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?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $R_{new} = n^2R$
$\text{Given: Original resistance } R,~\text{wire stretched to } n~\text{times its length}$
$\text{Resistance of a wire: } R = \rho \frac{L}{A}$
$\text{After stretching, new length } L_{\text{new}} = n L$
$\text{Volume of wire remains constant: } A \cdot L = A_{\text{new}} \cdot L_{\text{new}} \Rightarrow A_{\text{new}} = \frac{A}{n}$
$R_{\text{new}} = \rho \frac{L_{\text{new}}}{A_{\text{new}}} = \rho \frac{n L}{A/n} = \rho \frac{n^2 L}{A} = n^2 R$
$\text{Answer: } R_{\text{new}} = n^2 R$