Kirchhoff Current Law

There are some simple relationship between currents and voltages of different branches of an electrical circuit. These relationship are determined by some basic laws which are known asKirchhoff Laws or more specifically Kirchhoff Current and Voltage laws. These laws are very helpful in determining the equivalent resistance or impedance (in case of AC) of a complex network and the currents flowing in the various branches of the network. These laws are first derived by Guatov Robert Kirchhoff and hence these laws are also referred as Kirchhoff Laws.

Kirchhoff Current Law

In an electrical circuit the electric current flows rationally as electrical quantity. As the flow of current is considered as flow of quantity, at any point in the circuit the total current enters is exactly equal to the total current leaves the point. The point may be considered any where in the circuit.

Suppose the point is on the conductor through which the current is flowing, then the same current crosses the point which can alternatively said that the current enters at the point and same will leave the point. As we said the point may be any where on the circuit, so it can also be a junction point in the circuit. So total quantity of current enters at the junction point must be exactly equal to total quantity of current leave the junction. This is very basic thing about flowing of electric current and fortunately Kirchhoff Current law says the same. The law is also known as Kirchhoff First Law and this law stated that at any junction point in the electrical circuit, the summation of all the branch currents is zero. If we consider all the currents enter in the junction are considered as positive current then convention of all the branch currents leaving the junction are negative. Now if we add all these positive and negative signed currents obviously we will get result of zero.

The mathematical form of Kirchhoff Current Law is as follows,

We have a junction where n number of beaches meet together.

Let’s I1, I2, I3, …………………. Im are the current of branches 1, 2, 3, ……m and
Im + 1, Im + 2, Im + 3, …………………. In are the current of branches m + 1, m + 2, m + 3, ……n respectively.


The currents in branches 1, 2, 3 ….m are entering to the junction
whereas currents in branches m + 1, m + 2, m + 3 ….n are leaving from the junction.

So the currents in the branches 1, 2, 3 ….m may be considered as positive as per general convention
and similarly the currents in the branches m + 1, m + 2, m + 3 ….n may be considered as negative.


Hence all the branch currents in respect of the said junction are

+ I1, + I2, + I3,…………….+ Im, − Im + 1, − Im + 2, − Im + 3, ……………… and − In.


Now, the summation of all currents at the junction is
I1 + I2 + I3 + …………….+ Im − Im + 1 − Im + 2 − Im + 3………………− In.


This is equal to zero according to Kirchhoff Current Law.

⇒ I1 + I2 + I3 + …………….+ Im − Im + 1 − Im + 2 − Im + 3………………− In = 0


The mathematical form of Kirchhoff First Law is ∑ I = 0 at any junction of electrical network