The current divider rule states that the portion of the total current in the circuit that flows through a branch in the circuit is proportional to the ratio of the resistance of the branch to the total resistance. This rule allows for a shortcut in determining the branch current in a parallel circuit, which is simply to multiply the ratio of the resistances by the total current.
The current divider rule is derived from Ohm's law, which states that the current flowing between two points in a circuit equals the voltage divided by the resistance. Because the voltages between the multiple branches in a parallel circuit are equal to each other, the branch current equals the total voltage of the circuit divided by the resistance in that branch.
Ohm's law is again applied to substitute the total voltage for the product of the total current and the total resistance of the circuit. The branch current is solved in terms of the resistance ratios and the total current. Current flows through the path of least resistance, and the branch with the least resistance has the highest portion of the current flowing through it. This proportion remains constant as long as the resistance is unchanged even if the voltage increases or decreases.