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

The correct option is B increase by $0.2\%$

$R=\rho \frac{\ell }{A}=\frac{\rho \ell }{A}\times \frac{l}{l}=\frac{\rho l^2}{Vo{l}^m}$

$R\propto {\ell }^2$

$\frac{\Delta R}{R}=2\frac{\Delta \ell }{\ell }$

$\frac{\Delta R}{R}=2\times 0.1\%$

$\frac{\Delta R}{R}=0.2\%$

Option B