Capacitors combine differently from resistors
You will be able to: Determine equivalent capacitance and individual charges and voltages for ideal pairs.
Why do parallel capacitors store more charge at the same voltage?
Two capacitors across the same 6 V battery both have 6 V between their plates. Each stores charge Q=CV, so their charges add. In a series chain with initially uncharged, isolated intermediate connections, equal charge magnitudes appear on the capacitors instead.
A useful starting point: Charge balances at a junction →
Words and symbols before equations
- Capacitance C
- Charge magnitude on one plate per voltage across the capacitor, in farads (F).
- Equivalent capacitance
- C_eq=Q_source/V for the combination.
- μF
- Microfarad: 10⁻⁶ F.
- Plate charge Q
- Magnitude on one plate; the other plate has opposite charge in the ideal two-terminal model.
What this picture assumes
Ideal capacitors initially uncharged, connected across 6 V. Intermediate conductors in series are isolated and initially neutral. Readouts give plate-charge magnitudes at equilibrium, not net charge of a whole capacitor.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Series: C_eq=2 μF; charge drawn from source=12 μC. Plate-charge magnitudes Q₁=12 μC, Q₂=12 μC; V₁=4 V, V₂=2 V.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
In parallel, voltage is shared and Q_total=C₁V+C₂V, giving C_eq=C₁+C₂. This is like increasing effective plate area.
In series, initially neutral isolated intermediate conductors maintain zero net charge. Equal charge magnitudes Q result, while voltages add: V=Q/C₁+Q/C₂. Therefore 1/C_eq=1/C₁+1/C₂. The smaller capacitance has the larger voltage.
These simple equal-charge statements assume initially uncharged capacitors and no extra net charge on intermediate nodes. The capacitor dielectric prevents conduction through the gap, but external current can add charge to one plate while removing it from the other during charging.
| Connection | Resistors | Capacitors |
|---|---|---|
| Series | Resistances add | Reciprocal capacitances add |
| Parallel | Reciprocal resistances add | Capacitances add |
A worked example, step by step
Find C_eq and plate charges for 3 μF and 6 μF across 6 V, first parallel and then series.
- Parallel: C_eq=9 μF; Q₁=18 μC and Q₂=36 μC.
- Series: C_eq=(3×6)/(3+6)=2 μF.
- Series plate-charge magnitude Q=C_eq V=12 μC for each capacitor.
- Series voltages are 12/3=4 V and 12/6=2 V; they sum to 6 V.
Resistor combination formulas cannot be copied directly to capacitors: the series/parallel addition patterns are reversed.
Which series capacitor has more voltage when the charges are equal?
Compare with an explanation
The smaller capacitance, because V=Q/C.
Predict. Change one thing. Explain.
Switch between series and parallel. Vary C₂ and compare equivalent capacitance, individual voltage and plate-charge magnitudes.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Series: C_eq=2 μF; charge drawn from source=12 μC. Plate-charge magnitudes Q₁=12 μC, Q₂=12 μC; V₁=4 V, V₂=2 V.
Ideal capacitors initially uncharged, connected across 6 V. Intermediate conductors in series are isolated and initially neutral. Readouts give plate-charge magnitudes at equilibrium, not net charge of a whole capacitor.
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 questionTwo initially uncharged 4 μF capacitors are connected in series across 8 V. (a) Find C_eq. (b) Find plate-charge magnitude. (c) Find each voltage. (d) Find C_eq if reconnected in parallel after discharge.
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Compare with the answer and four-point rubric
- 1 point: C_eq=2 μF.
- 1 point: Q=16 μC on each capacitor.
- 1 point: Each has 4 V.
- 1 point: Parallel C_eq=8 μF.
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 1Which quantity do parallel capacitors share?
Voltage.
RECALL 2Why is series C_eq smaller than either capacitor?
For the same stored charge, their required voltages add.
RECALL 3Can electrons conduct through an ideal capacitor dielectric?
No; charging transfers charge through the external circuit to and from plates.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Capacitors combine differently from resistors
- Parallel capacitors: C_eq=ΣC_i.
- Series capacitors: 1/C_eq=Σ(1/C_i).
- Q_i=C_i V_i; initially uncharged isolated series nodes give equal |Q_i|.
Remember: Resistor combination formulas cannot be copied directly to capacitors: the series/parallel addition patterns are reversed.
Conditions: Ideal capacitors initially uncharged, connected across 6 V. Intermediate conductors in series are isolated and initially neutral. Readouts give plate-charge magnitudes at equilibrium, not net charge of a whole capacitor.
Refresh Kid · AP Physics 2 Unit 3 (official Unit 11) · Objectives 11.8.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 11.8, objectives 11.8.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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