Q. A cylindrical metal wire of length $l$ and cross sectional area $S,$ has resistance $R,$ conductance $G,$ conductivity $\sigma$ and resistivity $\rho.$ Which one of the following expressions for $\sigma$ is valid
A) $\frac{GR}{\rho}$
B) $\frac{\rho R}{G}$
C) $\frac{GS}{l}$
D) $\frac{Rl}{S}$
Explanation
(a) Conductivity $\sigma = \frac{1}{\rho}$ …(i)
and conductance $G = \frac{1}{R}$
$\Rightarrow GR = 1$ ….(ii)
From equation (i) and (ii) $\sigma = \frac{GR}{\rho}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.