Parallel: one voltage, several currents
You will be able to: Use shared voltage to find branch currents and equivalent parallel resistance.
How does current split between branches?
Two doorways let people take different routes to the same destination. In a parallel circuit, the branches share two electrical nodes. Each branch has the same voltage, but unequal resistances carry unequal currents.
A useful starting point: Series: one current, several drops →
Words and symbols before equations
- Branch
- One route between junctions.
- Shared nodes
- The same pair of endpoints; this defines parallel connection.
- Junction
- A connection where currents can split or combine.
- Reciprocal
- One divided by a quantity; for example 1/R.
What this picture assumes
Ideal wires and voltage source; positive, fixed resistances. Circuit geometry is schematic, not a physical length or speed scale.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Both branches 12 V. I₁=2 A, I₂=4 A; I_total=6 A. R_eq=2 Ω.
- 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 branches R₁ and R₂, both have voltage V. Branch currents are V/R₁ and V/R₂. Their sum equals source current: I_total=V(1/R₁+1/R₂), so 1/R_eq=1/R₁+1/R₂.
For two positive resistances, R_eq=R₁R₂/(R₁+R₂), smaller than either branch resistance. Adding a conducting branch provides another route and increases total current at fixed voltage.
Current splits equally only when the branch resistances are equal. It does not travel solely through the least-resistant branch: each finite-resistance branch with nonzero voltage carries current.
| Quantity | Series resistors | Parallel resistors |
|---|---|---|
| Shared quantity | Current | Voltage |
| Equivalent resistance | Sum of resistances | Reciprocal of sum of reciprocals |
| Charge paths | One path | Several branches |
A worked example, step by step
A 12 V source has 6 Ω and 3 Ω in parallel. Find branch currents and R_eq.
- Both branches have 12 V.
- I₁=12/6=2 A; I₂=12/3=4 A.
- I_total=6 A.
- R_eq=12/6=2 Ω, smaller than either individual resistance.
Branches in parallel share voltage, not necessarily current.
If one branch is opened, does the other still conduct?
Compare with an explanation
Yes, if its own path to the source is intact. Its voltage stays fixed for an ideal source.
Predict. Change one thing. Explain.
Vary one branch resistance while holding the other and the ideal source fixed. Compare the unchanged branch current with the changing total.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Both branches 12 V. I₁=2 A, I₂=4 A; I_total=6 A. R_eq=2 Ω.
Ideal wires and voltage source; positive, fixed resistances. Circuit geometry is schematic, not a physical length or speed scale.
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 6 V source has 3 Ω and 6 Ω parallel branches. (a) Give branch voltages. (b) Calculate currents. (c) Calculate source current. (d) Find equivalent resistance.
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Compare with the answer and four-point rubric
- 1 point: Each branch has 6 V.
- 1 point: Currents 2 A and 1 A.
- 1 point: Total 3 A.
- 1 point: R_eq=6/3=2 Ω.
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 1How can you recognize parallel elements?
Their two ends connect to the same pair of nodes.
RECALL 2Why is parallel R_eq smaller?
Additional current paths increase current at a fixed voltage.
RECALL 3Does all current choose only the easier path?
No. Every finite-resistance branch with voltage carries current.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Parallel: one voltage, several currents
- 1/R_eq=Σ(1/R_i) in parallel.
- Each parallel branch shares ΔV.
- I_total=ΣI_branch.
Remember: Branches in parallel share voltage, not necessarily current.
Conditions: Ideal wires and voltage source; positive, fixed resistances. Circuit geometry is schematic, not a physical length or speed scale.
Refresh Kid · AP Physics 2 Unit 3 (official Unit 11) · Objectives 11.5.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 11.5, objectives 11.5.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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