New Method for Calculating Parallel Resistors - Page 1
Forum section: electronics / general

author: paulfr
author_rank: Newbie
timestamp: May 11, 2019, 02:46:31 pm
content: I teach HS Physics part of which is Electric Circuits,I have discovered a rule / technique for parallel resistors that I never encounteredin all my 30+ years in electronics engineering, nor in any textbook on Circuits.It is what I call " The N + 1 Rule "We all know the Reciprocal Rule1 / RT = 1/R1 + 1/R2 + 1/R3 ..... + 1/RnANDwe know that for 2 resistors, this becomes the Product over the Sum of the 2 R'sBUTThe N+1 Rule is this1/ Find N = the ratio of the two R's2/ Add 1 to it to get N + 13/ Divide the largest R by N+1E.g.4 and 20 ohmsN = 20/4 = 5N+1 = 6RT = Rtotal = 20/6 or 10/3CheckProduct = 80Sum= 24RT = 80/24 = 10/3It is quite useful when the numbers are large and thus the Product is very large.No need to remember it and then do long division.e.g.300 and 50 becomes much easier and thus faster with N+1 than with Product-Sum.300/50 = 6 ==> Rtotal = 300/7Check with Product Sum Rule300 (50) / 300 + 50 = 15000/350 = 300/7It works even when N is not an integer.e.g.500 and 300 ohms500/300 + 1 = 5/3 + 1 = 8/3Rtotal = 500 / (8/3) = 1500/8Check with Product Sum Rule500(300) / (500 + 300) = 150000 / 800 = 1500/8Have any of you ever seen thisJust curious and wondering why it is not in all the textbooks on Circuits.Comments solicited

author: Kalvin
author_rank: Super Contributor
timestamp: May 11, 2019, 03:20:37 pm
content: Neat trick, but I would argue that the reciprocal rule is a) easier to remember and b) more universal applicable c) carries the physical meaning of the resistors in parallel. People are using calculators (numeric or symbolic) anyway which make this a bit outdated trick. And in real life (tm) one can either guesstimate the result of the parallel combination for quick ball park computations, or if more precision is needed one will reach for the calculator.

author: KaneTW
author_rank: Frequent Contributor
timestamp: May 11, 2019, 03:39:29 pm
content: Your trick follows from simple algebra for the 2-resistor case, and not entirely correct (it's not the largest of the two, but the dividend of N)1/R = 1/R1 + 1/R2R = 1/(1/R1 + 1/R2)R = R1/(1 + R1/R2)or R = R2/(1+R2/R1), same principle.

author: magic
author_rank: Super Contributor
timestamp: May 11, 2019, 03:43:23 pm
content: Why, that's a perfectly sensible technique, easy to remember and carries the physical meaning of paralleling resistorsI mean, if R2 is N times smaller than R1, it conducts N times more and therefore the network conducts N+1 times more than R1 alone. By Ohm's law, that's N+1 times less resistance.Can even trivially add a different R3, M times smaller than R1, then it is R1/(N+M+1).You can also produce this formula by taking the well known 1/(1/R1+1/R2+1/R3) and multiplying by R1/R1.

author: Siwastaja
author_rank: Super Contributor
timestamp: May 11, 2019, 03:56:54 pm
content: Seems handy and practical whenever you have the ratio N figured out already - this would be in a resistor divider circuit, where you design for a certain N, and need to calculate the parallel combination to figure out the output impedance.

author: Kalvin
author_rank: Super Contributor
timestamp: May 11, 2019, 04:06:39 pm
content: Quote from: magic on May 11, 2019, 03:43:23 pmYes, you are totally right!

author: RoGeorge
author_rank: Super Contributor
timestamp: May 11, 2019, 04:39:31 pm
content: Indeed, the 'change of variables' method (https://en.wikipedia.org/wiki/Change_of_variables) is a nice and well known math trick. Sometimes it's very helpful for symbolic evaluations too, not only for numerical evaluations.Now, should this be put in a physics textbook? No, because:- it is offtopic, it is math, not physics- it will only add confusion for the student- yet another "random" thing to be memorized for the exam, with no correspondence to the physics phenomena- for real life values, like e.g. 4.7 and 5.6, it doesn't helpIn a class about the physics of the harmonic oscillator, it would be very confusing to present an algorithm for fast numerical approximation of cos(x), wouldn't it?

author: vk6zgo
author_rank: Super Contributor
timestamp: May 12, 2019, 03:20:28 am
content: Quote from: Kalvin on May 11, 2019, 04:06:39 pmI use it all the time for applications where the ratio is easy to determine by observation.You can, of course use a similar process for any pair of resistors in parallel.Determine the LCM of the values of the resistors, so, for instance, calling the LCM Rm, if LCM = 3 R1, & also= 5 R2, then Rt = Rm/8.

author: Brumby
author_rank: Unknown
timestamp: May 12, 2019, 05:40:07 am
content: I have to agree with these (which make the exam point irrelevant):Quote from: RoGeorge on May 11, 2019, 04:39:31 pmI'll also add that where you havemorethan 2 resistors in parallel, it gets very awkward, very quickly.The standardreciprocal of the sum of reciprocalsis a very simple formula and works for any number of parallel resistors (and series capacitors).

author: magic
author_rank: Super Contributor
timestamp: May 12, 2019, 08:29:19 am
content: Quote from: Brumby on May 12, 2019, 05:40:07 amIt scales linearly with the number of resistors

author: T3sl4co1l
author_rank: Super Contributor
timestamp: May 12, 2019, 09:05:13 am
content: I do that implicitly when doing quick estimates mentally or on paper.Reduce the problem to its simplest form. If we have values of 4700 and 10000, obviously don't do long division by 14700. That'll take forever!First notice that 4700 is about half 10000. The approximate problem reduces to 1 || 2. We note the denominator is 3 and the numerator is 2, and we're done. We can go slightly further and write 3 || 6 = 2, all whole numbers. Multiply back up to the original values (i.e., by 10000/6) and you have your answer, 3.33k.4700 is not actually half, but a few percent low (about 6%), so our result will be not quite as many percent low as well (about 4%?). This gets into the range of typical resistor tolerance, so we might leave it as good enough, or further approximate it, or fully calculate it, or choose 4.99k resistors because hell, my time is literally worth a great many times the resistors themselves!I feel, in general, ratios are not taught nearly as well as they deserve to be. Grade school application as I recall seemed mostly to waste time evaluating factored expressions that could more easily be solved throwing everything together. I don't think you can motivate it in the fully abstract. The greatest power comes with units, dimensional analysis. You can avoid many algebra errors this way, by associating a unit to each variable in your expression and follow the unit parity through your work -- as soon as two different units are being added, you know exactly which terms encountered an error!Ratios also help with some algebraic and higher analyses, where a messy equation (typical electronic example, an RLC filter with piles of physical variables per term) can be greatly simplified, with judicious choice of ratios stuffed away into auxiliary expressions (e.g., ω_0, ζ).The highest level of this may be Feynman integration, where the limits of integration are pulled through the ratios, giving a dimensionless inner expression, which may be no easier to integrate, but only needs to be solved once and we can let a computer think about that instead.This is probably harder to justify at an early school level, because only technical fields will use much of it (these exact topics are usually covered in physics courses), but I think a good argument can still be made for a lighter-weight version for general use.Tim

author: Brumby
author_rank: Unknown
timestamp: May 12, 2019, 12:53:19 pm
content: Quote from: magic on May 12, 2019, 08:29:19 amHow good is your mental arithmetic?That's the only reason for trying this sort of "trick", IMHO.Quote from: T3sl4co1l on May 12, 2019, 09:05:13 amThis is the sort of thing I would do for rough calculation, understanding there is an error margin by doing so. If I wanted to be more precise, then I'd break out a calculator