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JEE Main 2004 (AIEEE) · Ohm's Law, Resistivity & Temperature

Ohm's Law, Resistivity & Temperature question from JEE Main 2004 (AIEEE)

Q68JEE Main 2004 · 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 $l_B/l_A$ of their respective lengths must be

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Answer: (d)

For the same $R$ : $l = \dfrac{RA}{\rho} \propto \dfrac{d^2}{\rho}$ .
$\dfrac{l_B}{l_A} = \left(\dfrac{d_B}{d_A}\right)^2 \dfrac{\rho_A}{\rho_B} = 4 \times \dfrac{1}{2}$
$\dfrac{l_B}{l_A} = 2$
So the answer is (d) $2$ .

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