Question:
A copper wire is stretched to make it $0.5 \%$ longer. The percentage change in its electrical resistance if its volume remains unchanged is:
Correct Option: , 3
Solution:
(3) Resistance, $R=\frac{\rho \ell}{A}$
$\mathrm{R}=\rho \frac{\ell}{\mathrm{A}} \times \frac{\ell}{\ell}=\frac{\rho \ell^{2}}{\mathrm{~V}}[\because$ Volume $(\mathrm{V})=\mathrm{A} \ell .]$
Since resistivity and volume remains constant therefore $\%$ change in resistance
$\frac{\Delta \mathrm{R}}{\mathrm{R}}=\frac{2 \Delta \ell}{\ell}=2 \times(0.5)=1 \%$