Notes

This law is also called Kirchhoff's first law, Kirchhoff's point rule, or Kirchhoff's junction rule (or nodal rule).

The principle of conservation of electric charge implies that:

At 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 stated as:

k1n Ik 0
n is the total number of branches with currents flowing towards or away from the node.

This formula is valid for complex currents:

k1n Ik 0
The law is based on the conservation of charge whereby the charge (measured in coulombs) is the product of the current (in amperes) and the time (in seconds).

Uses Edit
A matrix version of Kirchhoff's current law is the basis of most circuit simulation software, such as SPICE. Kirchhoff's current law combined with Ohm's Law is used in nodal analysis.

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

Kirchhoff's voltage law (KVL) Edit


The sum of all the voltages around a loop is equal to zero.
v1 + v2 + v3 - v4 = 0
This law is also called Kirchhoff's second law, Kirchhoff's loop (or mesh) rule, and Kirchhoff's second rule.

The principle of conservation of energy implies that

The directed sum of the electrical potential differences (voltage) around any closed network is zero, or:
More simply, the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop, or:
The algebraic sum of the products of the resistances of the conductors and the currents in them in a closed loop is equal to the total emf available in that loop.
Similarly to KCL, it can be stated as:

k1n Vk 0
Here, n is the total number of voltages measured. The voltages may also be complex:

k1n Vk 0
This law is based on the conservation of energy whereby voltage is defined as the energy per unit charge. The total amount of energy gained per unit charge must be equal to the amount of energy lost per unit charge, as energy and charge are both conserved.