# Min and Max of Parallel Resistors

I noticed that, for resistors in a parallel circuit, where R1 is < R2, the minimum value is (R1)/2, and the maximum approaches R1.
I was trying to work out why, so for two resistors, the calculation is:
R1.R2/(R1 + R2).
I thought of partial derivatives but not sure where to go after that, and after getting the curve in WolframAlpha, not sure what to do with that either.
http://www.wolframalpha.com/input/?i=plot+xy/(x+y)

Empirically, the nth case appears to be: min = (R1)/n and max = R1, but not sure how to prove it mathematically.

Any advice on what I could try next? This isn't homework, just noticed it and got curious.

## Answers and Replies

Office_Shredder
Staff Emeritus
Science Advisor
Gold Member
Assume that R1 is some fixed number. All that we know is that R2 must be bigger than R1. So to find the minimum resistance, R2 should be as small as possible, and to find the maximum resistance, R2 should be infinitely large.

Try seeing what happens to the resistance when you make R2 as small as possible (keeping in mind it must be bigger than R1) and what happens when R2 is arbitrarily large