3.7 Kirchhoff's Junction Rule

Charge Can't Pile Up

Kirchhoff's Junction Rule states that the total current entering a junction (node) equals the total current leaving it. This follows from conservation of charge: charge can't accumulate or disappear at a point in a steady-state circuit. A junction is any point where three or more wires meet.

Applying the Rule

Write it as ΣI_in = ΣI_out. Assign current directions arbitrarily; if a value comes out negative, the actual current flows opposite to your assumption. This rule, paired with Kirchhoff's Loop Rule, lets you solve for unknown currents in complex circuits with multiple branches and junctions.

Why It Matters

In parallel circuits, the junction rule explains why current splits among branches but the sum of branch currents equals the total current from the source. It's essential for analyzing circuits that can't be reduced to simple series/parallel combinations, such as Wheatstone bridges or multi-loop networks.

Key terms

Kirchhoff's Junction Rule

The total current entering a junction equals the total current leaving it; ΣI_in = ΣI_out.

Junction (node)

A point in a circuit where three or more wires/branches meet.

Physical basis of the Junction Rule

Conservation of charge — charge cannot build up or disappear at a point in a steady-state circuit.

Negative current result

Indicates the actual current direction is opposite to the arbitrarily assumed direction; magnitude is still correct.

Junction Rule in parallel circuits

The sum of currents in all parallel branches equals the total current supplied to the junction.

Try an AP-style question

What is the equivalent resistance of 6 Ω and 3 Ω in parallel?

1. 4.5 Ω
2. 2 Ω
3. 9 Ω
4. 18 Ω