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The resistance of a wire is $R$. If the length of the wire is doubled by stretching, then the new resistance will be:

1. 2 R
2. 4 R
3. R
4. 4 R

Correct answer: 4 R

Solution

For a stretched wire, volume remains constant, so doubling the length halves the cross-sectional area. Since $R=\rho L/A$, the new resistance becomes $\rho(2L)/(A/2)=4R$.

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