Gustav Kirchhoff

1824-1887

The German physicist who wrote down the two bookkeeping rules for circuits (currents balance at every node, voltages sum to zero around every loop) that turn a tangle of components into solvable equations.

Gustav Robert Kirchhoff was born in 1824 in Königsberg, Prussia, the son of a lawyer. He studied at the University of Königsberg, where he sat in the famous mathematics-physics seminar run by Carl Jacobi and Franz Neumann. He was barely out of his student years when he did the work that puts him in every electronics course. In 1845, still a student completing a seminar exercise, he formulated his two circuit laws. That exercise later became his doctoral thesis.

The two laws are deceptively simple. Kirchhoff's current law says that at any junction (node) in a circuit, the current flowing in equals the current flowing out, because charge has nowhere else to go. His voltage law says that if you add up all the voltage rises and drops around any closed loop, they cancel to zero, because you end up back where you started at the same potential. Together with Ohm's law, these two rules are enough to solve essentially any circuit of resistors and sources, no matter how tangled.

Kirchhoff did far more than circuits. He calculated that a signal in a resistanceless wire travels at the speed of light, decades before that connection was fully appreciated. Teaming up with the chemist Robert Bunsen, he built better spectroscopes and used them to read the composition of the Sun from its light, discovering the elements caesium and rubidium in the process. He coined the term black body, and his law of thermal radiation pointed Max Planck straight toward quantum theory. He even proved a theorem in graph theory, the matrix-tree theorem, that grew out of his circuit work.

When you analyze any non-trivial circuit (a sensor front end, a power rail with several loads, a bridge network), you are doing Kirchhoff's bookkeeping. Node-voltage and mesh-current methods, the backbone of every circuit simulator including SPICE, are just systematic ways of writing his current and voltage laws as equations and solving them. He gave electronics the grammar that lets you reason about a whole network instead of one component at a time.

Fun facts

Kirchhoff worked out his two circuit laws while he was still a student, as a class exercise. The same piece of homework that grade-school engineers now memorize became his actual doctoral thesis a couple of years later.
When he and Bunsen used spectroscopy to identify gold in the Sun, his banker scoffed that gold in the Sun was useless if you could not bring it to Earth. Kirchhoff then won the Rumford Medal (paid in gold sovereigns), deposited the coins with that same banker, and said: here is gold from the Sun.
He had a remarkable roster of students who became giants in their own right, including Max Planck and Heinrich Hertz. He is buried in Berlin just a few meters from the graves of the Brothers Grimm.