Emerging Technologies › Robotics and Hardware · Feature · Practical STEM, Part 5
Kirchhoff's two rules: the Königsberg student inside every device you own
In 1845, a 21-year-old student at Königsberg's university wrote down two simple rules about electric circuits. Every phone, laptop, car and power grid is still designed with them.
Open any electronic device and you will find a circuit board crowded with tiny parts. How do engineers know what current flows through each one? They follow two rules written by a student from Königsberg.
The student
Gustav Robert Kirchhoff was born in Königsberg in 1824. He studied at the city’s university, the Albertina, under the physicist Franz Neumann. In 1845, while still a student, he published the circuit laws that carry his name.
Rule one: what flows in must flow out
At any junction in a circuit, the current flowing in equals the current flowing out. Electric charge does not pile up or vanish. Think of water pipes: if three litres a second flow into a joint, three litres a second must flow out.
Rule two: every round trip comes back to zero
Go around any closed loop in a circuit, adding up the voltage gains and drops, and the total is zero. Think of a hiking trail that ends where it began: however many hills you climb, you finish at the same height you started.
With these two rules, any circuit — however complex — becomes a set of equations that can be solved.
Where they run today
- Chip design. Simulation software checks circuits by solving Kirchhoff’s equations before a chip is ever made.
- Power grids. Operators use the same rules to balance electricity across regions and to plan for faults.
- Electric vehicles. Battery systems track currents through hundreds of cells to keep them safe.
Kirchhoff did not stop at circuits. With Robert Bunsen, he showed that each chemical element gives off its own pattern of coloured light. Their spectroscope revealed two new elements, caesium and rubidium, and later helped astronomers learn what the Sun is made of.
The practical lesson
Kirchhoff’s laws are really about accounting: nothing appears from nowhere, and nothing disappears. That habit — follow the flow, and check that everything balances — works far beyond electronics. Budgets, supply chains and project plans all improve when you ask Kirchhoff’s two questions: Does everything that comes in go somewhere? Does every loop close?
Try it yourself
A battery feeds a junction that splits into two wires. One carries 0.3 amperes. The total from the battery is 0.5 amperes. What flows in the other wire? (Answer: 0.2 amperes — rule one.)
Sources: Kirchhoff, Annalen der Physik und Chemie 64 (1845) · Kirchhoff and Bunsen, “Chemische Analyse durch Spectralbeobachtungen,” Annalen der Physik (1860) · Nagel, SPICE2 (UC Berkeley, 1975).
How this story was made: drafted by Luise Hönig (Virtual Contributor), completed by Viktoria Kaiser, approved by Yoshihiro Horiuchi, Editor-in-Chief.
How this story was made: drafted by Luise Hönig (Virtual Contributor), completed by Viktoria Kaiser, approved by Yoshihiro Horiuchi, Editor-in-Chief.