Glossary term
Kirchhoff Laws
Two circuit laws expressing conservation of charge at nodes and conservation of energy around closed loops.
Definition
lawKirchhoff laws are circuit laws stating that currents sum to zero at a node and voltages sum to zero around a closed loop.
Kirchhoff's current law follows conservation of charge: the algebraic sum of currents entering and leaving a node is zero. Kirchhoff's voltage law follows conservation of energy in lumped circuits: the algebraic sum of voltage rises and drops around a closed loop is zero. Together with device laws such as Ohm's law and capacitor or inductor relations, they form the basis of circuit analysis.
Kirchhoff laws provide the structural equations for electrical circuits. They do not describe a particular component. Instead, they describe how currents and voltages must relate in a connected network.
Kirchhoff current law
Kirchhoff current law, or KCL, states that the algebraic sum of currents at a node is zero:
Equivalently, current entering a node equals current leaving it. This follows from conservation of charge. If charge is not accumulating at the node, current cannot disappear or appear from nowhere.
Kirchhoff voltage law
Kirchhoff voltage law, or KVL, states that the algebraic sum of voltage rises and drops around a closed loop is zero:
This expresses conservation of energy in a lumped circuit loop. The energy gained by a charge through sources is balanced by energy lost across loads, resistors, and other elements.
Engineering use
KCL is the basis of nodal analysis, where node voltages are the unknowns. KVL is the basis of mesh analysis, where loop currents are the unknowns. Combined with Ohm’s law, impedance relations, capacitance, inductance, and source models, Kirchhoff laws allow engineers to solve DC circuits, AC steady-state circuits, transient circuits, bridge circuits, filters, power networks, and electronic amplifiers.
Limitations
Kirchhoff laws assume the lumped-circuit approximation. At high frequency, large physical dimensions, fast transients, or strong electromagnetic coupling, voltage and current may vary along conductors, and transmission-line or full electromagnetic models may be needed. KVL can also require care in loops linked by time-varying magnetic flux, where induced electric fields are not captured by a simple lumped voltage sum unless modeled explicitly.
Common mistakes
A common mistake is using inconsistent sign conventions. The laws work only when current directions and voltage polarities are assigned consistently. Another mistake is applying ideal wire assumptions to circuits where lead resistance, parasitic inductance, capacitance, grounding, or measurement loading is significant.