The electric resistance of a certain wire of iron is R. If its length and radius are both doubled, then (a) The resistance will be doubled and the specific resistance will be halved. (b) The resistance will be halved and the specific resistance will remain unchanged. (c) The resistance will be halved and the specific resistance will be doubled. (d) The resistance and the specific resistance, will both remain unchanged.

Answer: (b). R = (ρ l)/(π r²) ∝ l/r² R' = R × 2/2² = R/2 ρ depends only on the material (iron), so it is unchanged. So the answer is (b) resistance halved, specific resistance unchanged.

The electric resistance of a certain wire of iron is R. If its length… | NEET 2004 (AIPMT)

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Ohm's Law, Resistivity & Temperature

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

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Answer: (b)

$R = \dfrac{\rho l}{\pi r^2} \propto \dfrac{l}{r^2}$
$R' = R \times \dfrac{2}{2^2} = \dfrac{R}{2}$
$\rho$ depends only on the material (iron), so it is unchanged.
So the answer is (b) resistance halved, specific resistance unchanged.

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