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If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is _____%.
Correct Answer: 44
$$R = \rho \frac{L}{A}$$
$$V = A \cdot L$$
$$R = \rho \frac{L^2}{V}$$
A 20% increase in length means the new length is $$L' = 1.2L$$.
$$\frac{R'}{R} = \left(\frac{L'}{L}\right)^2$$
$$\frac{R'}{R} = (1.2)^2 = 1.44$$
$$\% \text{ increase} = (1.44 - 1) \times 100 = 44\%$$
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