Parallel branches share voltage and split current
You will be able to: Use common-node voltage and current conservation to find parallel resistance.
Why does adding a parallel branch increase total current?
Two resistors connected across the same two battery terminals each receive the full terminal voltage. A second path lets more charge pass per second for that voltage.
A useful starting point: Series resistors share current and divide voltage →
Words and symbols before equations
- Parallel connection
- Elements connected between the same two nodes.
- Branch current
- Current in one route between the nodes.
- Conductance addition
- Parallel reciprocal resistances add.
What this picture assumes
Two resistor branches across the same ideal-voltage source. Voltage is common; branch currents add at the source.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- R_eq = 2 Ω; branch voltage = 12 V; I₁ = 2, I₂ = 4, source I = 6 A.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Each branch has voltage V, so I₁ = V/R₁ and I₂ = V/R₂. The smaller resistance carries the greater current.
The source current is I = I₁+I₂ = V(1/R₁+1/R₂), giving 1/R_eq = 1/R₁+1/R₂.
The equivalent resistance is below either individual resistance. Adding a branch increases source current at fixed ideal voltage while leaving the existing branch current unchanged. A nonideal source can behave differently.
| Property | Series resistors | Parallel resistors |
|---|---|---|
| Connection | Single unbranched path | Same two nodes |
| Shared quantity | Current | Voltage |
| Equivalent R | Sum of resistances | Reciprocal sum |
| Check | Voltage drops add | Branch currents add |
A worked example, step by step
A 12 V source feeds 6 Ω and 3 Ω in parallel. Find branch and source currents.
- Both resistors have 12 V across them.
- I₁ = 12/6 = 2 A; I₂ = 12/3 = 4 A.
- Source current is 6 A.
- R_eq = 12/6 = 2 Ω, smaller than 3 Ω.
Parallel is defined by the two shared nodes, not by whether components look side by side.
Do equal parallel voltages imply equal currents?
Compare with an explanation
Only if the branch resistances are equal.
Predict. Change one thing. Explain.
Change one branch resistance while keeping the ideal battery and other resistor fixed. Compare the unchanged branch current with the changing total.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
R_eq = 2 Ω; branch voltage = 12 V; I₁ = 2, I₂ = 4, source I = 6 A.
Two resistor branches across the same ideal-voltage source. Voltage is common; branch currents add at the source.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant current, circuit topology, charge or energy conservation, or RC 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 9 V battery feeds parallel 9 Ω and 18 Ω branches. Find all currents, equivalent resistance and total power.
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Compare with the answer and four-point rubric
- 1 point: Branch currents are 1 A and 0.5 A.
- 1 point: Source current is 1.5 A.
- 1 point: R_eq = 9/1.5 = 6 Ω.
- 1 point: Total power is 9(1.5) = 13.5 W.
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 equal across parallel elements?
The voltage between their common nodes.
RECALL 2Where does current split?
At a junction between paths.
RECALL 3Why is R_eq smaller?
An added route increases conductance.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Parallel branches share voltage and split current
- V₁ = V₂.
- I_total = I₁+I₂.
- 1/R_eq = 1/R₁+1/R₂.
Remember: Parallel is defined by the two shared nodes, not by whether components look side by side.
Conditions: Two resistor branches across the same ideal-voltage source. Voltage is common; branch currents add at the source.
Refresh Kid · AP Physics C: Electricity and Magnetism Unit 4 (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. This is E&M Unit 4: Electric Circuits, numbered Unit 11 in the official combined Physics C sequence. Topics 11.1–11.8 retain their official identifiers. Models include signed charge flow, prescribed current-density and resistivity integrals, DC resistor networks, nonideal batteries and meters, capacitor combinations and finite-resistance RC transients. Circuit schematics use conventional-current references and explicit node connectivity. Initial capacitor voltage and positive time constants are stated. Unequal ideal sources are never directly wired in parallel. The optional spatial wire view supplements a complete 2D current-density explanation. Checked with the Fall 2026 clarifications. 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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