Circuit Analysis Part 2: Resistance
By: Jason Hall
Tags: Ohms Law, Electrical Engineering, Electricity, Circuit Analysis, Electronics

In Circuit Analysis Part 1, I introduced the electrical principle of charge, voltage, current and Ohm’s law. In this post I want to provide a detailed discussion of electrical resistance beginning with metallic conductors, fixed and variable resistors, and nonlinear resistance devices.

Resistance

In part one I spoke of conductors, where the charge carriers are free electrons that are moved by voltage. As the electrons move about, they collide with each other and other atoms in the conductor. These collisions work like friction and the electrons lose some of their energy in the form of heat causing a voltage drop. This opposition to the movement of charge is known as resistance.

Georg Ohm

German physicist Georg Simon Ohm (1787–1854) is credited with discovering the relationship between voltage, current, and resistance. Ohm experimented by building DC circuits using batteries and wires of different materials and lengths. Ohm made two important discoveries that would form the basis of what we know as Ohm’s Law. First, that current was dependent on voltage and resistance. Second, that for a fixed voltage, the opposition to current was directly proportional to the length of the wire and inversely proportional to its cross-sectional area. In simpler terms it can be said that the longer the wire through which current flows, the greater the resistance, and the greater the thickness of the wire (the gauge), the lesser the resistance.

Describing Resistance with Water Analogy

The resistance to water flow through a pipe is analogous to electrical resistance. The longer the distance that water must flow through a pipe, the more friction will slow down the water. Conversely, the wider a pipe is, the faster that water will flow, provided there is sufficient pressure.

Resistance of Conductors

We know that conductors are materials that permit the flow of charge, but conductors do not all behave the same way. The resistance of a material is dependent of a few factors:

Constant of Proportionality and Temperature

As discussed in part one of this series, some materials conduct electricity better than others. The constant of proportionality is called the resistivity of the material. Resistivity is the measure of how strongly the material opposes the flow of electric current and is measured in ohm-meters. Resistivity does not only depend on the material, but also the temperature, since higher temperatures increase resistance. Here is the the resistivity of some common materials:

Resistivity of common materials

Calculating Resistance of Copper Wire

To calculate the resistance of 50 meters of 12 gauge copper wire (diameter 2.05 mm), you would use the following calculations:

Temperature Effects on Resistance

As the temperature of a conductor rises, an increasing number of electrons will escape their orbits causing collisions that disrupt the electron flow from atom to atom.

The temperature coefficient is the rate at which the resistance of a material changes with variations in temperature. Any material where the resistance increases with an increase in temperature is said to have a positive temperature coefficient. Conversely, any material where resistance decreases with an increase in temperature is said to have a negative temperature coefficient. In general, conductors have a positive temperature coefficient while insulators have a negative temperature coefficient.

For most conductors there is a relatively linear increase in resistance with rise in temperature as shown in the graph below. Due to the fact that the relationship between temperature and resistance isn’t actually linear (denoted by the dashed line near absolute zero), an inferred absolute temperature or temperature intercept is used for each material. For copper, the temperature intercept is -234.5 degrees Celsius.

As an example, let’s calculate the resistance of that same 50 meters of 12 gauge copper wire, this time at -40 degrees Celsius. With the temperature intercept of copper at -234.5 degrees C, we can calculate the new resistance value:

Resistors

Effective circuit design entails delivering the appropriate voltage and current levels to the load in the circuit. For example, the brightness of a Light Emitting Diode (LED) is dependent upon how much current it receives, but too much current will damage the LED. In such cases a resistor is used to limit the current to an appropriate level.

Fixed Resistors vs Variable Resistors

Fixed resistors have defined electrical resistance that is not adjustable. They are also the most commonly used. General purpose fixed resistors include carbon film, metal film, wire-wound, and surface mount resistors:

Variable resistors are those of which the electric resistance can be adjusted. Variable resistors are used for two principle functions: as a potentiometer and as a rheostat. Potentiometers are used to adjust voltage, while rheostats are used to adjust current within a circuit.

Resistor Notation Standards

Two main notation standards exist for circuit diagramming: ANSI and IEC.

ANSI and IEC standards for resistors

Resistor Identification

Larger resistors such as wire-wound resistors will often have their resistance value printed on their case. Small resistors such as carbon film and metal film are identified by colored bands printed on their body, the explanation for which can be found in numerous places online. In the image below, the resistor has a value of 3210 Ohms (321 x multiplier of 10), a tolerance of 1% (measure of the variation from stated value), and a temperature coefficient of 50 ppm/K.

Identifying markings on 3.21 kOhm resistor

Transducers

A transducer is a device that converts energy from one form to another. An electrical transducer converts physical quantities such as thermal energy, force, torque, light, position, etc. into an electrical signal. Two transducers that use the properties of resistance to convert physical quantities into electrical signals are thermistors and photoconductive cells..

Thermistors

Earlier we saw how temperature affects resistance. There are applications where a resistance change due to temperature is an intended function of the circuit. Such a case would be the use of a thermistor in a temperature sensor. Thermistors are constructed of materials such as cobalt, manganese, and nickel. These thermistors are said to have a negative temperature coefficient; as the temperature of the thermistor increases, the valence electrons break away from the atoms and are free to flow within the circuit, thereby reducing the resistance.

Thermistor, ANSI and IEC symbols and resistance/temperature graph of a thermistor

Photoconductive Cells

Photoconductive cells, photocells, or photo-resistors are transducers that have a resistance determined by the amount of light they are exposed to. An application where photo-resistors are commonly used are lights that turn and off, or dim automatically due to ambient light. Photocells are made of light sensitive materials such as cadmium sulfide or cadmium selenide. When these materials are exposed to light they release valence electrons thereby reducing the resistance of the component.

Photocell, ANSI and IEC symbols

Nonlinear Resistance

The components we have discussed so far have a constant resistance for a given temperature. This represents a linear current-voltage relationship. If a device has a linear current-voltage relationship, it is referred to as an ohmic device. Devices that do not have a linear current-voltage relationship are referred to as non-ohmic devices. Two non-ohmic devices I will introduce are diodes and varistors.

Diodes

A diode is a device that permits charge to flow in only one direction. Conventional current flow through a diode is from the anode toward the cathode:

When current is flowing from anode to cathode the diode is said to be forward biased and operating in its forward region. Since the diode has very little resistance in the forward region (cathode), the diode acts as a short circuit. When current is reversed and flowing from cathode to anode, the diode is said to be reverse biased and operating in its reverse region. In this case, the diode have very high resistance in its reverse region (anode) and acts an open circuit.

Diodes are used in many applications, one of which is the use of a rectifier in power conversion. A rectifier is a device that converts alternating current to direct current. Alternating current is so named because the current periodically reverses direction. A diode can be used to ensure that current flows in one direction (direct current).

Varistors

A varistor is a semiconductor device with a resistance value that changes automatically as the voltage applied to it changes. In other words, a varistor is a variable resistor that is voltage dependent. Varistors have a “breakdown value” and as long as voltage across the varistor is below this value, the resistance of the varistor will be very high. When voltage exceeds this breakdown value the resistance of the varistor becomes very low and current will flow. Varistors are often used to protect a circuit from transient over voltages. In such cases the transient voltage exceeds the breakdown voltage causing the resistance of the varistor to fall dramatically, allowing the damaging current to flow through the varistor rather than other sensitive components.

Varistor, ANSI and IEC symbols, resistance/voltage graph of varistor

Summary

Resistance is the opposition to the movement of electrical charge.

Conductors have a very low resistance while insulators have a very high resistance.

Resistivity is the measure of how strongly a material opposes the flow of electric current, and different materials have different levels of resistivity.

Resistivity of a material is also dependent on temperature, this property is known as it temperature coefficient.

Some materials have a positive temperature coefficient, where the resistivity of a material rises as temperature rises, and some materials have a negative temperature coefficient where the the resistivity of the material decreases as temperature rises.

Fixed resistors provide a constant resistance under most environments, where variable resistors are those where the resistance can be adjusted. Two examples are potentiometers and rheostats.

Potentiometers use variable resistance to adjust the voltage in a circuit, where rheostats use variable resistance to adjust the current in a circuit.

Two common notations for circuit diagrams are ANSI and IEC.

Carbon-film and metal-film resistors are identified by the colored bands on their surface.

A transducer is a device that converts one form of energy to another. Examples include thermistors and photocells.

is a device that converts one form of energy to another. Examples include thermistors and photocells. If a device has a linear current/voltage relationship it is known as an ohmic device. If device does not have a linear current/voltage relationship it is known as a non-ohmic device. Two examples of non-ohmic devices are diodes and varistors.

A diode is a device that allows current to flow in only one direction.

A varistor is a semiconductor device where the resistance changes according to the voltage applied to it. The resistance will be very high until voltage reaches the varistor’s “breakdown value”. Then resistance will fall, allowing current to flow through the varistor.

In the next article I will discuss Ohm’s law and the relationship between current and voltage in greater detail, as well as introduce electrical power, and energy. I will also introduce computer aided circuit analysis techniques.