Two wires of same length and thickness having specific resistances 6… | JEE Main 2021 (18 Mar, Shift 2)

Q49JEE Main 2021 · 18 MAR · SHIFT 2Medium

Combination of Resistors

Two wires of same length and thickness having specific resistances 6 $\Omega$ cm and 3 $\Omega$ cm respectively are connected in parallel. The effective resistivity is $\rho\ \Omega$ cm. The value of $\rho$ , to the nearest integer, is ____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 4

Same $l$ and $A$ , so $R \propto \rho$ . Parallel combination has length $l$ and area $2A$ .
$\dfrac{\rho_{eff} l}{2A} = \dfrac{l}{A} \cdot \dfrac{\rho_1\rho_2}{\rho_1 + \rho_2} \Rightarrow \rho_{eff} = \dfrac{2\rho_1\rho_2}{\rho_1 + \rho_2}$
$\rho_{eff} = \dfrac{2 \times 6 \times 3}{9} = 4\ \Omega\text{ cm}$

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Combination of Resistors question from JEE Main 2021 (18 Mar, Shift 2)

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