Electric Charges And Fields

Question

A wire of resistance R is divided in equal parts, then these parts are joined in parallel, the equivalent resistance of the combination will be

nR

$\frac{R}{n}$

$\frac{n}{R}$

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

Solution

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

A wire is divided into equal parts.

Let us consider the number of parts= n

$∴$ Resistance of one part $\frac{R}{n}$

Now equivalent resistance of n parts each of resistance $\frac{R}{n}$ in parallel is given by

$R' = \frac{\frac{R}{n}}{n} = \frac{R}{n^{2}}$