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Two metal wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the metal wires respectively, the effective conductivity of the combination is:
A
$\frac{\sigma_1\sigma_2}{\sigma_1 + \sigma_2}$
B
$\frac{2\sigma_1\sigma_2}{\sigma_1 + \sigma_2}$
C
$\frac{\sigma_1 + \sigma_2}{2\sigma_1\sigma_2}$
D
$\frac{\sigma_1 + \sigma_2}{\sigma_1\sigma_2}$
Detailed Solution
$R_{eq} = R_1 + R_2$: $\frac{2l}{\sigma_{eq}A} = \frac{l}{\sigma_1A} + \frac{l}{\sigma_2A}$
$\sigma_{eq} = \frac{2\sigma_1\sigma_2}{\sigma_1 + \sigma_2}$
$\sigma_{eq} = \frac{2\sigma_1\sigma_2}{\sigma_1 + \sigma_2}$