Walk a loop and account for every volt
You will be able to: Write a signed loop equation and interpret a potential-around-the-loop graph.
Why must voltage changes sum to zero?
Walk once around a trail and return to your starting point: the total elevation change is zero. Likewise, a loop’s signed potential changes return to the starting potential. Battery rises and resistor drops account for energy per coulomb.
A useful starting point: Measure current through; voltage across →
Words and symbols before equations
- Loop traversal
- Chosen direction in which you trace a closed circuit path.
- Signed potential change ΔV
- Final minus initial potential along a traversal segment.
- Reference potential
- A chosen zero at one node; changing it shifts all node values equally.
- Loop rule
- Sum of signed potential changes around a closed circuit loop is zero.
What this picture assumes
Ideal wires and voltage source; positive, fixed resistances. Circuit geometry is schematic, not a physical length or speed scale. Potential graph follows successive positions around the loop, not time or physical distance. Resistor voltage changes are schematic linear segments.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- R_eq=6 Ω; I=2 A. Loop: +12−4−8=0 V. Graph: source rise at 1, resistor drops over 2–3 and 4–5.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Across a battery from negative to positive, add +ε; going the other way, add −ε. Through a resistor in the assumed current direction, write −IR; against that direction, write +IR. Choose directions before inserting numbers.
For a source and two series resistors, +ε−IR₁−IR₂=0 follows energy conservation. The circuit transfers energy to resistors but does not lose total energy. Charge returning to its starting node has the same electric potential energy per unit charge.
A potential graph can use successive locations around the loop horizontally. Ideal wires are flat, a source gives a rise, and resistors give drops in the current direction. The horizontal axis is route position, not elapsed time; symbol widths are not physical distances.
A worked example, step by step
Trace a 12 V battery and series 2 Ω and 4 Ω resistors clockwise with I=2 A.
- Choose battery negative as 0 V and traverse through the battery to positive.
- Potential rises to 12 V. Across 2 Ω it drops 4 V to 8 V.
- Across 4 Ω it drops 8 V to 0 V.
- Loop sum +12−4−8=0 V; reversing traversal reverses every term.
A negative resistor term comes from the chosen traversal relative to current, not from negative resistance.
If you reverse the loop traversal, does the physical current reverse?
Compare with an explanation
No. Only your equation’s signs reverse; the circuit is unchanged.
Predict. Change one thing. Explain.
Change one resistance. Predict how the two drops redistribute, then follow the potential graph back to the starting node.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
R_eq=6 Ω; I=2 A. Loop: +12−4−8=0 V. Graph: source rise at 1, resistor drops over 2–3 and 4–5.
Ideal wires and voltage source; positive, fixed resistances. Circuit geometry is schematic, not a physical length or speed scale. Potential graph follows successive positions around the loop, not time or physical distance. Resistor voltage changes are schematic linear segments.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant current, voltage or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA 10 V source drives series 2 Ω and 3 Ω resistors. (a) Write a loop equation. (b) Find I. (c) Give successive potentials from source negative. (d) Reverse the equation signs.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: +10−2I−3I=0.
- 1 point: I=2 A.
- 1 point: 0 V → 10 V → 6 V → 0 V.
- 1 point: −10+2I+3I=0 describes the same circuit.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What is conserved in a loop equation?
Energy, expressed as potential change per unit charge.
RECALL 2What do ideal wires look like on a potential plot?
Flat segments.
RECALL 3Does choosing another zero change voltage differences?
No; differences are unchanged.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Walk a loop and account for every volt
- ΣΔV_loop=0.
- Battery −→+: +ε; +→−: −ε.
- Resistor with current: −IR; against current: +IR.
Remember: A negative resistor term comes from the chosen traversal relative to current, not from negative resistance.
Conditions: Ideal wires and voltage source; positive, fixed resistances. Circuit geometry is schematic, not a physical length or speed scale. Potential graph follows successive positions around the loop, not time or physical distance. Resistor voltage changes are schematic linear segments.
Refresh Kid · AP Physics 2 Unit 3 (official Unit 11) · Objectives 11.6.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 11.6, objectives 11.6.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Refresh Kid calls this the third AP Physics 2 unit; College Board numbers it Unit 11; the first unit in this course is official Unit 9. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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