KIRCHHOFF’S CURRENT LAW

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 (Fig. 1).
In a network of water pipes that does not leak and into which no water is added along the way, the total number of cubic meters going in has to be the same as the total volume going out. Water cannot form from nothing, nor can it disappear, inside a closed system of pipes. Charge carriers, thought Kirchhoff, must act the same way in an electric circuit.

Fig. 1. Kirchhoff’s current law. The current entering point Z is equal to the current leaving point Z. In this case, I₁ + I₂ = I₃ + I₄ + I₅.