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)

Resistance is given by,
$R=\frac{\rho l}{A}$ , where $\rho$ is the resistivity, $l$ is the length and $A$ is the area of the cross-section.
$\therefore R=\frac{\rho l^2}{Al}=\frac{\rho l^2}{Volume}$
As the volume and specific resistance $\rho$ remains constant, so
$R\propto l^2...(1)$
According to question $l_2=nl$
$\therefore \frac{R_2}{R}=\frac{l_2^2}{l^2}=\frac{n^2{l}^2}{l^2}$
$\Rightarrow R_2=n^{2}R$