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. $1.0\%$
• C. $0.5\%$
• D. $2.0\%$

Answer 1

The correct option is B $1.0\%$

Resistance, $R=\frac{\rho l}{A}$

$R=\rho \frac{l}{A}\times \frac{l}{l}=\frac{\rho l^2}{V}[\because \text{Volume (V)}=Al]$

Since resistivity and volume remains constant,
therefore $\%$ change in resistance

$\frac{\Delta R}{R}=\frac{2\Delta l}{l}=2\times \left(0.5\right)=1\text{\%}$

Hence, option $\left(C\right)$ is correct.