Kirchhoff’s laws


Kirchhoff’s laws are physical properties that apply to electrical circuits. These laws are named after the German physicist Gustav Kirchhoff who established them in 1845.

Both Kirchhoff’s laws are:

  • The Current law
  • The Voltage law

The purpose of these laws is to mathematically express the conservation of energy in an electric circuit. The current law and the law of the meshes are easy to understand and are part of the fundamentals to know electronics, as well as the Ohm’s law .


Current law

This important legislation in the electricity sector states that “the algebraic sum of the currents entering a node is equal to the algebraic sum of the currents that come out.” This means that if a node in the sum of the incoming electrical currents is equal to 20 amps, then the sum of outgoing electrical currents must be equal to 20 Amps also.



Diagram illustrating the current law

The above diagram shows a circuit diagram that illustrates perfectly the currant law. The current direction of this scheme is given the chance. It includes four trends:

  • I 1 coming out of node
  • I 2 entering the node
  • I 3 that enters the node
  • I 4 coming out of node

Using the law cited above, it is possible to deduce the following formula:

i1 +i4 = i2 + i3



Voltage law

The voltage law is the second law of Kirchhoff. This law is not complicated but requires rigor to avoid the blunders errors. This law states that “in a cell of a grid, the sum of tensions along the mesh is always zero.” In other words, if we made the rounds of a mesh and have added all the tension of it (being careful about the direction), the sum will be zero.


The diagram below shows a closed electrical circuit. Potential differences, also called voltage, are shown in green.The red loop represents the direction in which tensions will be listed.


Following the red loop and attention to the direction, tensions can be listed as follows:

V 1 + V 2 +  V 3 V 4 = 0

The equation below uses a positive sign when the potential difference is in the same direction as the loop in red.Similarly, voltages in the direction opposite to the red loop is added with a negative sign. Therefore, the formula can also be shown as follows:

V 1 – V 2 – V 3 – V 4 = 0



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