Kirchhoff's circuit laws

Lore & Background

Kirchhoff's current law, also called Kirchhoff's first law or junction rule, states that for any node in an electrical circuit, the sum of currents flowing into that node equals the sum of currents flowing out. Equivalently, the algebraic sum of currents meeting at a point is zero. This law can be viewed as an extension of the conservation of charge, relying on the fact that net charge in wires and components is constant. Kirchhoff's voltage law, also called his second law or loop rule, states that the directed sum of potential differences around any closed loop is zero. In the low-frequency limit, this is a corollary of Faraday's law of induction.

Reader's Guide

Kirchhoff's circuit laws form the basis for network analysis and are accurate for DC circuits and for AC circuits at frequencies where wavelengths are very large compared to the circuits. They can be understood as corollaries of Maxwell's equations in the low-frequency limit. The current law is used with Ohm's law to perform nodal analysis, and a matrix version of the current law is the basis of most circuit simulation software, such as SPICE. The laws are applicable to any lumped network irrespective of whether it is unilateral or bilateral, active or passive. However, they depend on the lumped-element model being applicable; when the model is not applicable—such as in high-frequency AC circuits where charge density in conductors changes constantly or where time-varying magnetic fields are not confined—the laws do not apply. Real circuits can be modeled using parasitic components to extend the laws' applicability.

Did You Know?

• Kirchhoff's circuit laws were originally obtained from experimental results.
• The current law relies on the fact that the net charge in the wires and components is constant.
• A matrix version of Kirchhoff's current law is the basis of most circuit simulation software, such as SPICE.
• In the low-frequency limit, the voltage law is a corollary of Faraday's law of induction.