Conductance

Conductance ($G$) is the reciprocal of resistance, measured in siemens (S, ${\Omega }^{-1}$).

$$G=\frac{1}{R}$$

In general, where we express in terms of resistance (i.e., Ohm’s law or power), we are also able to express in terms of conductance. This is especially useful in nodal analysis.

A useful conversion is:

$$R_{eq}=\frac{1}{G_{eq}}=\frac{1}{G_1+G_2+\dots }$$ $$\frac{1}{R_{eq}}=G_{eq}=\sum G_i$$

In general, the conductance is given by the slope of the i-v characteristic — this is useful for non-linear elements, because it means we can derive the conductance by taking the derivative:

$$G=\frac{\partial i}{\partial v}$$

See also

• Admittance