Kirchhoff’s Laws

Kirchhoff’s Laws are used to solve those networks or circuit where ohms law is may not be readily solved that circuit. Gustav Kirchhoff’s, a German Scientist, summed up his findings in a set of two laws which are called Kirchhoff’s Laws. Resistance of a complicated circuits and for calculating the currents flowing in the various branches of circuits or networks. The two laws are Kirchhoff’s current law and Kirchhoff’s voltage law.

Kirchhoff’s Current Law (KCL)

This law relates the currents flowing through the circuit that is why this law is called Kirchhoff’s current law. This law is also known as Kirchhoff’s point law.

This law states that, in any electrical network, the algebraic sum of the currents meeting at a junction or node is always zero.

Lets us consider a case in which few conductors meeting at a junction or point A, where some conductors have current entering to the point and some conductors have currents leaving out the point. Assuming currents entering to the point to be positive while the outgoing currents are negative.

kirchhoff's law current

We have,


I1+I4+I5= I2+I3

Incoming Currents = outgoing Currents

In other words we can say that incoming current is equal to outgoing current.

Kirchhoff’s Voltage Law (KVL)

This law relates the voltages in a closed circuit of an electrical network. It is also known as Kirchhoff’s mesh law.

Kirchhoff’s voltage law states that the algebraic sum of product of current and resistance in a closed network is equal to the algebraic sum of EMFs in that closed path that is in a closed circuit.

kirchhoff's laws voltage

V1+V2 = IR1+IR2

∑V = ∑IR = 0 or ∑IR = ∑V

In other way we can say that, in a closed circuit or mesh, the algebraic sum of all the EMFs plus the algebraic sum of products of currents and resistances is zero.

∑V + ∑IR = 0