Single Choice

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

A$$2.5\%$$
B$$0.5\%$$
C$$1.0\%$$
Correct Answer
D$$2.0\%$$

Solution

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

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