Kirchoff's Laws

Kirchhoff's Laws Of electric circuits; in any network of wires the sum of all the currents going into a junction is the same as the sum of all the currents going out (junction theorem). In a closed circuit, or loop, the sum of the emfs is equal to the sum of the voltages across each of the Resistances (loop equation).

Kirchhoff's circuit laws are a pair of laws that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws.

Both circuit rules can be directly derived from Maxwell's equations, but Kirchhoff preceded Maxwell and instead generalized work by Georg Ohm.

Source : wikipedia