Equivalent resistance between the adjacent corners of a regu... | Physics | SolveeIt | Solveeit

Today, August 18

Question

Equivalent resistance between the adjacent corners of a regular $n$ -sided polygon of uniform wire of resistance $R$ would be :

A

$\frac{(n-1) R}{(2 n-1)}$

B

$\frac{(n-1) R}{n}$

C

$\frac{n^2 R}{n-1}$

D

$\frac{(n-1) R}{n^2}$

Answer

$\frac{(n-1) R}{n^2}$

Explanation

Solution

Suppose resistance of each arm is r, then r=R/n
Req(AB)=R1+R2R1R2
r+(n−1)rr(n−1)r
=nrr(n−1)r
=nn−1r
=n2(n−1)R