---
title: "Charge-Voltage Relationship — AP Physics 2 Definition"
description: "The charge-voltage relationship C = Q/ΔV defines capacitance in AP Physics 2 Topic 10.6. Learn why C stays fixed by geometry while Q and ΔV scale together."
canonical: "https://fiveable.me/ap-physics-2-revised/key-terms/charge-voltage-relationship"
type: "key-term"
subject: "AP Physics 2"
unit: "Unit 10"
---

# Charge-Voltage Relationship — AP Physics 2 Definition

## Definition

The charge-voltage relationship, C = Q/ΔV, says the charge stored on each capacitor plate is directly proportional to the potential difference across the plates, with capacitance C as the constant of proportionality set only by the capacitor's geometry and dielectric material (AP Physics 2, Topic 10.6).

## What It Is

The charge-voltage relationship is the defining equation of [capacitance](/ap-physics-2-revised/key-terms/capacitance "fv-autolink"), written as C = Q/ΔV. When you separate [charge](/ap-physics-2-revised/unit-10/1-electric-charge-and-electric-force/study-guide/E6OYkOGeroCXwgw1 "fv-autolink") onto the two plates of a capacitor (equal amounts, opposite signs), that separation creates a potential difference ΔV between the plates. The ratio of the charge magnitude Q on each plate to that potential difference is the capacitance C.

Here's the part the CED really wants you to internalize (10.6.A.2.i): even though C is *defined* using Q and ΔV, it doesn't *depend* on either of them. Capacitance is fixed by the physical capacitor itself, its [plate area](/ap-physics-2-revised/unit-10/6-capacitors/study-guide/BalONZFM1MOIxU84 "fv-autolink"), plate separation, and the material between the plates. Double the voltage on a given capacitor and the stored charge doubles right along with it, so the ratio Q/ΔV never budges. Think of C like the size of a bucket. How much water you pour in changes, but the bucket's capacity doesn't.

## Why It Matters

This relationship lives in Topic 10.6 (Capacitors) in [Unit 10](/ap-physics-2-revised/unit-10 "fv-autolink"): Electric Force, Field, and Potential, and it directly supports learning objective 10.6.A, describing the physical properties of a parallel-plate capacitor. Essential knowledge 10.6.A.2 states it explicitly. Capacitance relates the magnitude of charge stored on each plate to the potential difference created by separating those charges, via C = Q/ΔV. It's also a perfect example of a proportionality argument, the kind of reasoning [AP Physics 2](/ap-physics-2-revised "fv-autolink") rewards everywhere. If you can say 'Q is directly proportional to ΔV for a fixed capacitor, so doubling one doubles the other,' you're doing exactly the kind of qualitative-quantitative translation the exam tests.

## Connections

### Parallel-Plate Capacitor Geometry (Unit 10)

The charge-voltage relationship defines C, but geometry sets its value. For a parallel-plate capacitor, capacitance is proportional to plate area and inversely proportional to plate separation (10.6.A.2.ii). Changing the plates changes C; changing the battery does not.

### Electric Potential Difference and Uniform Fields (Unit 10)

The ΔV in C = Q/ΔV comes straight from earlier in Unit 10. Between parallel plates the field is roughly uniform, so ΔV connects to the field through E = ΔV/d. Charge on the plates makes the field, the field makes the [potential difference](/ap-physics-2-revised/key-terms/electric-potential-difference "fv-autolink"), and capacitance ties the chain together.

### Capacitors in Circuits (Unit 11)

When capacitors show up in circuits, C = Q/ΔV is the tool you reach for constantly. Capacitors in series share the same Q, capacitors in parallel share the same ΔV, and a charging capacitor's [voltage](/ap-physics-2-revised/key-terms/voltage "fv-autolink") grows as charge piles onto its plates. Every one of those facts is this relationship at work.

### Energy Stored in a Capacitor (Unit 10)

Because Q grows linearly with ΔV, the [energy](/ap-physics-2-revised/unit-15/6-compton-scattering/study-guide/OoE2k26dtiHSsZEf "fv-autolink") stored is the area under the Q-vs-ΔV line, a triangle. That's where the ½ in the stored-energy expression comes from. The linear charge-voltage relationship is the geometric reason capacitor energy has that factor of one-half.

## On the AP Exam

No released FRQ uses the phrase 'charge-voltage relationship' verbatim, but C = Q/ΔV is one of the most-used equations in Units 10 and 11. Multiple-choice questions love proportionality traps, like asking what happens to capacitance when you double the voltage (answer: nothing, because C is fixed by geometry). Graph-based questions may give you a plot of Q versus ΔV and ask you to identify the slope as capacitance, or compare two capacitors by comparing slopes. On FRQs, expect to use Q = CΔV to find stored charge, justify why charge doubles when voltage doubles, or reason through series and parallel capacitor combinations. The skill being tested is rearranging and interpreting the relationship, not just memorizing it.

## charge-voltage relationship vs Capacitance vs. stored charge

Students constantly mix up what changes and what stays fixed. Stored charge Q changes whenever you change the applied voltage. Capacitance C does not; it's locked in by plate area, separation, and the dielectric material. If an MCQ says 'the voltage across a capacitor is doubled,' the charge doubles but the capacitance is exactly the same. C is the slope of the Q-vs-ΔV line, and a line through the origin keeps its slope no matter where you are on it.

## Key Takeaways

- The charge-voltage relationship is C = Q/ΔV, meaning the charge stored on each plate is directly proportional to the potential difference across the capacitor.
- Capacitance depends only on the capacitor's physical properties, like plate shape, separation, and the material between the plates, never on Q or ΔV themselves.
- Doubling the voltage across a fixed capacitor doubles the stored charge, but the capacitance stays exactly the same.
- On a graph of charge versus potential difference, the slope of the line is the capacitance.
- A parallel-plate capacitor holds equal amounts of charge with opposite signs on its two plates, and Q in the equation refers to the magnitude on one plate, not the total.
- This relationship is the foundation for analyzing capacitors in circuits, where series capacitors share the same Q and parallel capacitors share the same ΔV.

## FAQs

### What is the charge-voltage relationship for a capacitor?

It's the defining equation of capacitance, C = Q/ΔV, where Q is the charge magnitude on each plate and ΔV is the potential difference across the plates. It appears in AP Physics 2 Topic 10.6 under learning objective 10.6.A.

### Does capacitance increase if you increase the voltage?

No. Charge and voltage increase together in exact proportion, so their ratio C never changes. Capacitance is set only by the capacitor's geometry and the material between its plates (essential knowledge 10.6.A.2.i).

### How is C = Q/ΔV different from Ohm's law?

Ohm's law (ΔV = IR) relates voltage to the current flowing through a resistor, while C = Q/ΔV relates voltage to charge sitting stored on capacitor plates. A resistor dissipates energy as charge moves through it; a capacitor stores charge and energy without steady current flowing across the gap.

### Is the total charge on a capacitor zero?

Yes, in the sense that the two plates carry equal and opposite charges (+Q and -Q), so the net charge on the whole device is zero. The Q in C = Q/ΔV refers to the magnitude of charge on one plate, which is what the exam means by 'charge stored.'

### What does the slope of a charge vs. voltage graph represent?

The slope is the capacitance. Because Q = CΔV is linear through the origin, a steeper line means a larger capacitance, and AP Physics 2 graph questions often ask you to compare capacitors this way.

## Related Study Guides

- [10.6 Capacitors](/ap-physics-2-revised/unit-10/6-capacitors/study-guide/BalONZFM1MOIxU84)

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