Question

The resistance of a wire is '$R$' ohm. If it is melted and stretched to '$n$' times its original length, its new resistance will be

• A. $\frac{R}{n}$
• B. $n^{2}R$
• C. $\frac{R}{n^{2}}$
• D. $nR$

Answer 1

Answer: (B)

We know that, $R =\frac{\rho l}{A}$
or $R =\frac{\rho l^{2}}{\text { Volume }} $
$\Rightarrow \text{Ral}^{2}$
According to question $l_{2}=n l_{1}$
$\frac{R_{2}}{R_{1}}=\frac{n^{2} l_{1}^{2}}{l_{1}^{2}}$
or $\frac{R_{2}}{R_{1}}=n^{2} $
$\Rightarrow R_{2}=n^{2} R_{1}$