Current division is a technique that can be used to compute the current going through each resistor of a parallel combination of resistors when the current going through all the resistors is known. In general, if we have $n$ resistors connected in parallel and the total current going through them is $I$, the current going through resistor $R_i$ is equal to $$\begin{equation}I_i=I\frac{\frac{1}{R_i}}{\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n}}\end{equation}$$

In the case of only 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 current division we obtain $$I_{1}=6\ A \times\frac{\frac{1}{8}}{\frac{1}{4}+\frac{1}{8}}=4\ {\class{mjunit}{A}}$$ $$I_{2}=-6\ A \times\frac{\frac{1}{4}}{\frac{1}{4}+\frac{1}{8}}=-2\ {\class{mjunit}{A}}$$ Notice that, in the last equation, current $I_2$ has a negative sign because the current flows in opposite direction than the current induced by the $6\ A$ 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)