Two metal wires of identical dimensions are connected in series. If $v_{1}$ and $v_{2}$ are the conductivities of the metal wires respectively, the effective conductivity if the combination is: (1) $\frac{\sigma_{1} \sigma_{z}}{\sigma_{1}+\sigma_{z}}$ (2) $\frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}$ (3) $\frac{\sigma_{1}+\sigma_{2}}{2 \sigma_{1} \sigma_{2}}$ (4) $\frac{\sigma_{1}+\sigma_{z}}{\sigma_{1} \sigma_{2}}$