Kirchoff current law

German physicist Kirchoff explained two basic laws concerning the relationship between currents and voltages for an electrical circuit in 1847 that are KCL KVL. Kirchoffs law is according to Ohm’s law from the basic theory of circuit.

Fig: Kirchoff law

Kirchoff’s current law states that

“The sum of the currents entering a node is equal to the sum of
the currents are leaving the node.”

This law is also called KCL. KCL means kirchoff’s current law.
Mathematical form of KCL

Where N is the number of branches and i_n is the nth current entering or leaving a node.
Consider entering current in a node is positive and leaving is regarded as negative.

Now applying Kirchoff’s current law

Here currents i1, i2 are entering in the node and i2, i4, i5 are leaving the node.
Rearranging the equation,

The equation is an alternative form of kirchoff current law.