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AP® Physics 2: Algebra-Based · Unit 11 · Topic 11.7

Kirchhoff's Junction Rule: Revision Notes (Physics 2 11.7)

One-page recap of the junction rule: current in equals current out, why it follows from charge conservation, assumed directions, branches and combining it with the loop rule.

Short on time? This page is the recap. For explanations, Figures 1–2 and the worked examples, use the full study guide.

Recap

  • A junction is a point where three or more wires meet. A branch is the path between two junctions.
  • Junction rule: the charge entering a junction per second equals the charge leaving it per second.
  • It follows from conservation of charge. If charge built up at a junction, the currents would change until it stopped, so a steady circuit has no build-up.
  • The loop rule (Topic 11.6) is energy conservation. The junction rule is charge conservation. Most branched circuits need both.
  • The rule also works for a closed boundary drawn around any part of a steady circuit.

Key relationships

Relationship Meaning Use it to
ΣI_in = ΣI_out currents in A; in = out at a junction find an unknown current at a junction
I = ΔQ/Δt charge per second link the junction rule to charge
same I through every element in a branch no junction inside a branch find currents in series elements
ΔV the same across parallel branches, so I = ΔV/R less R, more I decide how current splits

Assumptions behind the numbers

  • Currents are steady (constant in time). Topic 11.8 deals with changing currents.
  • Batteries, wires and meters are ideal unless the question says otherwise.
  • Only one battery, or batteries in the same branch. Two batteries with different emfs wired in parallel are outside the course.

Mistakes to avoid

  1. Saying current is used up by a bulb or resistor.
  2. Splitting current equally between branches that are not identical.
  3. Sending more current through the larger resistance.
  4. Dropping a minus sign. A negative answer means the current flows opposite to your arrow.
  5. Writing the same junction equation twice and thinking you have two equations.
  6. Mixing up the rules: junctions are about current, loops are about potential difference.

Quick self-check

  1. At a junction, 4.0 A enters along one wire and 2.5 A leaves along a second wire. What does the third wire carry? (1.5 A, leaving the junction)
  2. An ideal 6.0 V battery is connected across a 4.0 Ω resistor and a 12 Ω resistor in parallel. Find the current in each and in the battery. (1.5 A, 0.50 A, 2.0 A)
  3. Which conservation law is behind the junction rule? (Conservation of electric charge)

Next: practice questions.

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