The resistance of a wire is R What will be its new resistance ($R_{new}$), if it is stretched to n times its original length?

$R_{new} = n^2R$

The correct answer is Option (2) → $R_{new} = n^2R$

$\text{Given: Original resistance } R,~\text{wire stretched to } n~\text{times its length}$

$\text{Resistance of a wire: } R = \rho \frac{L}{A}$

$\text{After stretching, new length } L_{\text{new}} = n L$

$\text{Volume of wire remains constant: } A \cdot L = A_{\text{new}} \cdot L_{\text{new}} \Rightarrow A_{\text{new}} = \frac{A}{n}$

$R_{\text{new}} = \rho \frac{L_{\text{new}}}{A_{\text{new}}} = \rho \frac{n L}{A/n} = \rho \frac{n^2 L}{A} = n^2 R$

$\text{Answer: } R_{\text{new}} = n^2 R$