Lesson : Kirchhoff’s current law

Kirchhoff’s current law or nodal rule states that the sums of currents flowing into any node or junction in a circuit will be equal to 0. In others words, the sums of current flowing into the node and out of the node will be equal.

$\sum\limits_{i=1}^n I_{i}=0$

where n is the total numbers of current flowing into and out of the node. Current flowing into the node will have a positive value and current flowing out of the node will have a negative value.

In this example, we have one node that is going to be analyse. Kirchhoff’s current law speculates that the sums of currents flowing into any node or junction in a circuit will be equal to 0.

$\sum\limits_{i=1}^n I_{i}=0$

Figure 1 : Kirchhoff's current law example — Kirchhoff’s current law example

Current flowing into the node will have a positive value and current flowing out of the node will have a negative value. $I_{1}$ is flowing into the node and therefore will be positive. $I_{2}\ and\ I_{3}$ are flowing out the node and will be negative. With this information and Kirchhoff’s current law, we can find the formula below:

$I_{1} - I_{2} - I_{3} = 0$

We can rearrange this formula to isolate $I_{1}$ :

$I_{1} = I_{2} + I_{3}$

The example above is very simple. In the next lessons, we will see that Kirchhoff’s voltage law and current law are very useful to solve circuits that contains series and parallel circuits mixed together.