Kirchhoff's current law

This law, also called Kirchhoff's first law, Kirchhoff's point rule, or Kirchhoff's junction rule (or nodal rule), states that, for any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node; or equivalently:

The algebraic sum of currents in a network of conductors meeting at a point is zero.

Recalling that current is a signed (positive or negative) quantity reflecting direction towards or away from a node, this principle can be succinctly stated as:

where n is the total number of branches with currents flowing towards or away from the node.

Kirchhoff's circuit laws were originally obtained from experimental results. However, the current law can be viewed as an extension of the conservation of charge, since charge is the product of current and the time the current has been flowing. If the net charge in a region is constant, the current law will hold on the boundaries of the region. This means that the current law relies on the fact that the net charge in the wires and components is constant.

Uses

A matrix version of Kirchhoff's current law is the basis of most circuit simulation software, such as SPICE. The current law is used with Ohm's law to perform nodal analysis.

The current law is applicable to any lumped network irrespective of the nature of the network; whether unilateral or bilateral, active or passive, linear or non-linear.