Capacitance is charge per potential difference
You will be able to: Interpret Q = CΔV and distinguish plate charge from net capacitor charge.
Why can a capacitor be neutral and still store charge?
A capacitor can have +6 nC on one plate and −6 nC on the other. Its net charge is zero, yet separating the charges establishes a voltage and stores energy.
A useful starting point: Disconnect ground before removing the inducing charge →
Words and symbols before equations
- Capacitance C
- Positive geometry-and-material property measured in farads (F).
- Plate charge Q
- Magnitude of charge on either plate for equal and opposite plates.
- Potential difference ΔV
- Positive voltage from the negative plate to the positive plate in this lesson.
- Farad
- 1 F = 1 C/V; pF means 10⁻¹² F.
What this picture assumes
Ideal linear capacitor with equal and opposite plate charges. Q is the magnitude on one plate, in pC; V is a nonnegative voltage magnitude. The Q-versus-V slope is capacitance even when the selected state is uncharged.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Q = 1000 pC per plate in magnitude; net charge = 0. Slope = 200 pC/V = 200 pF.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
For an ideal linear capacitor, Q = CΔV. The Q in this relation is the magnitude on one plate, not the sum of both magnitudes and not the net zero charge.
A graph of Q versus ΔV has slope C when geometry and dielectric remain fixed. Increasing voltage increases stored charge proportionally, without changing C in this ideal model.
The ratio Q/ΔV does not define a finite value from the single uncharged point 0/0. Capacitance still exists there; determine it from geometry or the slope. A battery maintains a potential difference by moving charge through the external path.
A worked example, step by step
A capacitor holds +9 nC and −9 nC at a potential difference of 3 V. Find its capacitance.
- Take Q = 9 nC from one plate, not 18 nC or zero.
- C = Q/ΔV = 9×10⁻⁹/3 F.
- C = 3 nF = 3000 pF.
- At 6 V with the same ideal geometry, Q doubles to 18 nC per plate; C stays 3 nF.
Stored charge means a plate-charge magnitude; it is not the net charge of the pair.
Does doubling voltage double capacitance?
Compare with an explanation
No. It doubles plate charge for a fixed ideal capacitor.
Predict. Change one thing. Explain.
Vary voltage at fixed capacitance and read the Q-versus-voltage graph. Then vary capacitance and compare slopes. Set voltage to zero without declaring capacitance zero.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Q = 1000 pC per plate in magnitude; net charge = 0. Slope = 200 pC/V = 200 pF.
Ideal linear capacitor with equal and opposite plate charges. Q is the magnitude on one plate, in pC; V is a nonnegative voltage magnitude. The Q-versus-V slope is capacitance even when the selected state is uncharged.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant conductor equilibrium, charge conservation, capacitance 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 Q-versus-voltage graph passes through (2 V, 400 pC) and (6 V, 1200 pC). Determine capacitance, charge at 10 V and what the zero-voltage point means.
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Compare with the answer and four-point rubric
- 1 point: Slope is (1200−400)/(6−2) = 200 pC/V.
- 1 point: C = 200 pF.
- 1 point: At 10 V, Q = 2000 pC = 2 nC on each plate in magnitude.
- 1 point: At zero voltage, Q = 0 but the same geometric capacitance remains.
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 a farad?
One coulomb per volt.
RECALL 2What fixes ideal capacitance?
Geometry and the material between conductors.
RECALL 3Why is Q not 2Q in the definition?
Q labels the magnitude transferred from one plate to the other.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Capacitance is charge per potential difference
- Q = CΔV.
- C = slope of Q versus ΔV for a linear capacitor.
- Net charge of equal opposite plates is zero.
Remember: Stored charge means a plate-charge magnitude; it is not the net charge of the pair.
Conditions: Ideal linear capacitor with equal and opposite plate charges. Q is the magnitude on one plate, in pC; V is a nonnegative voltage magnitude. The Q-versus-V slope is capacitance even when the selected state is uncharged.
Refresh Kid · AP Physics C: Electricity and Magnetism Unit 3 (official Unit 10) · Objectives 10.3.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 10.3, objectives 10.3.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. This is E&M Unit 3: Conductors and Capacitors, numbered Unit 10 in the official combined Physics C sequence. Topics 10.1–10.4 retain their official identifiers. Models state the electrostatic conditions, geometry approximations and whether charge or voltage stays fixed. Capacitor geometries include parallel plates, concentric spheres and long coaxial cylinders. Dielectric comparisons assume a fully filling ideal linear material. The optional 3D plate view uses explicitly different gap and lateral scales to show the small separation. 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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