Q. 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) $\frac{\sigma_1+\sigma_2}{\sigma_1\sigma_2}$
Explanation
[Solution] $\frac{2l}{\sigma A} = \frac{l}{\sigma_1A} + \frac{l}{\sigma_2A} \Rightarrow \sigma = \frac{2\sigma_1\sigma_2}{\sigma_1+\sigma_2}$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.