Kirchhoff's Junction Rule

Picture a point in a circuit where three wires meet: a node. Charge doesn't appear or vanish there, and it doesn't stack up there either. Whatever amount of charge flows in every second has to flow out every second, split among whatever branches leave the node. That statement, current in equals current out, is Kirchhoff's junction rule.

The reasoning behind it is charge conservation, the same law that says you can't create or destroy electric charge. Current is just charge per second passing a point. If more charge arrived at a node than left it, that extra charge would have to sit there, building up a growing electric field. That field would immediately push charge onward and out, faster, until the books balance again. So in practice the imbalance never gets a chance to show up: at every instant, sum of currents in equals sum of currents out.

The junction rule is one of two tools for solving circuits with multiple branches, the other being Kirchhoff's loop rule for voltage around a closed path. Together they let you write one equation per node and one per loop, enough equations to solve for every unknown current in a resistor network. The junction rule alone is often enough whenever branches simply split and recombine, like finding how current divides between two resistors in parallel.