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Kirchhoff’s Law

Updated on September 16, 2015

Kirchhoff’s Law

Kirchoff's law is one of the most basic electrical principles. Kirchhoff’s law allow calculation of the currents, voltages, and resistances of electrical networks. Gustav Kirchhoff made this remarkable contribution in 1845. He extended the theory of the German physicist Georg Simon Ohm and generalized the equations describing current flow to the case of electrical conductors in three dimensions.


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).

According to this law, ”In any network, algebraic sum of currents from various branches meeting at a point is always zero”.

That is, sum of the currents entering any node is equal to the sum of the currents leaving that node. Node is the meeting point of two or more branches.

Even simpler, sum of the current at any point of a circuit is zero.

It is not a safe assumption for AC circuits.

∑I(at any node) = Zero

From the diagram:

The sum of the incoming currents I1 and I2 is equal to the sum of the out going currents I3 and I4.

Current Law

Example problem

Find the value of Ix shown in the figure:x


According to KCL sum of incoming currents is equal to the sum of the out going currents.


0.2A + Ix = 0.3A + 0.15A


Ix=0.3A + 0.15A - 0.2 A

= 0.25A

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 algebraic sum of voltage drop across the elements of any closed path of the circuit is equal to the algebraic sum of emf in the path.

∑V= Zero

From the diagram.

The sum of voltages V1 , V2 , V3 and V4 is zero

Example problem

Find the value of R in the circuit.


According to KVL,

Sum of the voltages across the elements in a closed path is zero


10V = R*2 + 2 * 2

2R = 10 – 4 = 6

Therefore R=6/2= 3

Gustav Robert Kirchhoff

Gustav Robert Kirchhoff
12 March 1824
Place of birth
Königsberg, Kingdom of Prussia
17 October 1887 (aged 63)


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