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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) $\frac{2{\sigma }_{1}{\sigma }_{2}}{{\sigma }_{1}+{\sigma }_{2}}$

(b) $\frac{{\sigma }_{1}{\sigma }_{2}}{2{\sigma }_{1}{\sigma }_{2}}$

(c) $\frac{{\sigma }_{1}+{\sigma }_{2}}{{\sigma }_{1}{\sigma }_{2}}$

(d) $\frac{{\sigma }_{1}{\sigma }_{2}}{{\sigma }_{1}+{\sigma }_{2}}$

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