Which law states that the current through a node equals the current entering it?

Kirchhoff’s current law states that the current entering an electrical node equals the current leaving it.

The law 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. Engineers often assign entering currents positive signs and leaving currents negative signs, or use the reverse convention consistently.

Gustav Kirchhoff published his circuit laws in 1845 while developing methods for analyzing electrical networks. The current law is also called Kirchhoff’s first law or Kirchhoff’s junction rule.

The companion rule, Kirchhoff’s voltage law, applies around a complete closed loop and follows from conservation of energy. These rules allow unknown currents and voltages to be calculated in circuits containing multiple branches, even when a simple series or parallel formula is insufficient.