Kirchoff’s Circuit Laws

Gustav Kirchhoff formulated a number of principles or laws, which fall into three basic categories: electrical circuits, spectroscopy and thermochemistry.

Kirchhoff proposed two electrical circuit laws. His current law states that in a network of conductors meeting at a single point (called a “node”) the algebraic sum of the currents is zero. The voltage law states that in a closed circuit, the polar sum of all voltages is zero.

It is remarkable that Kirchhoff conceived these laws, today ubiquitous in electrical engineering, in 1845 at the age of 21, while still an undergraduate student. Later, they became the basis for his doctoral dissertation.

The circuit laws are a consequence of Ohm’s law, in no way conflicting with it. However, they greatly simplify the analysis of complex circuits, where there are multiple power sources and series/parallel loads and branching current paths. Moreover, the laws, especially the current law, are invaluable in troubleshooting faulty circuits and equipment and in visualizing the behavior of prototypes while in the design phase.

Kirchhoff came after Georg Ohm and before James Clerk Maxwell, and he may be seen as a vital link between them. Kirchhoff’s current law can be expressed in the form of a matrix, making possible most circuit simulation software, notably Simulation Program with Integrated Circuit Emphasis (SPICE).

Kirchhoff’s current and voltage laws are not applicable at high frequencies, although for the most part they are good for 50 and 60-Hz power circuits. The applicable frequency range of the current law can be extended if the circuitry includes parasitic capacitances along conductors. The voltage law likewise becomes increasingly problematic as the frequency rises because of the fluctuating magnetic field that links the closed loops. Here again, high-frequency performance of the voltage law can be extended by calculating parasitic inductances and representing them as virtual circuit elements.

Kirchhoff was a versatile researcher and theoretician. In addition to his electrical circuit theorems and other laws, he originated the concept of black-body radiation. This is the energy that is emitted by a non-reflective and non-absorptive object that is in thermal equilibrium with the surrounding environment. Black holes are substantially perfect black bodies because they absorb nearly all the radiation they encounter.

The notion of black-body radiation revealed some contradictions in classical physics, which were ultimately resolved by the introduction, long after Kirchhoff’s time, of quantum mechanics.