Question

If a wire is stretched to make it $0.1\%$ longer, its resistance will

• A. increase by $0.05\%$
• B. increase by $0.2\%$
• C. decrease by $0.2\%$
• D. decrease by $0.05\%$

Answer 1

Answer: (B)

Resistance of wire
$R=\frac{\rho l}{A} \ldots\left(i\right)$
On stretching, volume $(V)$ remains constant
So $V=Al$
or $A=\frac{V}{l}$
$\therefore \, R=\frac{\rho l^{2}}{V}$ (Using $\left(i\right))$
Taking logarithm on both sides and differentiating we get,
$\frac{\Delta R}{R}=\frac{2\,\Delta l}{l}$ ($\because$ $V$ and $\rho$ are constants)
or $ \frac{\Delta R}{R} \% =\frac{2\,\Delta l}{l} \%$
Hence, when wire is stretched by $0.1\% $ its resistance will increase by $0.2\%$