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A copper wire is elongated so that its length increases by 0.5%. If its volume is assumed to stay constant, what is the percentage increase in its electrical resistance?

1. 2.0%
2. 2.5%
3. 1.0%
4. 0.5%

Correct answer: 1.0%

Solution

When the length of a conductor increases while its volume remains constant, its cross-sectional area decreases. The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Therefore, a 0.5% increase in length leads to a 1.0% increase in resistance due to the combined effects of lengthening and area reduction.

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