Kirchhoff's laws

Kirchhoff's laws are two fundamental conservation laws that govern electrical circuits. Kirchhoff's current law (KCL) states that the algebraic sum of currents entering any node in a circuit equals zero — an expression of the conservation of electric charge. Kirchhoff's voltage law (KVL) states that the algebraic sum of voltages around any closed loop equals zero — an expression of the conservative nature of the electrostatic field. These laws are not engineering approximations; they are the macroscopic manifestation of Maxwell's equations under the quasi-static assumption, and they form the foundation upon which both nodal analysis and mesh analysis are built. The laws apply universally to any lumped-parameter circuit, regardless of linearity, and their applicability marks the boundary between lumped and distributed circuit theory.