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The resistance of a wire of uniform diameter \(d\) and length \(L\) is \(R\). The resistance of another wire of the same material but diameter \(d/2\) and length \(L/4\) will be

1. \(R/2\)
2. \(R\)
3. \(2/R\)
4. \(4/R\)

Correct answer: \(R\)

Solution

Resistance is given by \(R=\rho L/A\). If the diameter becomes half, area becomes one-fourth; if the length also becomes one-fourth, the two effects cancel, so resistance remains unchanged.

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