Kirchhoff's Circuit Laws

Kirchhoff's circuit laws are two equations describing the conservation of charge and energy within electrical circuits, formulated by German physicist Gustav Kirchhoff in 1845 while he was still a student. Kirchhoff's current law states that the sum of currents flowing into any junction, or node, of a circuit must equal the sum of currents flowing out of it, a direct consequence of the conservation of electric charge. Kirchhoff's voltage law states that the sum of the electrical potential differences, or voltages, around any closed loop in a circuit must equal zero, a consequence of the conservation of energy. Together the two laws provide the basic rules needed to analyze the current and voltage at every point in an electrical network of arbitrary complexity, and remain a standard starting point for circuit analysis in electrical engineering education, extending Georg Ohm's earlier single-branch relationship between voltage, current, and resistance to circuits containing multiple loops and junctions.