Series and Parallel Circuits - Combining Conductances

Combining Conductances

From Kirchhoff's circuit laws we can deduce the rules for combining conductances. For two conductances and in parallel the voltage across them is the same and from Kirchoff's Current Law the total current is

Substituting Ohm's law for conductances gives

and the equivalent conductance will be,

For two conductances and in series the current through them will be the same and Kirchhoff's Voltage Law tells us that the voltage across them is the sum of the voltages across each conductance, that is,

Substituting Ohm's law for conductance then gives,

which in turn gives the formula for the equivalent conductance,

This equation can be rearranged slightly, though this is a special case that will only rearrange like this for two components.