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JEE Main 2022 (29 Jul, Shift 1) · Combination of Resistors

Combination of Resistors question from JEE Main 2022 (29 Jul, Shift 1)

Q38JEE Main 2022 · 29 JUL · SHIFT 1Medium

Combination of Resistors

Two metallic wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of these wires respectively, the effective conductivity of the combination is:

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Answer: (b)

$R = \dfrac{l}{\sigma A}$ . In series the combination has length $2l$ and area $A$ .
$\dfrac{2}{\sigma} = \dfrac{1}{\sigma_1} + \dfrac{1}{\sigma_2} \Rightarrow \sigma = \dfrac{2\sigma_1\sigma_2}{\sigma_1 + \sigma_2}$
So the answer is (b).

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