Kirchhoff’s current law – KCL

Kirchhoff’s current law (KCL) also called Kirchhoff’s first law or Kirchhoff’s junction law states that the sum of currents entering a node in a network is equal to the sum of currents leaving the node. It can also be stated as the algebraic sum of currents at a node is zero.

Here node is a junction of two or more circuit elements connected in a circuit.

Example: consider the following single node network consisting three elements connected to a single node n.

single node network

The i₁ and i₂ are the entering currents and i₃ is the leaving current. The entering currents are indicated by positive value and leaving currents are indicated by negative value. Thus the KCL equation for the node n can be written as,

i₁ + i₂ - i₃ = 0

⇒ i₁ + i₂ = i₃

Law of conservation of electric charge

Kirchhoff’s current law (KCL) is based on the law of conservation of electric charge.

Consider the above equation

i₁ + i₂ = i₃

⇒ \[\frac{dQ_{1}}{dt}+\frac{dQ_{2}}{dt}=\frac{dQ_{3}}{dt}\]

⇒ Q₁ + Q₂ = Q₃.