11.7 Kirchhoff’s Junction Rule

Kirchhoff’s junction rule is a consequence of conservation of charge. It states that the total current entering a junction equals the total current leaving the junction:

Charge cannot pile up indefinitely at an ordinary circuit junction in steady state, so whatever current flows in must flow out. This rule is crucial in multibranch circuits where current splits and recombines.

This rule can be viewed as a rate statement. Since current is ${dq/dt}$, conservation of charge says the rate at which charge arrives at a junction must equal the rate at which it leaves. If not, the amount of charge at the junction would change with time, which does not happen in a steady-state circuit. So the junction rule is the current version of continuity.