Physics - Current Electricity Question with Solution | TestHub

Volume of wire will remain constant 

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

$\Rightarrow \boxed{A_2=\frac{A_1}{n}}$

The resistance of a wire with a length $l$, an area of $A$, and resistivity $\rho$ is stated as $R=\frac{\rho l}{A}$.

Now, the new length is $nl$.
$\therefore$New resistance $R^{\text{'}}=\frac{\rho nl}{A/n}\Rightarrow R^{\text{'}}=\rho n^2\frac{l}{A}$

$\Rightarrow \boxed{R^{\text{'}}=n^{2}R}$