Question

If a uniform wire of resistance $R$ is uniformly stretched to $n$ times the original length, then new resistance of the wire becomes :

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

Answer 1

Answer: (B)

Given: $l_1{A}_1=l_2{A}_2$
As the volume of wire does not change after stretching so,
$\Rightarrow \frac{A_2}{A_1}=\frac{l_1}{l_2}=\frac{l}{nl}=\frac{1}{n}$
The resistance of the wire is $R=\rho \frac{l}{A}$
$\Rightarrow R\propto \frac{l}{A}$
Hence, $\frac{R_1}{R_2}=\frac{l_1}{l_2}\times \frac{A_2}{A_1}$
$=\frac{1}{n}\times \frac{1}{n}=\frac{1}{n^2}$
Therefore, $R_2=n^{2}R$
$\left(\because R_1=R\right)$