Question

If a copper wire is stretched to make its radius decrease by $0.1$%, the percentage changes in its resistance is approximately

• A. $-0.4$%
• B. $+0.8$%
• C. $+0.4$%
• D. $+0.2$%

Answer 1

The correct option is A $-0.4$%

When a wire is stretched it’s volume remains constant-
$R=\rho \frac{L}{A}$
$=\left(\rho \frac{L}{A}\right)\times \frac{A}{A}$
$=\rho \frac{V}{A^2}$
$=\rho \frac{V}{\left({\pi }^2{r}^4\right)}$
From above-
$R\propto \frac{1}{r^4}$
$\delta R/R=4\times \frac{\delta r}{r}$
$=4\times 0.1$
$=0.4$
Resistance of wire is increased by $0.4percent.$