Kirchhoff's Current Law (KCL)

Formula

Description

Kirchhoff's Current Law states that the algebraic sum of all currents entering and leaving any node (junction) in a circuit must equal zero. This is a consequence of conservation of charge: charge cannot accumulate at a node. Currents flowing into the node are conventionally positive and currents flowing out are negative (or vice versa, as long as the convention is consistent). KCL is the basis of nodal analysis, the most widely used systematic method for solving circuit equations, and is essential for understanding current distribution in parallel networks.

Variables

• I₁, I₂, I₃... — Currents at the node (A), with sign convention: positive for currents entering, negative for currents leaving

Practical Notes

Enter currents entering the node as positive and currents leaving as negative. The sum should be zero for a valid node. KCL applies to any closed boundary, not just single nodes — it can be applied to a supernode enclosing multiple components. In AC circuits, KCL applies to the phasor currents including both magnitude and phase.