Kirchhoff's Current Law (Node with Three Branches)

The node rule is the charge-conservation twin of the loop rule: charge cannot pile up at a junction, so whatever flows in must flow out. Ten amps arriving at a splice feeding three branches, two of which are carrying 2.5 A and 3.5 A, leaves exactly 4 A for the third. No knowledge of the loads is needed, which is what makes it so useful — it is a constraint you get for free before any analysis begins.

The classic mistake is treating current as something a source "sends" to a load rather than something that circulates. A branch drawing less current does not leave the surplus somewhere; the source simply produces less. That is why removing a lamp from a parallel lighting circuit dims nothing else, and why removing one from a series string kills everything: the series case has one node current, so it is KCL that says they all must be equal.

In the field this is the arithmetic behind every panel schedule and every neutral calculation. It is also the basis of nodal analysis, the method every circuit simulator actually runs — SPICE writes one KCL equation per node, solves the matrix, and never touches KVL at all. And the counter-intuitive part for electricians: on a balanced three-phase four-wire system, three currents of 100 A each sum to zero in the neutral, because KCL sums phasors, not magnitudes.