Kirchhoff’s Loop Rule
Kirchhoff’s loop rule is conservation of energy applied around a closed circuit path: the algebraic sum of potential changes around the loop is zero. A potential-versus-position graph provides the same energy accounting visually.
Kirchhoff’s Loop Rule: quick answer
Kirchhoff’s loop rule is conservation of energy applied around a closed circuit path: the algebraic sum of potential changes around the loop is zero. A potential-versus-position graph provides the same energy accounting visually. The loop rule is energy conservation per unit charge. As you traverse a closed path, ideal wires stay at one potential, sources raise or lower potential depending on traversal, and resistive elements produce potential drops or rises according to traversal relative to current.
Choose a loop traversal direction and keep signs consistent. Treat ideal wires as zero potential change; avoid adding internal-resistance models unless the problem explicitly supplies a nonideal source.
What you should be able to explain and do
Use these as closed-note retrieval prompts before looking at worked examples.
Apply ΣΔV=0 with a consistent traversal convention.
Connect qΔV to energy changes of charges moving through circuit elements.
Sketch electric potential as a function of position around a loop.
Explain why ideal-wire segments have zero potential change.
Key terms you need for this lesson
Definitions stay beside the circuit model so unfamiliar terminology does not break the reasoning chain.
loop
loop is a closed path through connected circuit elements.
potential rise
potential rise is a positive change in electric potential along the chosen traversal.
potential drop
potential drop is a negative change in electric potential along the chosen traversal.
emf
emf is energy supplied per unit charge by an idealized source.
loop rule
loop rule is the statement that signed potential changes around any closed loop sum to zero.
potential-position graph
potential-position graph is a graph showing electric potential at successive positions as one moves around a circuit loop.
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 |
|---|---|---|---|
ΣΔV_loop = 0 | ΔV signed potential changes (V) | any closed loop in the lumped circuit model | source rises and resistor drops sum to zero |
ΔU_E = qΔV | ΔU_E electric potential-energy change (J); q charge (C); ΔV potential change (V) | connecting loop potential changes to energy per charge | a positive charge gains electric potential energy when it moves through a potential rise |
ideal wire: ΔV = 0 | ΔV potential difference (V) | points connected only by an ideal wire | all points on one ideal-wire node share the same potential |
What a strong circuit diagram or graph must show
Translate the same physical model among topology, arrows, graphs, equations, and energy/charge reasoning.
Signed loop equation
write each element’s potential change in traversal order.
Potential-position graph
horizontal on ideal wires; step up/down across idealized elements.
Energy-per-charge picture
source transfers energy to charges; resistive elements transfer it out of electrical form.
Multi-loop map
choose independent loops without changing the underlying node currents.
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.
One-loop circuit
Situation: A 12 V ideal battery drives two series resistors, 4 Ω and 2 Ω.
Reasoning: Rtotal=6 Ω, so I=2 A. The resistor drops are 8 V and 4 V. Around the loop: +12−8−4=0.
The loop rule is satisfied and the potential returns to its starting value.
Potential graph
Situation: Starting at the negative battery terminal, traverse an ideal battery then two resistors in the current direction.
Reasoning: Potential rises across the battery, remains constant along ideal wires, then drops across each resistor by IR.
After one complete traversal the graph returns to the initial potential.
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 11.6?
Use the loop rule when voltage rises and drops around a closed circuit path must satisfy energy conservation.
How this idea fits the course
The loop rule is the circuit-energy counterpart of Unit 10 conservation and works together with the junction rule in 11.7.
Scope check before solving
Choose a loop traversal direction and keep signs consistent. Treat ideal wires as zero potential change; avoid adding internal-resistance models unless the problem explicitly supplies a nonideal source.
Turn this topic into measurable evidence
Choose variables and meters that test the intended relationship without accidentally changing the circuit model.
Investigation target
Measure signed potential changes around a powered loop and verify their sum is approximately zero.
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 11.6 FAQs
Why does the loop sum equal zero?
Returning to the same point means returning to the same electric potential, so all signed changes must sum to zero.
Does loop direction matter?
No. Either traversal direction works if signs are handled consistently.
What happens to potential along an ideal wire?
It remains constant.
Why can a resistor produce a potential drop?
Electrical energy per unit charge is transferred as charges move through the resistive element.
Can I draw a potential-versus-position graph?
Yes. It is a powerful representation for checking where rises, drops, and equipotential wire segments occur.
Do I need source internal resistance by default?
No. Use the ideal-source model unless a problem explicitly introduces nonideal behavior.