Question

What is the relation between conductance and conductivity?

Answer 1

1. The measure of opposition/obstruction provided by a material through which current is flowing is known as resistance.
2. Conductance is the inverse of resistance, which means that it is a measure of how easily the current will flow through the material.
3. Conductivity is a property of a material that tells us how easily current will be able to flow through it. The inverse of conductivity is resistivity. The resistance provided by a volume of material of unit length and cross-sectional area is that material's resistivity. Both resistivity and conductivity are intrinsic properties of materials.
4. The relationship between resistivity and resistance is, $\rho =R\frac{A}{L}$, where $\rho$ is the resistivity, $R$ is the resistance, $A$ is the cross-sectional area and $L$ is the length of the material (conductor).
5. Since conductance is $G=\frac{1}{R}$ and conductivity is $\sigma =\frac{1}{\rho }$, we can use the relationship above in order to find a relationship between conductance $G$ and conductivity $\sigma$.

$\begin{array}{rcl}\rho & =& R\frac{A}{L}\\ \frac{1}{\sigma }& =& \frac{1}{G}\frac{A}{L}\\ \sigma & =& G\frac{L}{A}\end{array}$

Hence, the relationship between conductivity and conductance is $\begin{array}{rcl}\sigma & =& G\frac{L}{A}\end{array}$.