Kirchhoff’s Junction Rule
Kirchhoff’s junction rule is conservation of charge in a steady circuit: the total current entering a junction equals the total current leaving it. Current splits among branches and recombines; it is not consumed by circuit elements.
Kirchhoff’s Junction Rule: quick answer
Kirchhoff’s junction rule is conservation of charge in a steady circuit: the total current entering a junction equals the total current leaving it. Current splits among branches and recombines; it is not consumed by circuit elements. The junction rule is the steady-state statement that charge does not continuously pile up at a node. It is therefore a conservation equation for branch currents, and it works together with loop relationships when a network has several unknown currents.
The junction rule constrains current, not voltage. Apply it at nodes in steady-state circuits and combine it with loop or element relationships when more than one unknown branch current remains.
What you should be able to explain and do
Use these as closed-note retrieval prompts before looking at worked examples.
Apply ΣI_in=ΣI_out at a junction.
Choose and maintain a signed-current convention.
Explain current splitting and recombination using charge conservation.
Combine junction equations with loop/element equations in compound circuits.
Key terms you need for this lesson
Definitions stay beside the circuit model so unfamiliar terminology does not break the reasoning chain.
junction
junction is a node where three or more branch paths meet.
branch current
branch current is the current assigned to one path between junctions or nodes.
charge conservation
charge conservation is the principle that electric charge cannot be created or destroyed in an isolated accounting of a circuit node.
steady state
steady state is a condition in which macroscopic circuit quantities no longer change with time.
current splitting
current splitting is division of incoming current among two or more outgoing branches.
current recombination
current recombination is addition of branch currents when paths merge at a junction.
Know what each relationship means and when it applies
The relationship, variables, topology condition, and physical anchor belong together.
| Relationship / model | Variables & units | When to use it | Physical anchor |
|---|---|---|---|
ΣI_in = ΣI_out | I branch currents (A) | steady-state junction | 3 A entering and 1 A leaving one branch requires 2 A to leave through the remaining branch |
ΣI_signed = 0 | I signed branch currents (A) | algebraic node equation with a consistent sign convention | take entering currents positive and leaving currents negative, or vice versa |
I_total = I_1 + I_2 + … | I_total and branch currents (A) | current splitting or recombining at a junction | source current equals the sum of parallel-branch currents |
What a strong circuit diagram or graph must show
Translate the same physical model among topology, arrows, graphs, equations, and energy/charge reasoning.
Junction arrow diagram
mark every branch-current direction before writing the equation.
Signed equation
assign one sign to entering currents and the opposite sign to leaving currents.
Parallel-network current map
source current equals the sum of branch currents.
Charge-accounting picture
steady state means no continuing net charge accumulation at the node.
Change one circuit condition and inspect what responds
Make a prediction before moving a control, then explain the output using topology, conservation, or the governing relationship.
Two examples with the model choice shown
The solution exposes the circuit reasoning pathway rather than only the arithmetic.
Three-branch junction
Situation: A 5.0 A current enters a junction. One outgoing branch carries 1.5 A.
Reasoning: Charge conservation requires total current leaving to equal total current entering.
The other outgoing branch carries 3.5 A.
Assumed direction comes out negative
Situation: A branch current is assumed to leave a node while solving simultaneous circuit equations; the solution gives I=−0.80 A.
Reasoning: The algebra is valid; the negative sign means the actual current is opposite the assumed arrow.
The branch current has magnitude 0.80 A and actually enters the node.
Recognize the physics before reaching for an equation
Use the cue to choose the model, connect it to nearby ideas, then reject any method whose assumptions do not match the situation.
What should trigger Topic 11.7?
Use the junction rule when current splits or recombines at a node and charge cannot accumulate there in steady operation.
How this idea fits the course
Combine this charge-conservation rule with the energy-conservation loop rule in 11.6 to solve multi-loop networks.
Scope check before solving
The junction rule constrains current, not voltage. Apply it at nodes in steady-state circuits and combine it with loop or element relationships when more than one unknown branch current remains.
Turn this topic into measurable evidence
Choose variables and meters that test the intended relationship without accidentally changing the circuit model.
Investigation target
Measure branch currents before and after a junction to test current conservation.
Reasoning errors to eliminate
Repair the circuit model before doing more arithmetic.
Six things you should be able to do before moving on
Use these as closed-note transfer prompts.
- I can identify the circuit topology before applying series/parallel formulas.
- I can define every electrical quantity and give its SI unit.
- I can distinguish charge conservation at junctions from energy conservation around loops.
- I can interpret current, potential, resistance, and power from a graph or schematic.
- I can place ideal meters correctly and predict qualitative loading effects of nonideal meters.
- I can design or critique a circuit experiment and justify a claim from measured evidence.
Practice is kept on its dedicated pages
Finish the lesson first. Then open the separate topic bank when you want exam-style practice without replacing the teaching content above.
42 multiple-choice questions
Use the exact-topic MCQ bank to test model selection, representations, calculations and boundaries after learning the concept.
Open 42 Topic MCQs4 multipart free-response tasks
Use the exact-topic FRQ set for mathematical, representation, experimental and qualitative/quantitative reasoning.
Open 4 Topic FRQsTopic 11.7 FAQs
What is Kirchhoff’s junction rule?
The total current entering a steady-state junction equals the total current leaving it.
Why is the rule true?
It follows from conservation of electric charge.
Does current get smaller after a resistor?
Not merely because of the resistor. In a single unbranched steady path the same current enters and leaves the resistor.
Can a solved current be negative?
Yes. It means the actual direction is opposite the arrow you assumed.
How is the junction rule used with parallel branches?
The current before a split equals the sum of currents in the branches, and the branch currents recombine afterward.
Do I still need the loop rule?
Often yes. Junction equations constrain current conservation; loop equations constrain energy/potential changes.