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 1

Answer: (D)

Suppose resistance of each arm is $r$, then $r=R / n$
$R_{e q(A B)}=\frac{R_1 R_2}{R_1+R_2}$
$ \frac{r(n-1) r}{r+(n-1) r}$
$ =\frac{r(n-1) r}{n r}$
$ =\frac{n-1}{n} r $
$ =\frac{( n -1) R}{n^2}$