# Introduction and Explanation to Kirchhoff’s Current Law (KCL)

Kirchhoff’s Current Law also known as KCL is the Kirchhoff’s first law, it is sometimes also known as **Kirchhoff’s point rule** or **junction rule**. It is a fundamental law of electrical and electronics engineering. Anyone who is willing to do better in engineering needs to understand this concept and able to use this law in circuit theory.

Here in this blog, we will show you how to drive this law. We will present you how the idea of Kirchhoff’s law stated.

## Kirchhoff’s Current Law

Let us see following parallel circuit as an example.

Now let us solve all the values of voltage and current in this circuit.

At this stage, We know the value of each branch of current and total current in the circuit. The total current in a parallel circuit should and must be equal to the sum of the branch currents, however, there’s more going on in above circuit than just that. So, let’s see the currents at each wire junction point also known as a node in this circuit, we should able to see something else as given below:

*Fundamental Formulas of AC Circuit Equation*

If we look carefully, at the each node on the negative “rail” that is at the wire number 8,7,6,5 we can see the current splitting off the main flow to each successive branch resistor. While on the positive “rail” that is wire number 1,2,3,4 we can see current merging together to form the main flow from each successive branch resistor. To understand this concept, just visualise the water pipe circuit analogy with every branch node acting as a “tee” fitting, where the water flow splitting or merging with main piping as it travels from the output of the water pump toward the return to reservoir or sump.

If we have a closer look at one particular “tee” node, such as node 3, we can see that the current entering in that node is exactly equal in magnitude to the current existing that node.

Let’s see from a right side and from the bottom side, there are two currents entering the wire connections labelled as node 3. And to the left, we have a single current existing that node equal in magnitude to the sum of the two current entering. Again if we compare with plumbing analogy, considering there is no leaks in the pipe, amount of water entering the fitting must be equal to the amount of water exiting from the pipe. This holds true for any node (“fitting), no matter how many flows entering or leaving. Hence, mathematically we can derive the following expression

*Pay scale of Electronics and Communication Engineering in Various Countries*

Kirchhoff summarised this concept and expressed in his term giving mathematical equation as below and labelled this concept as *Kirchoff’s Current Law *

Hence Kirchoff’s law can be stated as:

“The algebraic sum of all currents entering and exiting a node must equal zero”

It means, if we assign a mathematical sign also know as polarity to each entering (+) and leaving current (-) at a node, we can add them together to arrive at a grand total of zero.

Let’s take an example of above circuit, at node 3 (number 3), we can determine the magnitude of the current leaving from the left by setting up a KCL equation with that current as the unknown value

The negative (-) sign on the value of 5 milliamps tells us that the current is *exiting* the node, as opposed to the 2 milliamp and 3 milliamp currents, which must both be positive (and therefore *entering* the node). Whether negative or positive denotes current entering or exiting is entirely arbitrary, so long as they are opposite signs for opposite directions and we stay consistent in our notation, KCL will work.

Together, Kirchhoff’s Voltage and Current Laws are a formidable pair of tools useful in analysing electric circuits.

To conclude, Kirchhoff’s current law states as

**“The algebraic sum of all currents entering and exiting a node must equal zero”**