What rule says that the total current entering an electrical junction equals the total current leaving it?

Kirchhoff’s current law says that the total current entering an electrical junction equals the total current leaving it.

The rule follows from conservation of electric charge. Charge cannot accumulate indefinitely at an ordinary circuit junction, so the algebraic sum of currents at that node is zero. Currents entering can be assigned one sign and currents leaving the opposite sign.

Gustav Kirchhoff published his circuit laws in 1845. Kirchhoff’s current law is especially useful in circuits with branches, where current divides and later recombines. For example, if 5 amperes enter a junction and 2 amperes leave through one branch, 3 amperes must leave through the remaining branches combined.

The law is an ideal circuit approximation in standard circuit analysis. At very high frequencies or in situations involving significant charge accumulation, electromagnetic field effects may require a more complete treatment.