Kirchhoff's Law

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  • Topic: Kirchhoff's circuit laws, Charge conservation, Electromagnetism
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  • Published : March 10, 2013
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Adrian R. Managbanag
Kirchhoff’s Circuit Law

Kirchhoff's circuit laws are two approximate equalities that deal with the current and voltage in electrical circuits. They were first described in 1845 by Gustav Kirchhoff. This generalized the work of Georg Ohm and preceded the work of Maxwell. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws (see also Kirchhoff's laws for other meanings of that term).

Both of Kirchhoff's laws can be understood as corollaries of the Maxwell equations in the low-frequency limit -- conventionally called "DC" circuits. They serve as first approximations for AC circuits.

Kirchhoff’s Current Law

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:

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:


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

This formula is valid for complex currents:


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).

Kirchhoff’s Voltage Law

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...
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