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:

• A. $2.5\%$
• B. $0.5\%$
• C. $1.0\%$
• D. $2.0\%$

Answer 1

Answer: (C)

$1.0\%$

$R=\frac{\rho \ell }{A}$ and volume $\left(V\right)=a\ell$.
$R=\frac{\rho {\ell }^2}{V}$
$\Rightarrow \frac{\Delta R}{R}=\frac{2\Delta \ell }{\ell }=1\%$