Q. If $\sigma_{1},\sigma_{2}$ and $\sigma_{3}$ are the conductances of three conductors, then their equivalent conductance, when they are joined in series, will be
A) $\sigma_{1} + \sigma_{2} + \sigma_{3}$
B) $\frac{1}{\sigma_{1}} + \frac{1}{\sigma_{2}} + \frac{1}{\sigma_{3}}$
C) $\frac{\sigma_{1}\sigma_{2}\sigma_{3}}{\sigma_{1} + \sigma_{2} + \sigma_{3}}$
D) None of these
Explanation
(d) In series, effective resistance,
$R_{eff} = R_{1} + R_{2} + R_{3} \Rightarrow \frac{1}{\sigma_{eff}} = \frac{1}{\sigma_{1}} + \frac{1}{\sigma_{2}} + \frac{1}{\sigma_{3}}$
$= \frac{\sigma_{2}\sigma_{3} + \sigma_{1}\sigma_{3} + \sigma_{1}\sigma_{2}}{\sigma_{1}\sigma_{2}\sigma_{3}}$
$\therefore\sigma_{eff} = \frac{\sigma_{1}\sigma_{2}\sigma_{3}}{\sigma_{2}\sigma_{3} + \sigma_{1}\sigma_{3} + \sigma_{1}\sigma_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.