Skip to content
Marlbridge

AP® Physics C: Electricity and Magnetism · Unit 11 · Topic 11.6

Kirchhoff's Loop Rule: Revision Notes (Physics C: E&M 11.6)

One-page recap of Kirchhoff's loop rule: energy and potential round a loop, the sign convention, loop equations and potential-against-position graphs.

Short on time? This page is the recap. For the figures, the graph and the worked examples, use the full study guide.

Recap

  • A charge moving through a potential difference ΔV changes its electric potential energy by ΔU_E = qΔV.
  • Every point in a steady circuit has one value of potential. Go once round a closed loop and you return to the same potential, so the potential differences add to zero.
  • That is Kirchhoff’s loop rule, and it is a statement of energy conservation: energy gained from sources equals energy transferred in the other elements.
  • The rule holds for every closed loop, including loops through branches and meters.
  • Only potential differences are physical. You may choose any point as V = 0.

Key relationships

Quantity Relationship
Energy change of a charge ΔU_E = qΔV
Loop rule ΣΔV = 0 round a closed loop
Single loop, real battery I = ℰ/(r + ΣR)
Battery delivering current ΔV_terminal = ℰ − Ir
Battery being charged ΔV_terminal = ℰ + Ir
Crossing… ΔV
resistor with the assumed current −IR
resistor against the assumed current +IR
battery, − to + +ℰ
battery, + to − −ℰ
ideal wire 0

Potential-against-position graphs

  • Rise of ℰ across a source (crossed − to +).
  • Straight-line fall of IR across a uniform resistor, in the direction of the current.
  • Flat along ideal wires.
  • Ends at the level where it started.

Mistakes to avoid

  1. Switching walking direction half-way round a loop.
  2. Giving a battery −ℰ when crossing it from − to +.
  3. Treating a negative current as an error.
  4. Drawing a drop along a wire on the potential graph.
  5. Forgetting internal resistance when the battery is not ideal.
  6. A graph that does not close.

Quick self-check

  1. A loop has a 12 V ideal battery and resistors with 5.0 V and 4.5 V across them, plus one more resistor. What is the potential difference across the last one? (2.5 V)
  2. You walk through a resistor against the current I. What term do you write? (+IR)
  3. A loop equation gives I = −0.40 A. What does this tell you? (The current is 0.40 A in the opposite direction to the one assumed)
  4. On a potential graph, what does a flat section show? (An ideal wire: no potential difference)

Next: practice questions.

AP® and Advanced Placement® are trademarks registered by the College Board, which is not affiliated with, and does not endorse, this website. Marlbridge is an independent tuition provider. It is not an authorized AP course provider, an AP school or an exam centre, and these resources are not official College Board materials. Reading them or doing simulations does not meet the laboratory requirement of an AP science course.