The resistance of a wire is \( R\,\Omega \) What will be its new resistance (\( R_{\mathrm{new}} \)), if it is stretched to n times its original length?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( R_{\mathrm{new}} = n^{2}R \)
The resistance of a wire is \( R = \rho l/A \). Stretching the wire keeps its volume constant, so when the length becomes \( nl \) the area of cross-section falls to \( A/n \).
\( \displaystyle l' = n l, \qquad A' = \frac{A}{n} \)
\( \displaystyle R_{\mathrm{new}} = \frac{\rho\,l'}{A'} = \frac{\rho\,(n l)}{A/n} = n^{2}\,\frac{\rho l}{A} = n^{2}R \)