Question

write a difference between maximum and minimum effective resistance

Answer 1

Given n resistors with resistance R1,R2,…,RnR1,R2,…,Rn, and we can connect them with wires arbitrarily (this statement is not rigorous, but I think you understand what I mean), what is the minimum and maximum effective resistance?

It's folklore that the minimum (which is R1∥R2∥⋯∥RnR1‖R2‖⋯‖Rn) is got when the resistors are connected in parallel and the maximum (which is R1+R2+⋯+RnR1+R2+⋯+Rn) is got when the resistors are connected in series, but I do not see a way to prove this. I searched and only found that this result is used without proof.



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