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There are three copper wires of length and cross-sectional area (L, A), (2L, \frac{1}{2}A), (\frac{1}{2}L, 2A). In which case is the resistance minimum?

1. It is the same in all three cases
2. Wire of cross-sectional area 2A
3. Wire of cross-sectional area A
4. Wire of cross-sectional area \frac{1}{2}A

Correct answer: Wire of cross-sectional area 2A

Solution

Resistance is given by R = ρL/A. For the three wires, substituting the respective values of L and A, we find that the wire with (L, 2A) has the least resistance because the ratio L/A is smallest for this case.

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