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
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
$\frac{{{\sigma _1}+{\sigma _2}}}{{{\sigma _1}{\sigma _2}}}$
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