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 :

Question

( A ) $\frac{ \sigma_1 + \sigma_2}{\sigma_1 \sigma_2}$
( B ) $\frac{ \sigma_1 \sigma_2}{\sigma_1 + \sigma_2}$
( C ) $\frac{2 \sigma_1 \sigma_2}{\sigma_1 + \sigma_2}$
( D ) $\frac{ \sigma_1 + \sigma_2}{2\sigma_1 \sigma_2}$