Kirchhoff's Junction Rule

A junction is a point where circuit branches meet. Charge does not pile up at an ordinary steady-current junction, so charge must leave as quickly as it arrives.

If 7 amperes enter a junction altogether and one outgoing branch carries 1 ampere, the other outgoing branches must carry 6 amperes altogether.

Kirchhoff's junction rule, also called the current law, relates currents at any node of a circuit. It is a direct consequence of conservation of charge.

From charge conservation to current conservation

Current is the rate of charge flow, I=dQ/dt. If a junction does not continuously store charge, the rate at which charge enters must equal the rate at which it leaves.

Using signed currents, the same statement becomes an algebraic sum.

Choosing a sign convention

One convenient convention is to treat currents entering a junction as positive and currents leaving as negative. Reversing every sign also works, provided the choice is consistent within the equation.

Current directions can be assumed before solving. If the result for an assumed current is negative, the magnitude is correct but the actual direction is opposite to the arrow.

Worked junction example

Currents of 5 A and 2 A enter a junction, while 1 A and an unknown I leave.

The total incoming current is 7 A and the total outgoing current is also 7 A, so charge does not accumulate.

Example with a negative result

Suppose I1=3 A enters, I2=5 A leaves, and I3 is assumed to leave.

The negative sign shows that I3 actually has magnitude 2 A entering the junction.

Junctions in a network

In a circuit with several nodes, junction equations are combined with loop equations and component relations such as V=IR. Not every node equation is independent because overall charge conservation can make one equation follow from the others.

For a network containing N nodes, at most N−1 independent junction equations are normally needed.

Physical meaning during steady current

Electrons may slow, speed up or change direction microscopically near a junction, but the macroscopic rate of charge flow remains balanced. Otherwise charge would accumulate, change the local electric field and rapidly adjust the currents.

Exam-ready method

• Mark each current arrow clearly.
• Choose one junction and one sign convention.
• Write ΣIin=ΣIout or the signed form ΣI=0.
• Substitute values with signs before rearranging.
• Interpret a negative result as reversed direction.
• Check that incoming and outgoing current totals match in the final answer.