Two metallic wires of identical dimensions are connected is series. If ${\sigma }_1$ and ${\sigma }_2$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :

• A

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

  $\frac{2{\sigma }_1{\sigma }_2}{{\sigma }_1+{\sigma }_2}$
• C

  $\frac{{\sigma }_1+{\sigma }_2}{2{\sigma }_1{\sigma }_2}$
• D

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

Hence, the correct answer is option: 'B'.