Parallel Circuit Rules

Parallel circuits are electric circuits that offer current more than one path to follow. Each path is referred to as a branch. The point at which current ‘splits’ through separate branches is called a node.

A pure parallel circuit has only one component per current path. Often, however, parallel paths are not purely parallel and have more than one component per path. In other words, a parallel branch will commonly contain series elements. In these cases, the series solutions in each path must be resolved before the branch as a whole can be analyzed.

In order to generalize the rules for parallel circuits, we use the term ‘branch’ for each rule below. If there is only one component, the two are identical. If there is more than one component in a path, then the rule only holds for the equivalent value of the combined components in that path.

Current in Parallel Circuit

Each path, or branch, may have a different current. The total current is equal to the sum of currents from each component or path, and the current through each path is determined by the resistance of that path, following Ohm’s Law.

I_T=I_1+I_2+I_3+...+I_N \\ ... \\ I_1 = \frac{V}{R_1}

Voltage in Parallel Circuits

The total voltage is equal to the voltage across each circuit branch. All components or paths share the same voltage.

V_T = V_1=V_2=V_3=V_N

Resistance in Parallel Circuits

The total resistance in a parallel circuit is less than any of the components or paths:

R_T = (\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_N})^{-1}