What is the common unit of conductivity if the dimensions are expressed in centimeter?
What is the common unit of conductivity if the dimensions are expressed in centimeter?
$\Omega \mathrm{cm}^{-1}$
$\Omega^{-1} \mathrm{~cm}^{-1}$
$\Omega \mathrm{cm}$
$\Omega^{-1} \mathrm{~cm}$
Solution
If $\rho$ is a resistivity and $\kappa$ is conductivity or specific conductance, then
$\begin{aligned}
\kappa &=\frac{1}{\rho} ; \quad \because \quad \rho=R \times \frac{a}{l} \\
\therefore \quad & \kappa=\frac{1}{R} \times \frac{\ell}{a} \Omega^{-1} m^{-1}\left(O R \mathrm{ohm}^{-1} \mathrm{~m}^{-1} \text { or } S \mathrm{~m}^{-1}\right)
\end{aligned}$
(In C.G.S. system, the units of $\kappa$ are $\Omega^{-1} \mathrm{~cm}^{-1}$ or $\mathrm{S} \mathrm{cm}^{-1}$ which are used commonly)