Two metal wires of identical dimensions are connected in series. If ${\mathrm{v}}_1$ and ${\mathrm{v}}_2$ are the conductivities of the metal wires respectively, the effective conductivity if the combination is:

• A

  $\frac{{\mathrm{\sigma }}_1+{\mathrm{\sigma }}_2}{2\mathrm{ }{\mathrm{\sigma }}_1\mathrm{ }{\mathrm{\sigma }}_2}$
• B

  $\frac{{\mathrm{\sigma }}_1+{\mathrm{\sigma }}_2}{{\mathrm{\sigma }}_1\mathrm{ }{\mathrm{\sigma }}_2}$
• C

  $\frac{{\mathrm{\sigma }}_1\mathrm{ }{\mathrm{\sigma }}_2}{{\mathrm{\sigma }}_1+{\mathrm{\sigma }}_2}$
• Correct answer
  D

  $\frac{2\mathrm{ }{\mathrm{\sigma }}_1\mathrm{ }{\mathrm{\sigma }}_2}{{\mathrm{\sigma }}_1+{\mathrm{\sigma }}_2}$