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JEE Main 2006 (AIEEE) · Ohm's Law, Resistivity & Temperature

Ohm's Law, Resistivity & Temperature question from JEE Main 2006 (AIEEE)

Q66JEE Main 2006 · AIEEEEasy

Ohm's Law, Resistivity & Temperature

A material 'B' has twice the specific resistance of 'A'. A circular wire made of 'B' has twice the diameter of a wire made of 'A'. Then for the two wires to have the same resistance, the ratio $\ell_B/\ell_A$ of their respective lengths must be

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Answer: (a)

$R = \dfrac{\rho l}{\pi d^2/4} \Rightarrow l = \dfrac{R \pi d^2}{4\rho}$ , so for the same $R$ , $l \propto \dfrac{d^2}{\rho}$ .
$\dfrac{l_B}{l_A} = \dfrac{d_B^2}{d_A^2} \cdot \dfrac{\rho_A}{\rho_B} = 4 \times \dfrac{1}{2}$
$\dfrac{l_B}{l_A} = 2$
So the answer is (a) $2$ .

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