Question

The resistance of a wire is $R$. If it is stretched such that its length becomes $n$ times its initial length, what will be the final resistance of the same wire?

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

Answer 1

The correct option is B $n^{2}R$

The volume of the wire will remain the same.

So, $A_1{l}_1=A_2{l}_2$

$\Rightarrow Al=A^{\prime }\left(nl\right)$

$\Rightarrow A^{\prime }=\frac{A}{n}$

Now,

$R^{\prime }=\rho \frac{l^{\prime }}{A^{\prime }}=\rho \frac{nl}{A/n}=n^2\rho \frac{l}{A}=n^{2}R$