Question

A wire is stretched such that its length -increases by $0.2 \%$. Its resistance

• A. increases by 0.2 %
• B. decreases by 0.4%
• C. increases by 0.4%
• D. increases by 0.1%

Answer 1

Answer: (C)

$R = \rho \frac{l}{A}$
After stretching, area of cross-section changes as the volume remains constant,
$ i e., \, V = Al$ or $A = \frac{V}{l}$
$ \therefore \, \, R = \rho \frac{l}{V / l} = \rho \frac{l^2}{V}$
or $ \frac{\Delta R}{R} =2 \frac{\Delta l}{l} = 2 \times 0.2 \% \, \, \, \, \, \, \, (\because \frac{\Delta l}{l} = 0.2 \%)$
$ = 0.4 \%$