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The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then:

1. the resistance and the specific resistance, will both remain unchanged
2. the resistance will be doubled and the specific resistance will be halved
3. the resistance will be halved and the specific resistance will remain unchanged
4. the resistance will be halved and the specific resistance will be doubled

Correct answer: the resistance will be halved and the specific resistance will remain unchanged

Solution

Resistance (R) is given by R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area. Doubling both length and radius increases the area by a factor of 4 (A ∝ r²), so the resistance becomes half (R ∝ L/A). Resistivity (specific resistance) is a material property and remains unchanged.

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