Kirchhoff's laws

Definition

Kirchhoff's two laws are the bookkeeping rules of circuits: charge can't pile up at a junction, and energy can't appear or vanish going around a loop.

$\sum I = 0,\quad \sum V = 0$

Technical definition

The current law (KCL): the sum of currents entering a node equals the sum leaving (ΣI = 0). The voltage law (KVL): the sum of voltage changes around any closed loop is zero (ΣV = 0). Together they solve any circuit.

Example

At a junction where 2 A arrives and branches carry 1.2 A and 0.8 A away, KCL checks out: 2 = 1.2 + 0.8. Around a loop with a 9 V battery and drops of 5 V and 4 V, KVL checks out: 9 − 5 − 4 = 0.

Common confusion

Kirchhoff's laws do not say current is 'used up' by components. Current is the same all around a series loop — what gets 'used' is voltage (energy per charge), which drops across each component and sums to the battery's voltage.