posts, BA and

BA'. Then the resistance in the galvanometer

circuit does not change as the potential lead is transferred from one point to another, and it is not necessary to change the damping resistance

for each reading. This is important when calibrating potentiometers and other instruments having

multiple settings. However, it is important that

the battery supply be adjustable in order to be

able not to overload the coils of the ratio set or the unknown when the balance point is near

either end.

An important application of the Universal

Ratio Set is its use for measuring voltage ratios in

calibrating potentiometers. This application will be explained in Part 3.

27
Part 2. Calibration of a Wheatstone Bridge

In some of the preceding sections the Direct

Keadmg Katio Set and its uses have been described. As a further iUustration of its use the

following detailed outline of the calibration procedure for a Wheatstone bridge is presented.

The bridge for which the calibration procedure

and data are given is of the open-dial type intended

for the measurement of resistance to a fairly high

accuracy. This type of bridge is chosen because

practically identical bridges of the same pattern

are made by several American manufacturers.

They have duphcate sets of ratio coils from 1 to 10 000 ohms and a five-decade rheostat with

steps of 0.1 to 1 000 ohms inclusive. Push-button

switches are provided, one in the battery branch

and one in the galvanometer branch of the bridge

circuit. The procedure for the calibration of this bridge is essentially the same as for other commercial Wheatstone bridges and the directions to be given may be readily adapted to almost any

such bridge.

11. Test Equipment

Standard resistors: Two 10-ohm standards and

one each of 1-ohm, 100-ohms, 1 000-ohms, and

10 000-ohms, nominal value.

Mercury stand

Shorting link

Direct Reading Ratio Set

Auxiliary rheostat: The rheostat arm of another

bridge or any resistance box with resistance

decades corresponding to the decades of the bridge

being tested. Sensitive galvanometer

Galvanometer damping resistance

Battery key, preferably a reversing key

Battery rheostat, a variable resistor to regulate

the voltage applied to the test circuit. Battery (10-12 v)

D-c voltmeter (0-10 v)

Thermometer, to determine room temperature

and the temperature of resistance standards during

the test.

12. The Wheatstone Bridge Circuit

The Wheatstone bridge is represented schematically by the well-known diamond-shaped

diagrams of figures 34A and B. The letters X, R, A, and B are used to represent the arms of

the bridge and also their respective resistances.

Resistors A and B form the ratio arms. One or both of these arms are variable. A" is a resistor

of unknown value. 7? is a resistor of laiown value

which may be fhxed, or R may be a calibrated

rheostat. is a sensitive galvanometer and BA

is a battery of suitable voltage. Whether the

battery and the galvanometer are connected as in

figure 34A, or as in figure 34B, the value of the

unknown resistor is given by the basic equation

X^-R

when no current through the galvanometer shows

that the bridge is balanced.

Figure 35 is a generalized diagram of a laboratory

bridge, showing binding posts and switches or keys.

Since the circuit may be either the circuit of

figure 34A or that of figure 34B, the binding posts

in this diagram are indicated by number. Binding

posts (2) and (4) may be battery binding posts,

BA, or they may be galvanometer binding posts,

G. The key may be between (2) and a, or between

(4) and c. Likewise, (3) and (5) may be either

galvanometer or battery binding posts and the

key may be between (3) and b, instead of the

position shown in the diagram. The binding

posts (1) and (6) are for connection of the unknown

resistor which forms the X arm of the bridge.

The small letters a, b, c, and d indicate branch

points where bridge arms and leads from the

binding posts join.

Figure ;34A and B. Conventional diagrams of Wheatstone

bridge circuit.

'-0 (2)

Figure 35. Generalized diagram of laboratory bridge.

28
12.1. Ratio Arms, A and B

A set of resistance coils of 1, 10, 100, 1 000, and

10 000 ohms, nominal resistance, is arranged so that any one of them may be connected into tlie cii'cuit by a plug or a switch to form the A arm. A corresponding set of resistors (or the same set)

may be connected into the circuit, one at a time,

to form the B arm. The ratio, A/B may be

varied from 1/10 000 to 10 000/1. The range of

obtainable ratios is not the same on all models.

12.2. Rheostat Arm, R

The rheostat arm of a five-dial bridge is illus- trated schematically in figure 36. The fu'st decade, 1 000 olims per step, contains nine or ten

1 000-ohm resistance coils in series. Any number

of these resistance coils, from zero to nine or ten, can be connected in series in the circuit b}^ a dial

switch to give a range of resistances from zero to

9 000 or 10 000 olims. The other decades are

similar, providing resistances of 100, 10, 1, and

0.1 ohm per step, respectively. The last decade

usually has ten steps, affording a range in 0.1-ohm

steps from zero to 1.0 ohm. With the dials set

at 9, 9, 9, 9, and 10, respectively, the resistance

of the arm is 10 000 ohms, nominal value. This

setting of the dials may be conveniently ^^Titten 9 999.x, in which X represents the reading of 10 on the right hand dial.

Figure .36. Schematic diagram of rheostat arm of bridge.

13. Outline of Test Procedures

13.1. Need for Testing

Due to manufacturing tolerances and to changes

in resistance with age, temperature, and humidity,

the true value of a resistor is very rarely the same

as its nominal value. Hence, the resistance

elements of a bridge should be recalibrated from

time to time. In addition to the true values of the resistors which compose the ratio arms and the

rheostat arm, it is also necessary to Icnow the

resistances of the switch contacts and the internal

leads.

It is assumed thac the bridge which is to be

tested is in satisfactory worldng condition. If it

is found defective, it should be sent to the factory

for repairs, or referred to someone who is ex- perienced in instrument repair. The beginner in

testing should not open the bridge.

13.2. Required Measurements

The measm-ements that are to b(; made; in testing a Wheatstone bridge are:

1. "Zero" resistance of tlie rlieostat aim and

the resistance of the leads from the X bijuHng posts

to the adjoining arms of the bridge.

2. The resistance of each coil In the rheostat arm.

3. The resistance of each coil in each ratio arm. The resistance measm-ements are made with a Dnect Reading Ratio Set used with a sensitive

galvanometer. It is not necessary to m.ake the

tests in the order given above.

Test 1. This test consists of two parts. The

zero resistance is the resistance at switch contacts

in the rheostat arm, m.easm-cd with all dials on

zero, plus the resistance of leads within tiie arm. The resistance is measured between the branch

points a and b, figm-e 35. It is usually reported

as the resistance for the zero setting of the highest

decade, and if significant, is included in the correction to each step of the decade.

The internal lead resistance is the resistance of

the leads from, the X binding posts, (1) and (6) figm-e 35, to the branch points a and d, respectively

Test 2. The resistance for each dial setting of

the rheostat arm is measm-ed with current leads

to binding posts corresponding to the conditions

of use.

Test 3. Each coil of each ratio arm is measured

by the interchange method. The resistors of the

A arm are measured between the branch points c and d. The resistors of the B arm are measured

between h and c. Even though the same resist- ance coil may be used in either arm, it should be

measured in both, because the lead resistance from

the coil to one arm may differ from the lead resist- ance to the other.

If A' , B' , and R' are corrected values of the

bridge arms, and r is the internal lead resistance

of the bridge, the value of the unknown is given

by the equation,

X=^; R'-r.

A complete equation, including the nominal values

of the resistors and cheir respective corrections, is

X=^(l+a-6)(i?i+Ci+i?o+C2+i?3+C3+i?4

+C4-hi?5+C5)-r.

In the above equation, A and B are the nominal

values of the ratio arms; a and 6 are then- respective corrections; R2, R3, Ri- ^md R5 are the

nominal values corresponding to the dial readings;

Ci, C2, C3, Ci, and Cs are their respective corrections;

and r is the internal lead resistance in the sam.e

arm. as the unknown resistance.

29
13.3. The Circuit Diagram

Before the test procedures Hsted above can be

apphed to a bridge, it is necessary to have a correct diagram of the bridge circuit. For example, it may be seen from figure 35 that the zero resistance

of the rheostat arm may be measured by taldng

cmrent leads to binding posts (1) and (6) and potential leads to binding posts (2) and (3) with the

key between (2) and a closed. Before the test can be made it is necessary to know the panel

designations of the nmiabered binding posts.

The worldng diagram wiU be figure 35 with the

binding post niunbers replaced by the panel designations. However, battery and galvanometer

keys ma}^ be in a position different from that shown

in figm'e 35. The usual panel markings on an American

bridge are: BA Battery

6A Galvanometer

X Unknown Resistor

In a circuit diagxam, the relative positions of the

binding posts on the panel are sho^vn by subscripts,

L and R for left and right, or L and U for lower

and upper.

The manufactm-er's diagram of the circuit is usually satisfactory. If a circuit diagram is not

available, it is necessary to produce one by tracing

the circuit. It is desirable to checlv SiHy diagram on hand because an occasional bridge may differ in some detail from the maker's diagram.

The circuit of the bridge can be traced with a simple tester, or volt-ohm-meter (VOM), by

measui-ing approximate resistances between pairs

of binding posts with keys open and with keys

closed. The rheostat arm and the ratio arms can be identified readily by varying the resistances in the respective arms. Test 1 can be carried out usually without refer- ence to a diagram. With the cinrent leads con- nected to the X binding posts, DRRS readings can be taken mth the potential lead to each binding

post on the panel. Then, the arrangement of the

circuit can be determined by comparing the DRRS

readings. The method will be explained in a later

section.

13.4. Reducing Contact Resistance

Plugs and the contact surfaces of open dial

bridges should be cleaned and lubricated. Clean

v\'ith a harsh cloth or specially prepared paper

wipers, not an abrasive. Lubricate with pure

vaseline or a highly piirified, light petroleum oil. A beginner should not open a bridge to clean and

lubricate concealed contacts. Mercury contacts on standard resistors should

be clean and amalgamated. Any crusted amalgam on the surfaces should be carefully scraped

and the clean surfaces re-amalgamated (sec. 5.2).

Current leads from test equipment should not

be taken through the key contacts of the bridge.

When apparatus is set up for testing, bindingpost connections should be weU tightened. Plugs

should be inserted with a firm, slightly rotary

motion.

13.5. Load Tolerance

If excessive current flows in any part of the

circuit, heat is generated in that part faster than

it can be dissipated, the temperature rises, and

the resistance changes. Measurements become

inaccurate.

If the galvanometer is satisfactorily damped,

it will generally indicate an overload. When the

battery key is closed, the galvanometer spot will move normally across the scale, come nearly to

rest, then slowly continue its motion as heat

accumulates in the circuit. With a galvanometer

of high sensitivity, overloading can be avoided if deflections are kept reasonably small.

A load of 0.1 w is usually safe. With a good

galvanometer, it is generally more than enough

for adequate deflections. In some cases, a some- what larger load may be tolerable if quick readings

are taken and the battery key immediately

opened.

M

I 0 1

Figure 37. Recommended test circuit.

In the circuit of figure 37, A and B represent

the arms of a DRRS, is a resistance standard,

and X is an unkno\t-n resistor of the same nominal

value as S". The current from the battery divides

at M into approximately equal parts in the left and right branches, MPO and MNO, of the circuit. The emf applied to each of these branches can be

adjusted by the battery rheostat, Rh, and can be

read on the voltmeter, V. For a given load, P (watts), in either branch,

the emf is V=^JPR when R is the resistance of

the branch in ohms. Hence, the voltage for a load of 0.1 w is y=V0.1 R. The voltage indicated

by this formula is usually more than sufficient.

30
13.6. Applicability of General Principles

The preceding pages have given pre-test preparations and precautions required for accuracy,

with a statement of the steps to be taken in the

test of a Wheatstone bridge. Since Wheatstone

bridges consist of the same basic parts, namely,

two ratio arms, a rheostat arm, and the internal

leads from the binding posts for the unknown

resistor, the testing problem depends only on

understanding the use of test equipment to make

the necessary measurements on each part.

The following section will explain the test of a

specific model in detail With a Imowledge of

the general principles and their application, it should be possible to make the minor modifications of procedure required for testing any of the

makes and models in common use

14. Test of Open Dial Bridge

The order in which the different parts of the

bridge circuit are tested, generally, is immaterial.

The tests will be presented in the following

order

Test 1 : Zero and internal lead resistance.

Test 2 : Rheostat arm.

Test 3 : Ratio arms.

14.1. Test 1: Zero and Internal Lead Resistance

This test may serve, in the absence of a ciruit diagram, to trace the bridge circuit and, at the same time, to obtain the desired resistance

measurements.

The connections for the test are shown schematically in figure 38. The measurements are made with a Direct Reading Ratio Set by the

method for the measurement of a small resistance

(sec. 8.5). The 10-ohm resistors are standards on a mercury stand. Since it is assumed that

the connections of the binding posts to the bridge

network are unknown, the notation of figure 35

is used in this figure.

The dashed line between b and d indicates that

the ratio arms have been short-circuited by inserting plugs on each side of the same stud between

the A and B bars. The "hooks" at the binding

posts represent bare, copper wire tabs for convenient "potential point" connections for a clip on the end of the battery lead. Leads from the DRRS go through the 10-ohm

standards to the X binding posts, (1) and (6), and the circuit is completed through the internal

leads, the rheostat arm, R, and the short across the ratio arms. Each dial of the rheostat arm is on zero. The "potential" leads pass through the

binding posts to the effective potential points,

(1), a, h, c, d, and (6). The BA and GA keys

must be closed to permit connection to the

potential points a and d. The assumption that

the keys are located as shown may not be correct. This test will show their true position.

(4) VWWWW (3)

Figure 38. Connections for zero and lead resistance {schematic)

A reading on the DRRS is taken at each

potential point. From figure 38, it is evident that a reading at (4) is superfluous. However, if it is not known which binding post on the bridge panel

is connected to the junction of the ratio arms, it is necessary to take a reading at each. The tabulated

data will show:

1. The identity of each binding post on the

bridge panel with the corresponding numbered

binding post of figure 38

2. The zero resistance (resistance between

branch points a and b with all dials on zero) ; 3. The internal lead resistance (resistance from

(1) to a plus the resistance from (6) to d. The connections of the bridge to the test circuit are shown in figure 39. A sample set of test data

is given in table A. If the bridge circuit is known

before the test, the tabulation is simplified. In

that case, the reader may turn to the paragraph

below, marked **. Column I of table A shows each reading taken on the DRRS as the battery clip was connected

to each binding post. Fu-st, the keys were open.

No reading could be taken at BA^ until the BA

key was closed which showed the location of the

battery key in the circuit. It is indicated in the

table by the letter "k." The location of the

galvanometer key was determined in the same

way.

31

mm 1
i i & 2)

D R R S

Figure 39. Connections to open-dial bridge for zero and

lead resistance.

Table A

I l-H HH 1III IV

6 648 Xu 4 673

0. 00046

1 Xu 4 673 kBAL 4 764

. 00718

2 kBAL 4 764 GAr 6 200

. 00099

3 BAr 6 398 BAr 6 398

. 00078

4 WAl 6 555 kGAL 6 555

. 00046

5 GAr 6 200 Xl 6 648 6

The data of column I were rearranged iii column

II in the order of magnitude of the DRRS readings.

Column II shows the order in which the binding

posts of the bridge are connected into the circuit. Column III gives the resistances between consecutive potential points (or branch porats). For

Figure 40. Identification of bridge binding posts with the post numbers of figure 35. example, the resistance between the upper X • bindmg post, Xjj, and the branch point to which ' the left battery bindmg post, BAl, is connected is

4 764-4 673 s

Since 10-ohm resistance standards were used, this

is 46 parts per million of 10 ohms, equal to 0.00046 ohm. This is the resistance of one of the

internal leads. The other internal lead is from

Xl to the branch point where the lead from GA^

joins the network. This lead also has a resistance

of 0.00046 ohm, making the total internal load

resistance 0.00092 ohm. (The two internal leads are not always equal.)

The largest resistance in column III is 0.00718

ohm. This is the zero resistance of the rheostat arm. Hence, GAr and BAl are connected to the

ends of that arm. The other resistance values in column III are not used.

Column IV of the table lists the binding-post

numbers of figure 35 which correspond to the

bridge designations in column II. Figure 40 is a

repetition of figure 35 into which the designations

of the bmding posts on the bridge panel have been

entered. The relative distribution may be differ- ent in another make of bridge and the location of

the BA and GA keys may be different. In any

case, the circuit diagram is the diagram of figure

35 with the numbers replaced with the correct panel designations of the binding posts, and the

location of the keys corrected, if necessary.

The completion of the circuit, figure 40, is based on the data of table A. From columns II and III, it is seen that the lead from Xu (0.00046

ohm) joins the lead from BAl at a branch point

which is at one end of the rheostat arm (0.00718

ohm). The other end of the rheostat arm is joined by the lead from GAr. Hence (1), (2), and (3) of figure 35 are replaced by A^, BAl, and

GAr, respectively.

32
At the bottom of the table, it is seen that tlic lead from A'^, (0.00046 ohm) johis the lead from

GAl at a branch point of the network. Hence,

(6) and (5) are replaced by Xl and GA^, respectively. That leaves BAr to replace (4) and complete the working diagram of the bridge circuit. **If the circuit diagram is available at the beginnmg of the test, the DRRS reading at BAr

will be omitted. The data may be tabulated as

follows

Table B

Pot. pt. Rdg. Computation Resistance

6 200

4 764

6 200-4 764 _ 2 —7i»

4 764-4 673

2 = 46

6 648-6 555

2 = 46

"Zero" = 0.007 ohm.

Xu

Xl

4 673

6 648 Lead = 0.0009 ohm.

GAl 6 555

Although the computations give values to

five decimal places, they are rounded off to the

values shown above. Measurements are rounded

off to conform to the degree of accuracy stated

in the NBS certificate, a sample copy of which

is included in this paper. A study of this copy

I will show the practice generally followed at the

National Bureau of Standards.

I The zero resistance is reported as the resistance

j at the zero setting of the top dial of the bridge.

The lead resistance is the quantity r in the

equation

jl x=^R'-r,

in which A', B', and R' are the corrected values

of the respective bridge readings, A, B, and R.

The complete equation has been given in section

13.2.

j 14.2. Test 2: The Rheostat Arm

; The method described here is applicable to

I any decade type of rheostat or resistance box.

0 ] In figure 41, let X be a resistance decade of the

\ rheostat arm of a bridge. Let Y be an auxiliary

!! rheostat, as the rheostat arm of another bridge,

\ or a resistance box with decades corresponding

jl to the decades of X. Evidently A^ and Y are

[ interchangeable in the cuxuit. Hence, both

I may be calibrated simultaneously.

The mercury contact surfaces, h and k, of a

I mercury stand, permit the convenient exchange

I of a shorting link for a resistance standard, or

vice versa, is a resistance standard with a nominal value ten times the value of the standard

I on the left. Its corrected value is not needed,

t A and B are the arms of a Direct Readmg Ratio

: Set.

I <7) 1

Figure 41. Schematic diagram of circuit for test of rheostat arm.

If the 100-ohms-per-step decade of A' is to be

calibrated, a 100-ohm standard is used on the

left. Each resistance coil of the decade is compared with this 100-ohm standard. A 1 000-ohm

standard is used at D. To test the first step of the decade, set the dial at zero, set Y at 900 ohms

(step 9 on the 100 ohms-per-step decade), and

place the 100-ohm standard on the mercmy

stand. The nominal resistance of the left upper arm is 1 000 ohms, corresponding to the 1 000

ohms in the right upper arm. Balance the circuit

and take a reading (Rdgi) on the DRRS. Then

advance the dial on X to step 1. Replace the

100-ohm standard with the link. This change

substitutes the first coil of the decade for the

standard. Balance the circuit and take Rdg2 on

the DRRS. Let Cs be the correction for the

standard and Cl the correction for the link. Then

the correction to the nominal value of the first step of the 100 ohms-per-step decade of X, in parts per million is, c^=10(Rdg2— Rdgi) +c,— Cz,. This equation gives the correction in parts per

million of the nominal value of the resistance coil which is being tested. The term, c^, is included

in the equation for completeness. However, it is negligible when the nominal value of the coil ex- ceeds ten ohms, provided that the resistance of

the link does not exceed 50 microhms. The

factor, 10, in the equation is necessary' because

the resistance of each of the upper arms of the

test circuit is 1 000 ohms. Therefore, Rdgo —Rdgi

is parts per million of 1 000 ohms. The dift'erence in the readings must be multiplied by ten to change it to parts per million of 100 ohms befoi'e the correction for the standard, Cs, is added.

For example, suppose the correction for the

standard is +45 ppm.

33
Rdgi, with standard in the circuit, X on zero, Y on

step 9 .... 5489

Rdgv, with the link in the circuit, X on step 1, Fon

step 9 5478

Rdg9 ... 5 478

Rdgi ... 5 489

Rdg2-Rdgx ... -11

X 10= . . . —110

+Cs . . . +45 (cz,, neghgible)

=Cx . . . —65 ppm

100X(—0.000065) = —0.0065 ohin, correction for

the first step.

The 1 000-ohm resistor in the right upper arm

of the test circuit, often referred to as the dumm}",

serves only to balance the circuit and does not

enter into the computations. Any reference to the "standard" is a reference to the standard

resistor in the left upper arm, with which the

coils of the decade are compared.

To find the correction for the second step of the

decade, leave the dial on step 1, replace the link

with the 100-olmi standard, set Y back to step

8 (800 olmis), and take Rdgs on the DRRS. Replace the standard with the link, advance the dial on X to step 2, and take Rdg*. Since Cl is negligible for this decade, the correction for the second

coil is 10 (Rdg4— Rdgs) +Cs. If Rdgs is 5 473 and

Rdg4 is 5 464, the correction is —45 ppm, or, 100X(—0.000045) = —0.0045 ohm.

Each step of the decade is tested in the same

way. At each step on A', the correspondingdecade on Y is set back one step to maintain a balanced circuit. The step-by-step measurements give the cor- rections for each individual coU of a decade.

When the bridge is used to measure an unknown

resistance, several coils may be in series. If the

dial of any decade is set on 5, the first five coils of that decade are in series. The correction to the nominal value at that setting is the sum of the

corrections to the five coils in use. Hence, a

step-by-step smnmation must be made of the

corrections to the coUs in the decade to find the

correction applicable to each dial setting.

14.2. a. Calibration of X and Y

As has been pointed out, the decades of the

two rheostats. A" and Y, may be calibrated simultaneously. Compare Rdg2, above, with the 100-

ohms-per-step decade of Y at step 9 and Rdgs

with Y at step 8. From these readings the cor- rection for the 9th coil on I"is 10 (Rdg2 —Rdgs) +Cs)

,

that is, 10(5 478-5473) +45= +95; 100X0.000095 =0.0095 ohm.

The corrections for each coil of the Y decade

will be in order downward from the 9th coil to the

1st. Hence, the summation of the corrections

begins with the first coil at the bottom of the col- umn and proceeds upward until the sum of the

corrections for all the coils in the decade is showi

at the top.

If there are ten coils in a decade, the procedur

differs only in that there is one more coil to bi measured.

Other decades (except the O.l-ohm-per-stej

decade) are measured in the same way. For thi

1 000 ohm.s-per-step decade, the standard will b(

1000 ohms and the dummy, D, will be 1000(

ohms. Likewise, for the 10-ohms-per-step decade

the standard will be 10 ohms, D will be 100 ohms

and for the 1-ohm-per-step decade, the standarc

will be 1 ohm, D will be 10 ohms. Note thaH

the correction for the 1-ohm standard must hi

its two-terminal value.

If the standard and the link are substituted, the one for the other, in the circuit as explained above,

it will be necessary to include the correction foi the link in the equation for when testing the

10-ohms-per-step and the 1-ohm-per-step decades.

For measurement of the resistance of the link, see' "Measurement of a Small Resistance" (sec. 8.5).

A copper link ji in. in diameter and 3 in. between

centers of contact surfaces will have a resistance

of approximately 40 microhms. With that re- sistance, the correction for the link will be 40 ppm

when used with a 1-ohm standard, or 4 ppm when

used with a 10-ohm standard.

The correction for the link may be avoided by

the arrangement shown in figure 42. With the

standard and the link on one end of a mercury

stand, as shown in the diagram, the link serves as a switch in the lead from the DRRS. When the

link is in the position shown by the solid curve, the

standard is in the measuring circuit. When the|

link is in the position shown by the dashed curve, the standard is cut out of the circuit. Since the

resistance of the link is a fixed part of the lead re- sistance, it does not enter into the computations.

When the standard is in the circuit, the resistance

of the bar between the link and the standard is included. This resistance is negligible for the

^8-in.-square nickel plated copper bars of the NBS

stand.

TO RHEO ARM

FROM DRRS

Figure 42. Use of link as a switch.

34
Table C. Data from test Temperature, 25.0

of 10-ohnts-per-step decades of bridges X and Y.

° C. Correction for 10-ohm standard, +6 ppm.

Bridge X Bridge Y

I II III ly V VI VII VIII IX X

A c, ppm Summation c, ohm c, ppm Summation c, ohm

U y

c

0 OUU -194 -194 -0. 002

1 y 5 480

-204 -2 546 -0. 025

1 QO

co 5 oUl -234 -428 -. 004

2 8 5 477 -344 -2 342 -. 023

oZ 7

ct O

C CIO 0 612 -364 -792 -. 008

3 7 5 475

-284 -1 998 -. 020

6 6

Cf O 5 504

+ 56 -736 -. 007

4 6 5 509

-324 -1 714 -. 017

4 5

c

5 542

-544 -1 280 -. 013

5 5 5 487

-334 -1 390 -. 014

5 4

ct b 5 521 -544 -1 824 -. 018

6 4 5 466

-274 -1 056 -. Oil 6 3 s 5 494

+ 446 -1 378 -. 014

7 3 5 538

-224 -782 -. 008

7 2 s 5 561 -524 -1 902 -. 019

8 2 5 508

-284 -558 -. 006

8 1 s 5 537

-594 -2 496 -. 025

9 1 5 477

-274 -274 -. 003

9 0 s 5 505

Some difficulty may be encountered in getting

galvanometer readings on scale when testing the

1-ohm-per-step decade. This difficulty results from badh^ unbalanced resistance of the leads from

the stand to the rheostats. It is easily overcome by modif3dng the lead resistance.

Figure 43 shows the arrangement of apparatus

for the simultaneous test of the rheostat arm.s of two bridges. Reference to figure 40 shows that

current leads should be taken to binding posts Xu

and GAr. A current lead should not be connected

to BAl because the BA key contact may not m.aintain constant resistance. The battery or potential

lead goes to the junction between the dum.my, D,

and bridge Y. Table C gives the data obtained from a test of

the 10-ohms-per-step decades of the two bridges.

S was a 10-ohm resistance standard. D was 100

ohms. Since the link, L, was used as a switch as

shoAvn in the diagram, no Imk correction entered

into the computations.

Column I in the table gives the settings of the

dial of bridge X; column II, the settings of the dial of bridge Y. Column III shows the standard in

the circuit at certain dial settings. The DRRS

readings for each pair of dial settings are given in

column IV. Columns V, VI, and VII mclude data

for bridge X. In column V are the corrections in

parts per million for each resistance coil of the

decade. Colunm VI is the step-by-step sunmiation of the corrections in Column V. The corrections of column VI, which are in parts per million, are rounded off and expressed as fractions of an ohm in column VII. The latter are the corrections

to be used for each dial settino; of the decade.

Columns VIII, IX, and X give the corresponding

data for bridge Y, reading upward from the bottom

of the table.

35
Figure 43. Connection of two rheostat arms into test circuit.

14.2.b. The 0.1-Ohm-Per-Step Decade The steps of this decade are compared dhectly

with the steps on the XI 000 dial (or 0.1-ohmper-step decade) of the Direct Reading Ratio

Set. In figure 44, A and B are the arms of the

DRRS. The dummy resistor, D, is 100 ohms.

As in preceding tests, the rheostat arm of the

bridge and the auxihary rheostat are in series in

the left upper arm of the test circuit. Set the

auxiliary on 99.5 ohms. Set the dials of the

bridge on zero. Balance the circuit with the dials

of the DRRS. It may be necessary to change the

setting of the auxiliary slightly, so that, when the

circuit is balanced, the X 1 000 dial of the DRRS

will read zero, corresponding to the zero reading

of the dial to be tested. Advance the 0.1-ohm-per-step dial of the bridge,

step by step, taking a reading on the DRRS at each setting of the bridge dial. Subtract the

reading at step zero from each subsequent reading.

The results will be the true values for the corre- sponding settings of the bridge dial. Subtracting

the indicated value from the true value of each

step will give the correction.

If the bridge has a 0.01-ohm-per-step decade, it is tested in the same way by comparing it with the

steps of the corresponding decade of the DRRS.

Figure 44. Test of O.l-ohin-per-step dial.

Table D. Sample data from a test of a 0.1-ohm-per-step decade

Step DRRS Resistance Correction

0 0 456 0. 0000 0. 0000

1 1 458 . 1002 +. 0002

2 2 457 . 2001 + . 0001

3 3 456 . 3000 . 0000

4 4 456 . 4000 . 0000

5 5 456 . 5000 . 0000

6 6 456 . 6000 . 0000

7 7 456 . 7000 . 0000

8 8 455 . 7999 -. 0001

9 9 454 . 8998 -. 0002

10 10 455 . 9999 -. 0001

The corrections for this dial (all less than 0.0005

ohm) were negligible.

14.3. Test 3: The Ratio Arms

The connections on the panel for selection of the

ratio arms consist of two heavy bus bars marked

A with a third bus bar, B, between them.

Between each A bar and the B bar is a row of studs, each of which may be connected to either

bar by a plug. Each stud is connected by a

resistor of the denomination marked on the stud

to a bus wire which extends internally underneath the B bar and terminates at the bindmg

post BAr. The connections of the bus wire, the

A bars, and the B bar to the binding posts are shown m the diagram, figure 45. "With a plug inserted between any stud and the

A bar, the A bar is connected through the indicated resistor to BAr. Likewise with a plug

inserted between any stud and the B bar, the B

36
, , RHEO

A PLUGGED TO 10 B PLUGGED TO 1000 RATIO- A/B= 10/1000

GA|_ BAr

Figure 45. Block and plug arrangement for ratio arms

BA,

Figure 46. Plugs set for ratio 1:1.

bar is connected through the resistor to BAr.

With studs inserted on both sides of the same

stud, the ratio arms are short-circuited. A oneto-one ratio may be obtained by plugging the A

bar and the B bar to two different studs of the same denomination. In figure 46, the A bar is shown plugged to stud 10, the i? bar to stud 10' for a ratio of one to one. Figure 45 shows that

any one of the ten resistors may be plugged to either arm.

Plugs should be well fitted, clean, lubricated,

and inserted with a firm, slightly rotary motion.

The measured correction for any resistor when

measured in one arm should agree reasonably with

the measurement in the other arm. However,

contact and lead resistances between the resistor

and the terminals of one arm differ from the

resistances between the resistor and the terminals

of the other. These differences are small relative

to a 10 000-olma resistor, large with respect to a 1-ohm resistor. The measurements on a 10 000-

ohm resistor in each arm will usually agree within

2 ppm. Corresponding measurements on a 1-ohm

resistor may disagree by more than 100 ppm.

The effect of contact and lead resistance is such

that the use of a 1-olmi resistor in either arm is to be avoided, if possible, when precision is important.

14.3. a. The A Arm

Reference to the circuit diagram, figure 47,

shows that to measure the resistors of the A arm,

current leads may be taken to and BAr,

potential leads to GAl {GA key locked down)

and GAr. The resistances are measured between

the branch points d and c by the interchange

method.

Figure 47. Schematic bridge circuit.

(J A ARM

Figure 48. Test connections for A arm.

The arrangement of the test circuit is shown in figure 48. To measure resistor 1 (1 ohm), plug

stud 1 to the ^4 bar, stud 1' to the B bar. Place

a l-olmi resistance standard on the left of the

stand and a link on the right. With the battery

lead to GAl, take Rdgi on the DRRS. Exchange

places between the standard and the link, connect

the battery lead to GAr, and take Rdgo.

To measure 1', plug stud 1 to the B bar, plug

1' to the A bar. Repeat the above procedure.

With stud 1 still plugged to the B bar, plug each

remaining stud in turn to the xi bar and take the

readings, using appropriate standards.

37
For each resistor in the arm substitute the

corresponding readings in the following equation:

c.=^^fc^^+c.-L (sec. 8.3).

The correction for a l-ohm standard must be its two-terminal value (sec. 8.6). The correction, L,

for the link was discussed in connection with the

test of the rheostat arm. If the link is used with

a l-ohm standard the correction will be equal to

its resistance in microhms. If used with a 10-ohm

standard, the correction Avill be one-tenth of that

value. TVith resistance standards in excess of

10 ohms, the correction is usually negligible.

The results in the fifth column of table E are

corrections in parts per million. The corrections

m the last coliunn are in proportional parts,

rounded off as they appear in the certificate.

14.3.b. The B Arm

Reference to the chcuit diagram shows that

measurements on the B arm can be made by taking cmrent leads to BAr and GAr and the potential lead alternately to Xl and Xu as shown

schematically in figure 49. The A bar should be

plugged to a one-ohm stud, but not one being

Table E. Test of A arm.

Sample data from laboratory notes. Bridge S/N Cmrent leads to Xl and BAk. Potential leads to GAl and GAe. Resistance of lint, 40 microlims. Date.

Plug

Std., temp.,

and corr.

DRRS ]

Std. at

left

Readings

Std. at

right

Computations Correction

1 #31/24.8

+ 77

7 437 7 058

7 058-7 437

2 +77-40= -153 -0. 0002

1' Same. 7 453 7 057

7 057-7 453

2 + 77-40= -161 -. 0002

10

#24/24.8

+ 6

5 573 5 544

5 544-5 573

2 +6-4 =- 12 -. 00001

10' Same. 5 567 5 546

5 546-5 567

2 + 6-4 = -8 -. 00001

100

#26/24.8

+ 45 5 343 5 423

5 423-5 343

2 ^ + 45 =+85 +. 00008

100' Same. 5 332 5 432

5 432-5 332

2 +^^5 =+95 +. 00010

1 000

#400/24.9

-19 5 261 5 467

5 467-5 261

2 =+84 +. 00008

1 000' Same. 5 247 5 480

5 480-5 247 „

2 =+97 +. 00010

10 000

#5/24.9

+ 624 5 969

" 4 754

4 754-5 969

2 +624 = + 16 +. 00002

10 000' Same. 5 957 4 766

4 766-5 957

2 +624 =+28 +. 00003

C B ARM b GAr

-O fVWWWNAf OPOT. LEADS J

FiGUEE 49. Test connections for B arm.

tested on the B arm. The potential lead through

XV goes through the rheostat arm to the branch

point h. Therefore, all dials should be on zero. The resistances measured are between the branch

points c and 6. Plug the B bar to each stud va turn and measm'e the corresponding resistance coU. Differences

in the measurements in the A arm and in the B

arm have been explained above. These differences

usually become progressively smaller as the measurements proceed from a one-ohm coil to a \ 10 000-ohm coil. After the first tests on a bridge are completed, a second worker repeats the tests, using difl^erent equipment, if possible, especially diflerent resist- ance standards. A comparison of the results will

38
reveal any mistakes or eri'ors. Tlic results of two

tests on a resistance coil should differ by much

less than 0.01 percent of the nomuial value of the

coil. The certified values are the average values

determined by the two tests.

14.3. c. Working Test

After a bridge has been tested, some of the

results may be spot checked by usuig standard

resistors us unknowns and coinjjiu-ing ihr; vaJu(;s

measured on tiie bridge with th(! corrected values

of the standards. DiU'erent resistance values may

be measured at different settings of the ratio arms.

Substitution of the readings on the l)i-idge and

their respective corrections in the equation foi- X

should give for each resistance standard measured,

a value whicii agrees well within 0.01 jxTcent w itii the calibrated value of the standaid.

15. The National Bureau of Standards Certificate

The following text of a certificate contains data

from the test of a bridge of the make and model

described in the preceding pages. (The heading

of the certificate and the identification of (he bridge

have been omitted.)

The above-described apparatus was tested in (month

and year) at a room temperature of about^ ^ C. When

the bridge is in a balanced condition, the value of the unknown resistance connected between tlae "A'" terminals

of the bridge is given in ohms by the following equation:

X=^a + a-b){Ri + Ci + R2 + c2 + fls + C3 + /?4 + C4 + fls + cs) - 0 . 0009.

Here A is the nominal value of the resistor plugged to the A bar, B is the nominal value of the resistor plugged

to the B bar, and a and b are the respective corrections to these nominal values expressed in proportional parts. The readings of the decades in the rheostat are denoted

7?i, Ro, Rs, Ri, and R^; and c,, Co, Cs, C4, and C5 are the

respective corrections to these readings. The term 0.0009

is the resistance of that part of the bridge which is in series with the resistor being measured.

The corrections are given in the following tables:

Ratio resistors, A, B, and corrections a, b

AoT B a b

1 -0. 0002 + 0. 0001

1' -. 0002 . 0000

10 -. 00001 -. 00001

10' -. 00001 00001

100 +. 00008 + . 00008

100' + . 00010 + . 00010

1 000 + . 00008 +. 00008

1 000' + . 00010 + . 00010

10 000 + . 00002 + . 00002

10 000' + . 00003 + . 00003

Rheostat arm

Ri R2 C2 R, C3 Ri c*

0 + 0. 007 0 0. 000 0 0. 000 0 0. 000

1 000 + . 16 100 -. 002 10 002 1 . 000

2 000 + . 35 200 + . 006 20 -. 004 2 -. 001

3 000 + . 5 300 . 00 30 -. 008 3 -. 001

4 000 + . 5 400 + . 01 40 -. 007 4 002

5 000 + . 6 500 +. 01 50 -. 013 5 -. 002

6 000 +. 6 600 + . 02 60 018 6 -. 003

7 000 +. 8 700 +. 04 70 -. 014 7 -. 003

8 000 + . 9 800 + . 05 80 -. 019 8 003

9 000 + 1. 0 900 + . 06 90 -. 025 9 -. 004

The corrections to the one-tenth ohm-per-step decade were found to be less than 0.0005. The corrections given above are not in error by more than 0.01 percent of the readings to which they apply for readings of 10 ohms or more, nor by more than 0.001 ohm for smaller readings; however, the corrections to the 1-ohiu readuigs

of the ratio arms are probably not in error hy more than 0.0002 ohm.

Other tests revealed no defects in the bridge.

39
Part 3. Testing General-Purpose Potentiometers

16. The Potentiometer—General Description

The dial and panel markings on different makes

of potentiometers are usually clear. In this section, the following symbols will be used

:

Battery binding posts: BA+ and BA —

Emf binding posts: EMF+ and EMF— , or E+ and EGalvanometer : GA

Standard cell : SC

Standard cell binding posts: SC+ and SC —

or STD CELL+ and STD CELLEmf-standard cell dial or switch: EMF-SC.

16.1. The Potentiometer Circuit

The potentiometer is designed primaril}^ to measure an unknown emf by comparing it with the

known emf of a standard cell. The basic principle

of the instrument may be imderstood from the

schematic diagram, figure 50, which represents the

potentiometer circuit when the galvanometer key

is closed. When a battery is connected to the BA

binding posts the ratio of the fall of potential

across the emf segment of the circuit, E, to the fall of potential across the standard cell segment, S,

is equal to the ratio of the resistances of the re- spective segments. It is immaterial if the seg- ments, E and S, overlap.

A selector switch, the EMF-SC switch, not

shown in the diagram, connects the standard-cell

binding posts to the circuit when the switch is on

SC, and connects the emf binding posts to tlie cir- cuit when the switch is on EMF. A dial switch, the

standard cell dial, is used to vary the resistance of

segment S. Figure 50 shows the resistance variable

at the SC+ end. In some potentiometers, it may

be variable at the SC— end. If there are two SC

dials, one for coarse, the other for fine adjustment,

the segment is variable at both ends, with one dial switch at each end.

The graduations on the SC dial, or dials, cover

the range of standard cells in common use. Wlien

the potentiometer is used to measure an unknown

emf, the SC dial is set on the calibrated value of the standard cell in use. The resistance of segment E of the potentiometer

circuit is adjusted on the Crompton-type potentiometer by a main dial which varies the resistance

at one end of the segment, and a slide-wire of eleven turns on a drum, which varies the resistance

at the other end of the segment. A modification

FiGURE 50. Simplified schematic diagram of potentiometer.

of the Crompton type replaces the long slide-wire

with an intermediate dial and a slide-wire of one

turn. Usually, the intermediate dial and the slide- wire vary the resistance at the same end of the

segment. Other potentiometer types use several

dials. The dials are graduated to indicate the

value of the emf applied at the EMF binding posts.

When a potentiometer is used for measurements,

a stable battery with the voltage specified by the

maker is connected to the binding posts BA+ and

BA— . A standard cell is connected to the standard cell binding posts and the unknown emf is con- nected to the emf binding posts. It is necessary to observe correct polarity. A sensitive galvanometer

is connected to the galvanometer binding posts.

There are usually three or more galvanometer keys

ranging from low sensitivity to high sensitivity.

When the EMF-SC switch is set on SC, the emf

of the standard cell imposed across the S segment

is opposed by the emf across the S segment due to the current from the battery. The potentiometer

current is adjusted by the rheostat (Rheo, fig. 50)

until depression of the galvanometer key results in zero (or minimum) galvanometer deflection, indicating that the opposing emf's are equal and bal- anced. Only a very small current should be drawn

momentarih^ from the standard cell. While making the current adjustment, a galvanometer key is depressed momentarily to observe the direction of deflection, beginning with the low-sensitivity key

and changing in turn to otlier keys as it becomes

necessary to observe the deflection. With perfect

adjustment, there is no current from the standard

cell.The ideal zero deflection of a sensitive galvanometer is rarely obtainable. Hence, "zero deflec- tion" will be used in the sense of the rrinimum

deflection attainable by careful adjustment.

After the potentiometer has been "standardized"

by balancing the emf due to the potentiometer

current against the emf of the standard cell, the

EMF-SC switch is set on EMF. This disconnects

the standard cell from the circuit and connects

the imknown emf across the E-segment (fig. 50)

of the circuit. To measure the unknown emf, the

main dial, or the dial with the largest step value,

is adjusted first and the adjustment is finished

with the slide-wire, or the dial with the smallest

steps. The adjustment is complete when depression of the high-sensitivity button produces zero

deflection of the galvanometer. Then the un- known emf is balanced by the emf across the

segment due to the potentiometer current. The

readings of the dials, after corrections have been

made, express the value of the unknown emf.

The current in the potentiometer may change,

with the result that the instrmnent is no longer

standardized and the readings of the emf dials are

incorrect. Without disturbing the setting of the

emf dials, the EMF-SC switch may be turned to

XIo

40
8C and tlie current checked. If the gulviinonieteJ'

shows that the circuit is not bahxnced, the current should be readjusted with the rheostat, the switcli returned to EMF, and therneasurenients continued.

The sinipUfied diagram of figure 50 represents

the potentiometer as a single resistance circuit. Most general purpose potentiometers have one or two extra branches covering additional emf ranges. The branch required for a given measurement is selected by a range or factor switch. A variation

is the use of a plug to connect the appropriate

branch. With the circuit selector, switch, or plug, on 1, the main circuit, which covers the maximum

range of the potentiometer, is in use. Since dial

tests are made over the maximum range, no

correction is required for factor 1. The maximum

range of several models is from zero to 1.61 v. With the circuit selector on 0.1 the range is reduced to one-tenth (zero to 0.161 v), and the

indications of the emf dials are to be multiplied

by 0.1. A factor setting of 0.01 is usually included. At

that factor, the range is correspondingly reduced

and the dial readings are to be multiplied by 0.01. The different factor settings do not affect the

standard cell part of the circuit or the indications

of the SC dial. The standardization of the potentiometer is the same for all factor settings, but

should be done with the selector at the factor

setting at which the potentiometer is to be used

if possible.

As a result of necessary tolerances in manufacture and the inherent instability of resistors, the

resistance components of a potentiometer rarely or never agree with their design values. Hence,

when a potentiometer is used for the precise

measurement of an unknown emf, corrections,

which have been found by accurate testing, must

be applied to both dial readings and factor settings.

17. Adaptability of the Universal Ratio Set to

Testing Potentiometers

The test circuit for a potentiometer is shown

schematically in figure 51 in which the Universal

Ratio Set is represented as a slide-wire. Note the

preferred connections of battery and galvanonieter

when four-terminal measurements are to be made

at multiple settings. The test connections of the

ratio set to a widely-used type of potentiometer

are shown in figure 53.

17.1. Measurement of Voltage Ratios

Ijet He and /)*., be the resistances of segments E

and S respectively, (figure 51), and let Fg and

be the voltage drops across the I'espective seg- ments when a battery is connected to the terminals

of the potentiometer. The potential points are the binding posts SC + , SC - , EMF+ and EMF-

The selector switch is on SC for measurements at SC+ and SC— , and on EMF for measui'ements at EMF+ and EMF-. Let 5,, S^, e,, and e.., be the

URS readings taken at the respective potential

points.

Then, from section 10.2,

Pe^^e^ e^ —ei

_ Ps Ps S2 —Si

Pe =PsX S2—S1

Assume that the SC dial is set on 1.019000 volts. Substituting 1.019000 for P,,

P,= 1.019000X

e^ —ei Si —Si

Generally, the potentiometer rheostat can be

adjusted' to make /S'2 —5'i= 1 019.000 (the setting

of the standard cell expressed in millivolts).

Then, in the same units.

and

Ps — S2 — Si

P,=e-i—e^.

Figure 51. Testing a potentiometer with URS (schematic).

The URS is then "direct reading," that is, the

dift'erence in readings at two potential points may

be interpreted directly as an emf without coniputation.

17.2. Interpretation of URS Readings

The Universal Ratio Set is primarily a resist- ance instrument with its dials usually graduated

in ohms of resistance of the left ratio arm. As- sume that the potential lead from the ratio set

in figure 51 is connected to EMF+ and that the

test circuit is balanced. Referring to the slide- wire counterpart of the URS, the slider on the

wire is at Cj. The reading of the dials of the URS

is the resistance in ohms of the slide-wire seg- ment, ACi. Using the earlier notation, call this Rdgi instead of ei. When the lead is transferred

to EMF— and the circuit balanced, the reading of the URS dials is the resistance of AC2. Call this Rdg2. Rdg2 —Rdgi is the resistance of the slide- wire segment, C1C2. None of these resistances

is a resistance of any known part of the potentiometer circuit, but Rdg2— Rdgi is proportional

to the emf (Pj across the segment. Therefore,

emf=^:(Rdg2-Rdg,).

in which K is a constant for any fixed value of current.

41
The current from a battery across the BA

terminals of a potentiometer can be adjusted by

the potentiometer rheostat. Generally, the rheostat can be adjusted so that the difference in URS

readings taken at the SC binding posts is equal to the reading of the SC dial. Then

K=l

and

emf =Rdg2—Rdgi.

This is the direct reading equation previously

expressed in the form,

Pe=e-2—ei.

An outline of the procedure for making the URS

direct reading will be found in section 18. Assume that the SC dial is on 1.019000 v, that

the URS is direct reading, and that URS readuigs

taken at the SC potential points are as follows:

Rdgi 1 090.259 (resistance in ohms of Ad)

Rdg2 2 109.259 (resistance in ohms of ACj)

Difference 1 019.000 (resistance in ohms of CiC,)

The above difference corresponds to a differ- ence of potential across segment S of the potentiometer circuit of 1 019.000 mv, equivalent to the

settuag of the SC dial of 1.019000 v. Therefore,

readings on the URS are not to be thought of as

resistances, but, if the URS is direct reading, the difference in two readings is to be interpreted as

millivolts. This is equally true for readings taken

across segment E.

Ignore the decimal point on the URS panel

(that is, move it three places to the right) and the

difference becomes microvolts. Point off six decimal places and the difference becomes volts. The

above difference may be read as,

1.019000 V,

1 019.000 mv, or

1 019 000 nY.

The advantage of direct reading is that differ- ences in URS readings at settings of the emf dials

may be read directly as units of emf, —voKs,

millivolts, or microvolts, depending on whether

six, three, or no decimal places are pointed off.

17.3. "Direct Reading" Versus "Not Direct Reading"

The following examples illustrate the difference

in the woi'k involved when the Universal Ratio

Set is direct reading and when it is not. Six

places have been pointed off in the URS readings

so that the differences are expressed in volts.

Example 1. URS direct reading.

SC dial Readings on URS

SC- 1.019000 1.119619

SC+ 1.019000 .100619

Difference 1.019000 v. Main dial . Readings on URS

E- 0 .219777

E- 1.2 1.419590

Difference 1.199813 v. That is, a reading of 1.2 v on the potentiometer

corresponds to a true value of 1.199813 v. The

correction to the dial setting is 1.199813-1.200000=-0.000187 v = -187 /XV. Example 2. URS not direct reading, from a test of another potentiometer of same type.

. SC dial Readings on URS

SG+ 1.019000 0.101139

SC- 1.019000 1.126151

Difference 1.025012

Since the difference is not the same as the setting

of the SC dial it is not in volts. Main dial Readings on URS

E- 0 0.220884 (Rdgi)

E- 1.2 1.427907 (Rdga)

Difference 1.207023 (Rdga-RdgO

To change tlie latter difference to volts, use the,

equation

emf =K(Rdg.,- Rdgi) = 1.207023i? V.

Setting of SC dial Difference in readings at SC potential points

1.019000 = =0.9941347.

1.025012

Substituting the value of K in the equation for

emf,

emf = 1.207023 X0.9941347 = 1.199943 V,

which is the measured value for a reading of 1.2 V on the potentiometer. The correction to the

potentiometer reading is

1.199943-1.200000= -0.000057 v = — 57 MV.

In the test of the potentiometer from which the

data for example 2 were taken, there were 39 URS

readings which were multiplied by 0.9941347.

Much tedious computation could have been

avoided by making the URS direct reading.

42
17.4. General Outline of Test Procedures

The usual tests of a potentioineter are:

a. Dial tests. b. Factor tests.

c. Standard cell dial.

! The connections of a Univ^ersal Ratio Set to

j the BA terminals of a potentiometer are shown in

j figure 53 and also in the schematic diagram,

I figure 51. Short tabs of bare copper wire at the

SC and the EMF binding posts serve for convenient connection of an alligator clip on the end

of the potential lead from the URS. The connections to the BA terminals of the potentiometer

may be interchanged. Generally, two tests are made, by dift'erent observers, using different con- nections to the BA terminals. The URS readings

in the two tests will dift'er, but the computed

results should agree within the limits of observational error. The results of the two tests for each

dial step and each factor are averaged to obtain

the reported values.

17.4.a. Dial Tests The URS may, or mav not be direct reading.

In either case, the potentiometer rheostat should

not be changed during the dial tests. The URS

readings at SC+ and SC— should be checked

occasionally. Any appreciable change in the

dift'erence of the readings indicates a change in the resistance of the potentiometer circuit which

may produce excessive errors in the readings.

It may be necessary to repeat a dial test from the

beginning.

A dial test should be made as rapidh* as is consistent with careful work. If some time

elapses between the tests on two dials, it may be

necessary to readjust the potentiometer rheostat

to make the URS direct reading for the test of the second dial; or, if the URS was not direct

reading, it may be necessary to calculate a dift'erent factor for correction of the URS readings taken on the second dial. The SC dial is set on 1.0190 for dial and factor

tests, and the factor switch is set on 1.0 for the

dial tests. Readmgs at the SC potential points can be

taken only if the EMF-SC switch is on SC. The

difference in the readings should not change

during the tests, though a variation of two or

three units in the last place of a six dial ratio set

is tolerable. The difference in the readings

should be checked not less often than at the

beginnmg and the end of each dial test. The EMF-SC switch is set on EMF to take

readings at each step on each dial, except that

the slide-wire dial is tested at selected settings, as each fifty or each hundred dial units. While

one dial is being tested the other emf dials remain

on zero.

For each (Hal. rcachiigs are taken on tlie ratio

set at E+ 0 and at E— 0, that is, witli tlie dial on zero, readings are taken with tlie potential

lead to E-1- (EMF+) and E- (EMF-), respectively. These readings sliould not chan.ge significantly during the tests. One reacHng, say the

reading at E— 0, is used as tlie zero reatling for all emf dials. The potential point for each succeeding step on

the dial may be EMF-l or EMF-. The correct binding post may be found by trial. If the wrong

post is selected, the readings on the ratio set will not change as the dial is advanced.

The record of the test should show the make and

serial number of the instrument, the flate aiul the room temperature at the time of test. The record for each dial should show the potential point, the dial setting, and the URS readuig

for each step on the dial. The readings at tlie SC

potential points should be recorded as well as the

reacUngs at the EMF potential points. For

illustration, a partial record for the test of one

potentioineter follows:

Main dial URS

Dial setting Reading

SC- 1. 0190 1 119 627

SC+ 1. 0190 100 627 E+ 0 219 782 E- 0 219 790

E— 0. 1 319 769 E- 0. 2 419 752 E- 0. 3 519 736

etc. The readings on a ratio set usually need correction. The URS readings shown above are corrected readings. It is convenient, however,

to record the readings while testing and apply the

corrections later. Readings on the ratio set taken during a dial

test may increase or decrease as the dial is advanced, depending on which dial is tested and on

the connections of the URS to the BA terminals

of the potentiometer. In the above illustration

the readings increase. The dift'erence in the

readings at" SC— and SC+ is 1 019 000 nv or 1.019000 V. which shows that the URS was direct

reading. Therefore, the correct value at any dial

setting is the reading taken at the dial setting

minus the zero reading. The zero reading is 219 790. The correct value for a dial setting 0.1 V is 319 769 —219 790 =99 979 fiv

or 0.099979 v and the correction is

0.099979-0. 100000 = -0.000021 v

or —21 fiv. A shortcut in computing corrections is to use only the last two or three digits of each reading.

In the above example, subtraction of 90 (last two

digits of zero reading) from the last two digits of

43
each succeeding reading gives the correction in microvolts:

Dial setting

0. 1

. 2

. 3

etc.

Correction in microvolts

69-90=-21

52-90--38

36-90=-54

If the shortcut is used in computing corrections,

it is important to note whether successive readings on the ratio set increase or decrease. In another

test on the same dial the following readings were

obtained

:

Dial setting

EEEE0

0. 1

. 2

. 3

URS reading

1 891 342

1 791 362

1 691 378

1 591 394

etc.

In this example successive readings decrease.

Therefore, each reading nmst be subtracted from

the zero reading. The same order must be observed if the last two or three digits are used to compute corrections, as in the following.

Zero reading= 1891342

Dial

setting

0. 1

. 2

. 3

Correction in

microvolts

42-62 = -20

42-78= -36

42-94=— 52

If the corrections are quite large, it may be

necessary to use the last three digits. The shortcut saves considerable computation and reduces the

chance of making mistakes.

The differences in the results of the two tests are

well within the limits of probable error. Tlie last digit is uncertain. The average of the results for each dial step is rounded off and reported to the nearest 0.00001 v. If the Universal Ratio Set is not direct reading,

the certified corrections to the ratio set should be

applied before the readings are multiplied by the

factor, K. The determination of tliis factor and its use has been explained and illustrated by an ex- ample in section 17.3. The products of the cor- rected readings times the factor are equivalent to the corrected readings which would have been obtained if the URS had been direct reading and are

to be used in the same way to find the dial corrections.

17.4.b. Factor Tests

Since the dial tests are made with the .facto^^ switch on 1.0, there is zero correction for factor 1.0 The other factor circuits are designed to change

the indicated values of emf on the potentiometer

dials by a factor of 0.1, or 0.01, when the factor

switch is on the respective settings. As in all resistance circuits, design values are subject to cor-^ rection.

The design of the factor circuits in different makes and models of potentiometers differ widely.

The test method to be outlined will apply to Crompton-type potentiometers and others of similar design.

The connection of the URS to the potentiometer

is the same as for the dial tests. The potentiometer

rheostat is set on mininmm, the emf dials on maximum.

Let Si and S2 represent readings on the URS

taken at the SC potential points, and let ei and 62 be the readings of the URS at the EMF potential

points for a setting on factor 1.0. Let S\' , So', e/, and 62' be the corresponding

readings for factor 0.1, and Sj", S2", e/', and 62"

the corresponding readings for factor 0.01. Then

factor 0.1= S2 -Si_ 62' /A 'S2'-Si'^ e2-ei

factor 0.01 = S2 02 —Oi //A

-ei e2—ei

17.4.C. Standard Cell Dial The object of this test is to detect any significant

departure from a uniform change in resistance as the standard-cell dial is advanced in equal steps.

The EMF-SC switch is set on SC, the factor

switch on 1.0, and the emf dials on zero. The

correct potential point, SC+ or SC— may be

found by trial. Beginning with the lowest set- ting of the SC dial, take readings on the URS for each four or five divisions on the dial. The readings of the URS should increase, or decrease,

about 1 00 (on a 6-dial ratio set) for each graduated

division on the dial. The differences may vary

by ±2 or ±3 per dial division.

17.5. Some Modifications of Prccedure

The preceding general outline of test procedures

applies, with minor modifications, to the dial tests of most potentiometers in common use. Attention will be given now to some of the problems

which the worker may encounter.

It should not be assumed that the same potential

point is correct for a given dial test of different

makes of the same type. The determination of the potential poirit by trial has been explained.

It is well to enter in the laboratory notebook, for future reference, the correct potential points for each model tested. In section 18, detailed instructions for testing a

selected model of the Crompton type include the

steps for making the LTRS direct reading. Exactly

tlie same steps, with a different model potentiometer, may cause successive readings of the URS

to diverge from instead of converge to 1.019000.

It will be necessary to interchange "SC — " and

"SC+" in the instructions, then follow the steps

as outlined.

44
Figure 52. Testing a potentiometer with the range of the URS extended. When testing some potentiometers, it is impossible to take readings on the URS for ail settings

of the potentiometer dials. This is due to extra

resistance in tlie potentiometer circuit, which

makes it necessary to extend the range of the

URS by adding a resistance to the right hand end

as shown schematically in figure 52. The added

resistance may be any laboratory-type dial box

or plug box, which is stable in use, but it need not

be calibrated. The required value may be several

hundred ohms, which can be found by trial. The

value should he entered in laboratory notes for reference when another potentiometer of the same

kind has to be tested. Since the added resistance

is a part of the modified URS circuit, the righthand galvanometer connection should be made

between the resistance box and the potentiometer.

The added resistance does not change the use of the URS readings to compute emf's.

It is impossible to make the URS direct reading

to test some potentiometers. It is usually possi- ble to adjust the potentiometer rheostat so that

the difference in the URS readings at the SC

potential points is some simple fraction (say onehalf) of the standard value. The following readings were obtained in one test

SC-1. 019000 2.111068

SC + 1. 019000 1.601568

Difference 0. 509500

vSince the difference is exactly one-half of 1.019000, differences in readings taken at settings

of the emf dials will be one-half the correct value.

For example, readings taken at settings of the

main dial were:E-0 0.850104

E-1.5 .100081

Difference .750023

2X0.750023 = 1.500046 v. That was the emf

value at a setting of 1.5 and the correction to the

dial setting was -|-46 fxv. Some types of potentiometers require special

testing techniques. This is particularly true of factor tests. It is not practical, within the limits

of this paper, to outline test procedures for all tA^pes.

The outline of general principles which has been

given, together witli the (h-lailcd [Jioccdures given

in the next section for the test of a selected ino(h'i,

should serve as a guides to the test of most potentiometers in coinmon use.

18. Details of Procedure As Applied to a

Specific Model

18.1. Description of Potentiometer—Crompton Type

The main dial has a range in 0.1-v steps from 0

to 1.5 V. The slide-wire consists of a coil of

eleven turns of resistance wire on a cylinder. A

drum fitted over the cylinder can be rotated to move a contactor over the length of tlie wire. The

edge of the drum is divided into 100 scale units,

each of which is subdivided into two parts. A

glass plate at the front of the di'um has a scale which is read against the edge of the drum showing

the number of rotations from 0 to 11. An index

line on the glass plate is used to read the graduations on the edge of the drum. Each scale unit

corresponds to 0.0001 v. The range of tlie slide- wire is from 0 to 0.1100 v. By estimating fifths of the smallest division on the drum, readings are obtained to one tenth of a scale unit or 0.00001 v. The middle dial on the left of the potentiometer

is the factor switch which may be set at any one

of three points : 1, 0.1, or 0.01. Depending on the

factor setting, the EMF measured is nominally

1, 0.1, or 0.01 times the reading on the scales. The Std Cell dial is set to the calibrated EMF

of the standard cell used when potentiometer

measurements are made. For tests on the potentiometer, the dial is set on the nominal value,

1.0190.

The EMF-Std Cell switch connects the EMF

leads or the standard cell leads into the circuit,

depending on the setting of the switch.

The rheostat dials on the right end of the in- strument adjust the current in the potentiometer

circuit.

18.2. Test Equipment

Universal Ratio Set (URS), 6-dial or 5-dial

Battery (3-6 v)

Rheostat to regulate battery voltage

Key (preferably with reversing switch)

Sensitive galvanometer

18.3. Tests Required

Main dial—test each step to determine cor- rections.

Slide-wire—test each 50 dial units to determine corrections.

Standard cell dial—test each four divisions

for linearity.

Factor—test to find corrections for the 0.1 factor and the 0.01 factor. Tests should be made at a temperature as near

as possible to the temperature at wliich the potentiometer is to be used.

45
Universal Ratio Set connected for calibration of a potentiometer.

The detector is mounted between the two instruments and the test current is switched on and re- versed by the operator's feet.

18.4. Points to Remember

1. Older models of Universal Ratio Sets are

5-dial. With a 5-dial set, it is desirable to interpolate one place.

2. The dial readings of most commercial Universal Ratio .Sets require corrections. These cor- rections must be used for accurate results.

3. The galvanometer binding posts of the potentiometer must be shorted and the High GA

Sens button must be depressed during tests.

4. Potential points and the EMF-Std Cell

switch must agree; that is, the switch must be on EMF if an EMF potential point is in use, on Std

Cell if a Std Cell potential point is in use.

5. The potential point for measurements on the

main dial is EMF— ; for measurements on the

slide-wire, EMF+ ; for measurements on the Std

Cell dial, Std Cell-f.

6. The Std Cell dial should remain on 1.0190

except when testing that dial. Most standard

cells have a nommal value of about 1.0190 v.

7. The battery rheostats of the potentiometer

should remain michanged after adjustment for direct reading on the URS, except to make factor

tests.

8. All electrical connections must be clean and

tight.

9. Turn the dials back and forth several times

to wipe the contacts clean to reduce contact

resistance. This applies to the URS as well as

to the potentiometer.

18.5. Testing Procedures

18.5.a. Connections and Dial Settings

(a) Short the GA binding posts with a short

piece of bare copper wire.

(b) Connect the BA binding posts of the potentiometer to the right and left binding posts of

the URS as shown in figure 53.

(c) Connect the galvanometer leads to the

extra end posts of the URS.

(d) Connect short pieces of bare copper wire to the Std Cell and the EMF binding posts to be

used as potential points.

(e) Connect one batterv lead to the middle

post of the URS.

(f) The other batter}' lead should end in a test

clip to permit ready transfer from one potential

point to another.

(g) Set the Std .Cell dial on 1.0190.

(h) Depress the High GA Sens button and hold

it down with a weight.

(i) Set the factor switch (middle dial on the

left) on "1."

(j) Set both the main dial and the slide wire on zero.

18.5. b. To Make the URS "Direct Reading"

Set the EMF-Std Cell dial on Std Cell. On the right end of the potentiometer (fig. 53) are three knobs which control a variable resist- ance or rheostat made up of three sections, a coarse

46
P 0 C P r SHORT

Lflf L-CT Lct Lffl Mai—HI

SLIDE WIRE DRUM ^'GLASS SCALE

TO POTENTIAL POINTS

-o o

Figure 53. U RS connected to a Crompton tijpe potentiometer for testing. Binding posts not used in tests are not shown in diagram.

adjustment, a medium adjustment, and a fine adjustment, as indicated on the panel. Tlie arrows on the panel show in which direction to turn each knob to increase or decrease the resist- ance in the battery circuit. The purpose of the

rheostat is to regulate the battery current to make the difl^erence of potential between the SC

binding posts equal to the reading of the vStd Cell

dial.The URS will be "direct reading" when, the

rheostat is adjusted to make the difference between

the URS readings taken at the two Std Cell

potential points equal to 1 019 000.

^ith the right side of the URS connected to the BA— binding post of the potentiometer an.d the circuit adjusted for direct reading, the reading on the URS will usuallv be near 1 119 600 with

the battery chp at Std Cell— and near 100 600 with

the battery at Std CeU+ (See table I, page 48).

These settings will be time-saving guides for the

initial adjustments.

With the battery clip connected to Std Cell—

turn the URS dials to 1 119 600 and adjust the

rheostat on the potentiometer to get a zero deflection on the galvanometer when the battery

key is closed. Start with the coarse adjustment.

When the current has been regulated as closely as possible with the coarse adjustment, proceed with

the medium adjustment, and then tlae fine adjustment. If it is impossible to get a zero deflection

of tlie gulvajioiiietcr, adjust tlic rlicostnl for miii- iimnn (k'fleclioji.

Next, move the battery clip to Std Coll-|-.

Adjust the dials of the URS until tlic circuit is baluiiced (zero or mininnim galvanometer defh-ction). If tlie URS is 5-dial, interpolate foj' the

last digit of the reading. Add 1 019 000 to tl)0 dial reading obtained and set the cUals of the URS

on this value. Transfer tlie battery clip to vStd Cell— and adjust the rheost at for zero (h^flccf ion

of the galvanometer.

Move the battery clip to Std Cell-1- and icpcat

the adjustment of the URS (Hals as above.

Continue the proceeding, adjusting tlie rheostat

wlien the battery chp is at the Std Cell— potential point and adjusting the URS dials when the

battery clip is at the Std Cell-|- potential point

until the dift'erence between the URS readings

taken at the two potential points is 1 019 000.

The adjustment usually can be made very ac- curately. If necessary, a tolerance of two or three units in the last place is permissible.

If there are any corrections to the dial readings

of the URS, use the corrected readings for the final adjustment.

A second test should be made on a potentiometer to check the accuracy of measurement.

For the second test, the connections between the

potentiometer and the URS should be reversed,

that is, if in the first test the right side of the URS

was connected to the BA— post of tlie potentiometer, in the second test it should be connected to the BA+ post and the left side of the URS to the

BA— post.

The procedure for direct reading will be the same as the preceding, except that 1 019 000 will be subtracted from the Std Cell+ reading to obtain the next setting on the URS for Std Cell—.

The dial readings on the URS wiU be near 991 500

for the Std Cell— potential point and jiear 2 010 500 for the Std CeU+ potential point (see

table II). In each case, adjust the potentiometer rheostat on Std CeU-, the URS on Std Cen + . It is convenient, though not necessary, that the

URS be direct reading. The alternate procedure

will be explained later.

18.6. Measurements on the Main Dial

Set: Main dial and slide-wire on zero. Std CeU dial on 1.0190. Factor switch on 1. EMF-Std Cell dial on Std Cell. Take readings on the URS with pot en I ia I points at Std Cell+ and at Std Cell— and record.

If the URS is 5-dial, interpolate one place. If the URS is direct reading, the dift'erence between

these readings wiU be 1 019 000.

Change the EMF-Std CeU dial to EMF.

Take readings on the URS with potential

points at EMF+ and at EMF-. Then with

the potential point stiH at EMF— , take and re- cord readings for each step of the main dial.

47
Set the main dial back to zero and repeat readings for Std Cell + , Std Cell-, EMF+ 0, and

EMF— 0. These should not differ from the

initial readings by more than five steps on the

sixth dial of the URS.

18.7. Measurements on the Slide Wire

Initial dial settings as in section 18.6. Repeat

the readings for Std Cell + , Std Cell-, EMF+ , and EMF-. Remember to set the EMF-Std

Cell dial on Std Cell when reading at a Std Cell

potential point, on EMF when reading at an EMF

potential point.

With the potential point at EMF+ , take readings for each 50 dial units on the slide wire. When

the slide wire is returned to zero, readings at Std Cell+, Std Cell-, EMF+ , and EMFshould not have changed by more than five divisions on the sixth dial of the URS.

Correct the URS reading if corrections are re- quired.

(A good practice is to record all readings in

black, make all corrections and enter all results

of computation in red.)

For a second test, on both the main dial and

the slide wire, reverse the connections between

the URS and the potentiometer and proceed as in the first test.

18.8. Measurements on the Standard Cell Dial This is a test for linearity, that is, a test to find whether or not the steps on the dial correspond

to uniform changes of resistance. With the

potential point at Std Cell + , take readings for each four divisions on the dial. These readings

(corrected) should decrease (or increase) uniformly. Deviations should be less than, fifteen units on the URS.

18.9. Finding Corrections for the Main Dial

Following is the recorded data for a few steps on the potentiometer (URS readings are recorded

without pointing ofl" decimal places).

Table I. First test, with URS "direct reading" and right side of URS to BA-.

I Ila lib III

'

SC-10 190 SC+10 1901 119 629

100 631

1 119 627

100 627

1 019 000

'

EMF+ 0 EMF- 0 EMF- 0. 1

. 2

. 3

A

. 4

. 5

219 782

219 790

319 772 419 756

519 740

719 709

219 782

219 790

319 769

419 752 519 736 CIO 1 c biy /lb 719 701

0 -21

-38

-54 — '7 A /4 -89

1. 5 1 719 522 1 719 529 -261

Column I—^Potential points and dial settings.

Column Ila—URS readings; column lib

corrected URS readings.

Column III—The difference, 1 019 000, between

the Std Cell readings shows that the URS was

"direct reading." The other numbers in this column are the corrections to the dial readings

expressed in microvolts. These are found by

the following procedure: The reference value is the reading for EMF-0. Since the URS readings

increase each step, the reference value is subtracted from the reading for each succeeding

step, then the indicated value of the dial setting

is subtracted from the result to obtain the correction.

Dial step O.lv 0.319769-0.219790=0.099979 or (0.1 -0.000021)v.

0.2v 0.419752-0.219790 = 0.199962 or (0.2 -0.000038) v. 0.3v 0.519736-0.219790=0.299946 or (0.3- 0.000054)

v

And so on. The computation is simplified by using only

the last two or three digits of the readings to find the corrections;

O.lv 769-790=

0.2v 752-790=

0.3v 736-790=

-21 /XV -38 MV

-54 fiv. Table II. Second test, with connections between URS and potentiometer reversed.

1 Ila lib III IV V

SC+ 10 190 SC- 10 190

2 010 488

991 473

2 010 494

991 494

1 019 000

EMF+ 0 EMF- 0 EMF- 0. 1

_ 2

'. 3

. 4

. 5

1 891 317

1 891 310

1 791 334

1 691 355

1 591 368

1 491 398

1 391 415

1 891 349

1 891 342

1 791 362

1 691 378

1 591 394

1 491 412

1 391 431

0 -20

-36

-52

-70

-89

0 -21

-38

-54

-74

-89

0. 00000

00002

00004 -. 00005 -. 00007 -. 00009

1. 5 391 571 391 589 -247 -261 -. 00025

48
Columns T, Ha, lib, and 111 correspond to llio first four columns in the tabulated data for the

first test. Since the readings decrease, subtract the URS

reading for each step from the reading for zero

to find the corrections in column HI. For ex- ample, to find the correction for 0.3 v,

1.891342-1.591394 =0.299948 or (0.3-0.000052) volt.

If only the last three digits of the readings are

used,

342 -394 = -52 nv. Cohunn IV contains the corresponding corrections found in the first test. Step by step, the

corrections found in the two tests should not

differ by more than 20 or 30 /xv. Column V shows the reported corrections as

fractions of a volt. These were derived from the

average of the results of the two tests for each

step. The final digit was uncertain, so the value was rounded off to that shown in the table. The

initial readings in the preceding tables and in those which follow may be useful, time-saving,

guides for beginning a corresponding test on a Crompton-type potentiometer. As a rule these

readings for difl'erent instruments by the same

manufacturer do not diflfer greatly.

18.10. Finding Corrections for the Slide Wire

The tables for the slide wire which fijllou nrc

similar to the corresponding tables for the iimm

dial, hence, should iummI no furllici- cxplinialion.

Table III. /''trs^ lefil. with UliS "direcl reading" right Hide to BA-.

I Ila lib III

bC— 10 190

SC-t- 10 190

1 119 629

100 631

1 119 627

100 627

1 010 000

EMF- 0 EMF+ 0 EMF+ 50 100 150

200 250

219 790 219 782 214 777

209 772 204 765

199 737

194 738

219 790

219 782 214 776

209 769

204 761 199 761 194 761

0 + 8 4-14 + 21 + 29 + 29 + 29

1 100 109 634 109 632 + 158

The readings on the URS for the slide wire are taken at the potential point EMF+ , but the

reference point is EMF-0, the same as for the

main dial. The correction for EMF+0 was entered under

"slide wire," only. It should not be entered

twice.

Table IV. Second test, with connections between URS and potentiometer reversed.

I Ila lib III IV V

SC + 10 190 2 010 485 2 010 494

1 019 000

sc- 10 190 991 473 991 494

EMF 0 1 891 310 1 891 342 0 0 0. 0 EMF + 0 1 891 317 1 891 349 + 7 + 8 +. 1 EMF + 50 1 896 323 1 896 356 + 14 + 14 +. 1 100 1 901 348 1 901 353 + 11 + 21 + . 2 150 1 906 358 1 906 364 + 22 + 29 + . 3 200 1 911 358 1 911 366 + 24 + 29 +. 3 250 1 916 368 1 916 377 + 35 + 29 + . 3

1 100 2 001 489 2 001 495 + 153 + 158 + 1. 6

Column IV shows the corrections for each step

as found in the first test. These were averaged

with the corrections in Colunm HI and the value

rounded off. The results were then entered in Column V as tenths of a dial unit on the slide wire.

For example, the correctioTi.s found in the two tests for a setting of 250 were +35 and +29, respectively. The average was +32 /xv, or +0.000032 v. The last digit was dropped as uncertain, giving

+0.00003 V. A dial unit on the slide wire is 0.0001 V. Hence, the correction is +0.3 of a slide wire unit. This is the form in which it would

be used in the formula which will be presented

later.

18.11. Tabulation of Data for Standard-Cell Dial

The potential point is Std Cell + . The meas- urements in the following table were nnulo for every fourth dial division with the left side of the

URS to BA— . The graduations on the dial were

accepted as linear because the deviations from

uniformity in the last cohunn are within the range

of experimental error. 49

m
Table V. Data from test of standard cell dial. Table VI. Example: {Right side of URS to BA-).

Std cell dial URS URS (cor- rected)IDifTcrpncBS

10 176 2 009 084 2 009 086

401

10 180 2 009 485 2 009 487

396

10 184 2 009 881 2 009 883

402

10 188 2 010 282 2 010 285

399

10 192 2 010 681 2 010 684

400

10 196 2 Oil 081 2 Oil 084

405

10 200 2 Oil 486 2 Oil 489

391

10 204 2 Oil 877 2 Oil 880

18.12. Factors The potentiometer has three ranges: the uonnal

range (0 to 1.6100 v) with the factor switch set on

"1;" a range of one tenth the dial readings with

the factor switch set on "0.1;" and a range of one hundredth the dial readings with the factor switcli on "0.01." Imperfections in circuit compensation may require that corrections be applied to the

factor readings. However, there will be no cor- rection for the "1" factor because the dial corrections were determined at a factor setting of "1."

To find the factor corrections, set Main dial and slide wire at maximum

readings

;

Battery rheostats of the potentiometer at minimum. However, back off the medium and

fine rheostat dials somewhat from the end points

because good contact may not be obtained at the

end settings.

With potential points alternately at Std Cell +

and Std Cell—, take readings at each factor switch

setting and find the difference between the Std

Cell readings for each. (See tabulated example,

table VI.)

With potential points alternately at EMF+

and EMF— , take readings for each factor switch

setting and find the difference between the EMF

readings for each.

Divide the difference between the Std Cell

readings for factor 1 by the difference between the

EMF readings for factor 1. Call this quotient Ql.

Divide the differeace between the EMF readings

for factor 0.1 by the difference between the Std

Cell readings for factor 0.1. Call this quotient

Q.i.

Divide the difference between the EMF readings

for factor 0.01 by the difference between the Std

Cell readings for factor 0.01. Call this ciubtient

Q.Ol. Then

The 0.1 factor =(?1X(?.1

The 0.01 factor=(?lX(?.01

Factor switch 1 0.1 0.01

Std CellStd Cell +1 275 553

114 627

1 275 487

114 637

1 275 478

114 632

Difference 1 160 926 1 160 850 1 160 846 EMF— EMF+

1 959 006

124 908

308 309

124 899

143 244

124 905

Difference 1 834 098 183 410 18 339

The above URS readings are corrected values.

The 0.1 factor=^?lX<?.l

""""-"X . !!-^f'.° =0.1000067.

1 834 098 1 160 850

This may be wi-itten "0.1(1 +67 ppm)".

Hence, the Correction for the 0.1 factor is -\-67

pnm.

The 0.01 factor=f?lX(?.01

1 160 926

X:

18 339

1 834 098' 1 160 846 =0.00999961, or 0.01 (1-39 ppm)

The correction for the 0.01 factor is —39 ppm.

A secoad test with connections to the URS

reversed gave:

correction for 0.1 factor + 50 ppm.

correction for 0.01 factor —89 ppm.

The average of the results for each factor was

found and rounded off to give the following results.

Table VII.

Factor Aver. cor. Reported

ppm correction

1 0. 00000

0. 1 + 58 + . 00006

0. 01 -64 0001

Experimental errors in the measurement of the

0.01 factor may amount to 100 ppm. Hence, only

four places are retained in the reported connection.

The difference in the results of two tests of the

0.1 factor should be less than 50 ppm; for the 0.01

factor, the difference should be less than 200 ppm.

18.13. Application of Corrections

The meaning of the corrections reported in the

preceding pages may be better understood by an

application to a hypothetical measurement. As- sume that when the potentiometer was used to

50
measure an unknown EMF, the following readings were taken:

factor switch 0. 1 main dial . 3 sUde wire 229. 0

The formula is:

E is the potential difference between the "EMF"

terminals of the potentiometer expressed in the same units as the standard cell used with the in- strument. F, B, and Rs are the factor, main dial,

and slide wire readings respectively; and d, c, and

Cs are the corresponding corrections to these

readings.

When the above readings and the correspondingcorrections from the preceding tables are substituted in the formula, the result is: ^=0.1(l + .00006)[. 3-.00005+.0001(229.0 + . 3)]. ^=0.032290 V.

18.14. Procedure When the URS Is Not "Direct Reading"

This is illustrated by a selection of da In from

tlie record of the nniiu dial of anolhci- potciitioineter. In the table which follows, column I la shows

the corrected readings of the UK8. The difference

of the Std Cell readings, 1 015 884, shows that tlic URS was not "direct reading." Hence, the lunnbers in column Ila must be multiplied by a coi'i'ec- tion factor to obtahi the "direct reading" values

recorded in colunm Tib. To find this factor,

divide 1 019 000 by the difference of the Std Cell

readings. In this test, the correction factoi- was

1 019 000

1 015 884'

= 1.003067.

This is the coefficient K used in section 17. Col- umns III, IV, and V correspond to columns of the same number in preceding tables.

T;\BLE VIII. Data for main dial, URS nol "direcl reading".

I Ila lib III IV V

SC-10 190 1 116 194 1 015 884

Mult, by

SC + 10 190 100 310 1. 003067

EMF + 0 218 950 219 622 EMF-0 218 952 219 624 0 0 0. 00000

EMF-0. 1 318 646 319 623 -1 -1 . 00000

. 2 418 338 419 621 -3 _ 2 . 00000

. 3 518 0;32 519 621 -3 -2 . 00000

. 4 617 726 619 621 -3 -2 . 00000

. 5 717 420 719 620 -4 -3 . 00000

l."5 1 714 357 1 719 615 -9 -3 -. 00001

The same procedure applies to the slide wire readings.

18.15. A Working Test This is a spot check at one setting of the dials of the potentiometer, corrected according to the

preceding tests. The connections of accessory

equipment to the binding posts of the potentiometer are shown in figure 54. Other details of the

panel of the potentiometer are shoAvn in figure 53. The calibrated value of the standard cell is not

important, nor is the setting of the standard cell dial.

1. Connect a 2-v storage cell to the BA

binding posts of the potentiometer according to indicated polarity. Allow the current from the

storage cell to flow long enough to become steady.

This may require 3 or 4 hrs.

2. Connect a sensitive galvanometer to the

galvanometer bhiding posts.

3. Connect one pair of end posts of a doublepole double-throw (DPDT) switch to the SC

binding posts of the potentiometer. Connect the

other pair of end posts of the switch to the EISIF

Is.

+ STD CELL- + EMF -

rO

STORAGE

BATTERY

POT

Figure 54. Working test.

51
binding posts. Make sure that both positive

posts are connected to the same side of the switch.

In figure 54 the left side of the DPDT switch is the positive side.

4. Take leads from the middle posts of the

switch, to which the knife blades are attached, to the standard cell. Take care that the positive

side of the switch is connected to the positive post of the cell. To avoid accidental short-circuiting of the

cell, make connections to the standard cell last. When

the test is finished, disconnect the standard cell first.

5. Set the factor switch of the potentiometer on 1. 6. Set the Std Cell dial on any convenient

value, as 1.01900.

7. Set the EMF-Std Cell dial on Std Cell.

8. Set the main dial and slide wire to give the same reading as the Std Cell dial. Final adjustment to balance the circuit probably will require

only a small change in the setting of the slide wire.

9. Throw the DPDT switch to connect the

standard cell to the Std Cell binding posts.

10. Tap Low GA Sens key and observe the

deflection of the galvanometer. Only a very

small current should be drawn momentarily from

the standard cell. The button should not be

held down.

11. Adjust the current through the potentiometer with the potentiometer rheostat (itnobs on the

right hand end), until there is no deflection (or

minimum deflection) of the galvanometer when

the galvanometer key is depressed. Start with

the coarse adjustment, then the medium, and

then the fine adjustment.

12. Continue adjustment of the rheostat using

the low, med, and high GA sens keys in succession,

until the galvanometer shows that the emf is balanced by the emf across the standard cell segment of the potentiometer circuit. It may be

impossible to get perfect current regulation. Set

the fine adjustment to get the smallest possible

deflection of the galvanometer. Do not change

the current adjustment during the next step of

the test. 13. Immediately, throw the DPDT switch to connect the standard cell to the EMF binding

posts. Balance the circuit with the emf dials of the potentiometer. It will usually be necessary

to change the setting of the slide wire only, using

the galvanometer sensitivity keys in succession as

in paragraph 12 above.

14. When the circuit is balanced, record the

readings of the main dial and the slide wire.

Estimate the reading on the slide wire to one

tenth of a scale unit (one fifth of a division).

Reset the switches (DPDT and EMF-Std Cefl) on Std Cell and check for any change in the

potentiometer current. If it has changed significantly, readjust the rheostat, return the switches

to EMF, and repeat the adjustment of the slide wu-e. If there is a readable change in the setting

of the slide wire, it is probable that more time is needed for the current in the potentiometer to become steady. Make another trial and repeat

trials until slide wire readings can be repeated.

15. After the final reading, apply the relevant

corrections found in the preceding dial tests to the

readings of the main dial and slide wire. Compute

the emf. Since the factor is 1 with zero correction, the equation for E becomes

- E=R+c +Q.OQO\ {B,+c,)

Compare the result with the reading of the SC

dial. Unless the potentiometer is defective, or there is some fault in the results of the preceding

tests, the two values will agree quite closely.

Two trials of the working test which were made

on the same potentiometer using different standard

cells and different standard cell dial settings gave

the following results:

First Trial

R, reading of main dial 1. 0

c, correction to main dial reading —0. 00006

Rs, reading of slide wire 191. 2

Cs, correction to slide wire rdg. -j-O. 1 E, (from equation) 1. 01907

Setting of SC dial 1.01906

Difference 0. 00001

Second Trial

R, reading of main dial 1. 0

c, correction to main dial reading —0. 00006

Rs, reading of slide wire 192. 3

Cs, correction to slide wire rdg. -f-0. 1 E, (from equation) 1. 01918

Setting of Std Cell dial 1. 01918

Difference 0. 00000

Note that the results of the working test are independent of the 'Calibrated value of the standard

cell and the setting of the standard cell dial.

52
19. Sample Certificate for Crompton Potentiometer

UNITED STATES DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

WASHINGTON- 25, D.C. NATIONAL BUREAU OF STANDARDS

CERTIFICATE

for POTENTIOMETER

(Maker) Serial No

Submitted by

Tests of the adjustments of the main dial, the standard-cell dial, the slide-wire, and the factors of the abovedescribed apparatus were made in (date), at a room temperature

of about ° C. With the current adjusted so as to produce a potential difference between the standard-cell terminals equal to the reading of the standard-cell dial, the potential difference between the "E.M.F." terminals can be expressed by the following equation

E=F{l + d)[R + c+0m01{Rs + c,)]

Here E is the potential difference between the "E.M.F."

terminals expressed in the same units as the electromotive

force of the standard cell used with the instrument; F, R, and Rs are the factor, main dial, and slide-wire readings

respectively; and d, c, and are the corrections to these

readings. The corrections are to be taken from the fol- lowing tables.

Factor Switch Reading F and Correction d

F d

1 0. 00000

0. 1 -I- . 00006

0. 01 - . 0001

Main Dial Reading R and Correction c R c _K_ c

0. 0 0. 00000 0. 8 — 0. 00014

. 1 - . 00002 . 9 - . 00016

. 2 - . 00004 1. 0 - .00018

. 3 - . 00005 1. 1 - . 00019

. 4 - . 00007 1. 2 - . 00021

. 5 - . 00009 \ . .i - . 00022

. 6 - . 00011 1. 4 - . 00024

. 7 - . 00012 I. 5 - . 00025

Slide Wire Reading R, and Correction c.

Rs c. R, c. 0 + 0. 1 550 4-0. 9 50 + . 1 600 -1- .9

100 + . 2 650 -HI. 0 150 + .3 700 -HI. 1 200 + .3 750 + 1. 2 250 + .3 800 + 1. 2 300 + .4 850 + 1. 4 350 + . 5 900 + 1. 3 400 + . 5 950 + 1. 5 450 + . 7 1000 -HI. 5 500 + . 7 1050 -HI. 6 1100 + 1. 6

Values obtained by use of the above equation and

corrections are not in error by more than 0.01 percent if R

is equal to or greater than 0.2, nor by more than 0.4 of the

smallest subdivision of the slide-wire for smaller values of R. To obtain this accuracy, however, in case Bis less than

0.02 volt, usually it will be necessary to correct for ther- moelectromotive forces within the potentiometer and within the circuit of the connected galvanometer.

When the reading of the factor switch is changed, the current through the potentiometer should be readjusted,

if necessary, to produce a potential difference between the

standard-cell terminals equal to the reading of the standard-cell dial. Other tests revealed no defects in the potentiometer. For the Director

U.S. GOVERNMENT PRINTING 0FF1CE:I962

53

U.S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

THE NATIONAL BUREAU OF STANDARDS

The scope of activities of the National Bureau of Standards at its major laboratories in Washington, D.C., and

Boulder, Colorado, is suggested in the following listing of the divisions and sections engaged in technical work! In

general, each section carries out specialized research, development, and engineering in the field indicated by its

title. A brief description of the activities, and of the resultant publications, appears on the inside of the front cover. WASHINGTON, D.C.

Electricity. Resistance and Reactance. Electrochemistry. Electrical Instruments. Magnetic Measurements.

Dielectrics. High Voltage.

Metrology. Photometry and Colorimetry. Refractometry. Photographic Research. Length. Engineering

Metrology. Mass and Scale. Volumetry and Densimetry.

Heat. Temperature Physics. Heat Measurements. Cryogenic Physics. Equation of State. Statistical Physics.

Radiation Physics. X-Ray. Radioactivity. Radiation Theory. High Energy Radiation. Radiological Equipment. Nucleonic Instrumentation. Neutron Physics.

Analytical and Inorganic Chemistry. Pure Substances. Spectrochemistry. Solution Chemistry. Standards

Reference Materials. Applied Analytical Research. Mechanics. Sound. Pressure and Vacuum. Fluid Mechanics. Engineering Mechanics. Rheology. Combustion

Controls. Organic and Fibrous Materials. Rubber. Textiles. Paper. Leather. Testing and Specifications. Polymer

Structure. Plastics. Dental Research. Metallurgy. Thermal Metallurgy, Chemical Metallurgy. Mechanical Metallurgy. Corrosion. Metal Physics.

Electrolysis and Metal Deposition.

Mineral Products. Engineering Ceramics. Glass. Refractories. Enameled Metals. Crystal Growth. Physical

Properties. Constitution and Microstructure. Building Research. Structural Engineering. Fire Research. Mechanical Systems. Organic Building Materials. Codes and Safety Standards. Heat Transfer. Inorganic Building Materials. Applied Mathematics. Numerical Analysis. Computation. Statistical Engineering. Mathematical Physics.

Operations Research. Data Processing Systems. Components and Techniques. Digital Circuitry. Digital Systems. Analog S3'stems. Applications Engineering.

Atomic Physics. Spectroscopy. Infrared Spectroscopy. Solid State Physics. Electron Physics. Atomic Physics.

Instrumentation. Engineering Electronics. Electron Devices. Electronic Instrumentation. Mechanical In- struments. Basic Instrumentation.

Physical Chemistry. Thermochemistry. Surface Chemistry. Organic Chemistry. Molecular Spectroscopy,

Molecular Kinetics. Mass Spectrometry.

Office of Weights and Measures. BOULDER, COLO.

Cryogenic Engineering. Cryogenic Equipment. Cryogenic Processes. Properties of Materials. Gas Liquefaction.

Ionosphere Research and Propagation. Low Frequency and Very Low Frequency Research. Ionosphere ResearchPrediction Services. Sun-Earth Relationships. Field Engineering Radio Warning Service. Radio Propagation Engineering. Data Reduction Instrtimentation. Radio Noise. Tropospheric Measurements.

Tropospheric Analysis. Propagation-Terrain Effects. Radio-Meteorology. Lower Atmosphere Physics.

Radio Standards. High Frequency Electrical Standards. Radio Broadcast Service. Radio and Microwave

Materials. Atomic Frequency and Time Interval Standards. Electronic Calibration Center, Millimeter-Wave

Research. Microwave Circuit Standards. Radio Systems. High Frequency and Very High Frequency Research. Modulation Research. Antenna Research. Navigation Systems. Space Telecommunications.

Upper Atmosphere and Space Physics. Upper Atmosphere and Plasma Physics, Ionosphere and Exosphere

Scatter. Airglow and Aurora. Ionospheric Radio Astronomy.
7




BOUND TO PLE&SI

N. MANCHESTER.

INDIANA