Question

A cylindrical metal wire of length $l$ and cross sections 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. $\frac{Gl}{S}$

Answer 1

Answer: (A)

$\frac{GR}{\rho }$

Conductivity $\sigma =\frac{1}{\rho }$............(i)
and conductance $G=\frac{1}{R}$
$\Rightarrow GR=1$.....(ii)
From equation (i) and (ii) $\sigma =\frac{GR}{\rho }$