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  4. A copper wire is stretched to make it 0.5 % longer. The percentage change in its electrical resistance if its volume remains unchanged is:

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Q. A copper wire is stretched to make it $0.5 \%$ longer. The percentage change in its electrical resistance if its volume remains unchanged is:

JEE MainJEE Main 2019Current Electricity

Solution:

$R = \frac{\rho\ell}{A} $ and volume (V) = A$\ell$.
$ R = \frac{\rho\ell^{2}}{V} $
$ \Rightarrow \frac{\Delta R}{R} = \frac{2\Delta\ell}{\ell} = 1\%$