Understanding Kirchoff's Laws

Kirchoff's Laws - his current and voltage laws are key to circuit analysis and provide the basis for understanding how electrical and electronic circuits work


Kirchoff's laws Includes:
Basics of Kirchoff's Laws     Kirchoff's Current Law (First Law)     Kirchoff's Voltage Law (Second Law)    


Kirchoff's laws are key to being able to calculate how circuits will respond. While Ohm's law can describe what happens with a simple resistive network, Kirchoff's laws describe the action of a more complicated network.

Kirchoff's laws are essential to working out many networks of electronic components that can be seen in many circuits.

There are two laws which Kirchoff formulated: his first law which is also known as Kirchoff's Current Law (KCL), and Kirchoff's Second law which is also known as Kirchoff's voltage law.

Diagram showng the basics of Kirchoffs Laws: showing a closed circuit for the voltage law and a node for the current law

Who was Kirchoff?

Gustav Robert Kirchhoff was a physicist who was born in Konigsberg in what was then Prussia and this region is now Kaliningrad in Russia in 1824.

Kirchoff died in 1887 in Berlin, again, this was in Prussia, but is now in Germany.

Kirchoff undertook work in many areas of science. He is possibly most well known because he contributed to the fundamental understanding of electrical circuits by developing his laws for current and voltage in a circuit.

Kirchoff formulated these laws in 1845 when he was still a student, undertaking the work as a seminar exercise, but completing it for his doctoral dissertation.

He moved to the University of Heidelberg where he investigated elements of spectroscopy with Robert Bunsen as well as contributing to our understanding of black body radiation, even coining that term himself.

Another of his discoveries was that an electric signal moved along a resistance-less wire at the speed of light

In addition to this, he discovered the elements Caesium and Rubidium in work he undertook with Robert Bunsen.

After his death, Kirchoff was buried in the St Matthaus Kirchoff Cemetery in Schonenberg in Berlin.

Kirchoff's Laws

There are two Kirchoff's laws dealing with electrical and electronic circuit analysis. The first one, Kirchoff's first law addresses the current in a circuit and is often referred to as Kirchoff's current law. The second one, obviously called Kirchoff's second law addresses the voltages within a circuit, and similarly it is often called Kirchoff's voltage law.

A basic summary of the laws is given in the bullet points below:

  • Kirchoff's Current Law (1st Law):   This states that the current flowing into a node, i.e. a junction in a circuit is be equal to the current flowing out of it. This is a results from the charge conservation, i.e. charge cannot just appear or disappear..

  • Kirchoff's voltage law (2nd Law):   This law states that in any complete loop within a circuit, the sum of all voltages from components that supply electrical energy, i.e. cells or generators, will equal the sum of all voltage drops across the other components in the same loop. This law is a direct consequence of the conservation energy and also the conservation of charge.

Both laws, Kirchoff's current law and Kirchoff's voltage law deserve a more detailed explanation with some examples, and they will be given separately below.

Kirchoff's Current Law (1st Law)

Kirchoff's current law is the first of his laws and looks at the current flowing into and out of a junction.

The current law is important when looking at nodes within a circuit as it enables a good number of issues and problems within circuit analysis to be solved relatively easily.

The basis of Kirchoff's current law is that it uses the concept of the conservation of charge, in other words charge cannot mysteriously appear or disappear.

Accordingly the current flowing into and out of a junction must add up to zero, i.e. the same charge flows in as flows out.

Read more about . . . . Kirchoff's Current Law (First Law).

Kirchoff's Voltage Law (2nd Law)

Kirchoff's voltage law is used in many problems associated with electronic circuit analysis. Often there are loops within larger electrical or electronic circuits that need to be analysed and the voltage law provides a way of looking at these to find the answer.

Kirchoff's second law enables circuits to be analysed where Ohm's law on its own would not be able to provide the solution.

Similar to Kirchoff's current law, the voltage law states that the sum of the voltages around a look in an electrical or electronic circuit is zero.

This law is based upon both the conservation of charge and the conservation of energy.

Read more about . . . . Kirchoff's Voltage Law (Second Law).


Kirchoff's laws are at the very centre of electrical and electronic circuit analysis. They provide a way forwards for fully analysing circuits that might not be possible any other way.

Although Kirchoff's laws have been existence for many years, they are still central to electrical and electronic circuit analysis, today as much as they ever were.


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