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An iron wire has resistance R. If both its length and its radius are made twice their original values, what happens?

1. The resistance becomes half, while the resistivity stays the same.
2. The resistance becomes twice, while the resistivity becomes half.
3. The resistance becomes half, while the resistivity becomes twice.
4. The resistance becomes twice, while the resistivity stays the same.

Correct answer: The resistance becomes half, while the resistivity stays the same.

Solution

Doubling L and r: R' = rho*(2L)/(pi*(2r)^2) = rho*(2L)/(4*pi*r^2) = R/2. Resistance halves; resistivity is intrinsic and unchanged.

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