### Current Electricity Question 22

#### Question 22 - 01 February - Shift 2

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

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

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

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

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

## Show Answer

#### Answer: (1)

#### Solution:

#### Formula: Combination of Resistances

Suppose resistance of each arm is $r$, then $r=R / n$

$R _{\text{eq }(A B)}=\frac{R_1 R_2}{R_1+R_2}$

$\frac{r(n-1) r}{r+(n-1) r}$

$=\frac{r(n-1) r}{n r}$

$=\frac{n-1}{n} r$

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