A copper wire is stretched to make it 0.5% lo | vedclass

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(C) The resistance $R$ of a wire is given by $R = \frac{\rho \ell}{A}$.Since the volume $V = A \ell$ remains constant,we can write $A = \frac{V}{\ell}

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(C) The resistance $R$ of a wire is given by $R = \frac{ho \ell}{A}$.Since the volume $V = A \ell$ remains constant,we can write $A = \frac{V}{\ell}$.Substituting this into the resistance formula: $R = \frac{ho \ell^2}{V}$.Since $ho$ and $V$ are constant,$R \propto \ell^2$.Taking the logarithmic derivative,we get $\frac{\Delta R}{R} = 2 \frac{\Delta \ell}{\ell}$.Given the percentage change in length $\frac{\Delta \ell}{\ell} 	imes 100 = 0.5\%$.Therefore,the percentage change in resistance is $\frac{\Delta R}{R} 	imes 100 = 2 	imes 0.5\% = 1\%$.

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

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