Question

The resistance of a wire is $R$. After melting it is remoulded such that its area of cross-section becomes $n$ times its initial area of cross-section, its new distance will be

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

Answer 1

The correct option is D $\frac{R}{n^2}$

$R=\rho \cdot \frac{l}{A}$
$R^{\prime }=\rho \cdot \frac{l^{\prime }}{A^{\prime }}$
$I^{\prime }{A}^{\prime }=I.A$
$I^{\prime }=\frac{I}{n}$
$R^{\prime }=\rho .\frac{I}{n.nA}=\frac{1}{n^2}\rho .\frac{I}{A}$
$R^{\prime }=\frac{R}{n^2}$
Hence, option $\left(4\right)$ is correct.