Kirchhoff’s first law

The physicist Gustav Robert Kirchhoff (1824-1887) was a researcher and experimentalist in electricity back in the time before radio, before electric lighting, and before much was understood about how currents flow.

Kirchhoff reasoned that current must work something like water in a network of pipes, and that the current going into any point has to be the same as the current going out. This is true for any point in a circuit, no matter how many branches lead into or out of the point. Two examples are shown in Fig. 1.

Fig. 1: Kirchhoffs First Law. At A, the current into either X or Y is the same as the current out of that point: I = Il + I2. At B, the current into Z equals the current out of Z: Il + I2 = I3 + I4+ I5.