Two metal wires of identical dimensions are connected in series. If σ… | NEET 2015 (AIPMT)

Q68NEET 2015 · AIPMTMedium

Combination of Resistors

Two metal wires of identical dimensions are connected in series. If $\sigma$ 1 and $\sigma$ 2 are their conductivities, the effective conductivity of the combination is

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Answer: (c)

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

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