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

If a wire is stretched to make it $0.1 \%$ longer, its resistance will :
  1. increase by $0.2 \%$
  2. decrease by $0.2 \%$
  3. decrease by $0.05 \%$
  4. increases by $0.05 \%$

Solution

$\mathrm{R} \propto \ell^2$ (for a given volume) $ \Rightarrow \frac{\Delta \mathrm{R}}{\mathrm{R}} \%=\frac{2 \Delta \ell}{\ell} \% $ Thus when wire is stretched by $0.1 \%$ resistance increases by $0.2 \%$

Asked in: JEE Main 2011

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