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A cylindrical wire is stretched so that its length becomes twice the original length. If the resulting reduction in diameter is taken into account, by what percentage does its resistance change?

1. 200%
2. 100%
3. 50%
4. 300%

Correct answer: 300%

Solution

With volume fixed, doubling length halves the area, so R = rho*L/A increases by factor (2)*(2) = 4, i.e. R -> 4R. The increase is 300%.

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