Current division is a technique used to compute the current through each resistor of a parallel combination of resistors when the total current through the parallel combination is known. In general, if we have $n$ resistors connected in parallel and the total current through them is $I$, the current through resistor $R_i$ is $$\begin{equation}I_i=I\frac{\frac{1}{R_i}}{\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}}=I\frac{G_i}{G_1+G_2+...+G_n}\end{equation}$$ where $G_i=\frac{1}{R_i}$ is the conductance of each resistor. In the case of two resistors, the previous equation gives $$\begin{equation}I_1=I\frac{R_2}{R_1+R_2}\end{equation}$$ $$\begin{equation}I_2=I\frac{R_1}{R_1+R_2}\end{equation}$$

Currents $I_1$, $I_2$,... are defined such that their direction is the same as the direction of current $I$. For instance, consider the circuit shown in Fig. 1.

Applying the current division equations we obtain $$I_{1}=6\ {\class{mjunit}{A}} \times\frac{\frac{1}{8}}{\frac{1}{4}+\frac{1}{8}}=6\ {\class{mjunit}{A}} \times\frac{8}{4+8}=4\ {\class{mjunit}{A}}$$ $$I_{2}=-6\ {\class{mjunit}{A}} \times\frac{\frac{1}{4}}{\frac{1}{4}+\frac{1}{8}}=-6\ {\class{mjunit}{A}} \times\frac{4}{4+8}=-2\ {\class{mjunit}{A}}$$ Note that, in the last equation, current $I_2$ is negative because it flows opposite to the direction implied by the $6\ {\class{mjunit}{A}}$ current source.

• Current division
  Circuit with 3 resistors and 1 current source (analytical)
  Circuit with 3 resistors and 1 current source (numerical)
  Circuit with 3 resistors and 1 current source (numerical design)