# Capacitance

> CIE A-Level Physics · 9702
> Source: https://www.owlsprep.com/study/cie-9702-u22-overview/
> Weight: n/a

This unit introduces capacitors, key energy storage devices used in all modern electronic circuits. You will learn core properties of capacitance, how to combine capacitors, and analyze their dynamic charging and discharging behavior.

**Prerequisites:** Understanding of electric potential difference and electric fields

## Learning objectives

- Define capacitance and relate it to stored charge and potential difference across a capacitor
- Derive and apply the formula for capacitance of a parallel plate capacitor, including dielectric effects
- Calculate energy stored in a charged capacitor using multiple equivalent formulas
- Calculate total capacitance for capacitors in series and parallel combinations
- Analyze the exponential behavior of capacitor charging and discharging in RC circuits

## Unit at a glance

We progress from basic core definitions to more complex dynamic behavior in this unit. After learning what capacitance is, we cover the most common capacitor type (parallel plate), then energy storage, combination rules for circuits, and finish with the exponential behavior of charging and discharging.

Capacitance questions appear regularly in both multiple-choice and structured papers, with common exam questions focusing on combination problems, time constant calculations, and exponential decay graphs.

This unit is split into the following sub-topics:
- [Capacitance concepts](https://www.owlsprep.com/study/cie-9702-u22-capacitance-concepts/) — Learn the core definition of capacitance and the relationship between charge, capacitance and potential difference.
- [Parallel plate capacitor](https://www.owlsprep.com/study/cie-9702-u22-parallel-plate-capacitor/) — Derive and use the formula for capacitance of a parallel plate capacitor including the effect of dielectric materials.
- [Energy stored in capacitor](https://www.owlsprep.com/study/cie-9702-u22-energy-stored-in-capacitor/) — Calculate energy stored in a charged capacitor using multiple equivalent formulas.
- [Capacitors in series and parallel](https://www.owlsprep.com/study/cie-9702-u22-capacitors-in-series-and-parallel/) — Derive and apply rules for total capacitance for series and parallel combinations of multiple capacitors.
- [Capacitor charging and discharging](https://www.owlsprep.com/study/cie-9702-u22-capacitor-charging-and-discharging/) — Analyze exponential charging and discharging of capacitors through resistors, including time constant calculations.

## Common pitfalls

- **Wrong:** Confusing series and parallel rules for capacitors and resistors
  - Why it fails: The order of combination rules is reversed for capacitors compared to resistors, leading to common calculation errors
  - Correct: Remember $1/C_{\text{total}} = 1/C_1 + 1/C_2$ for series, which is the opposite of the equivalent resistance rule for series resistors
- **Wrong:** Forgetting the $\frac{1}{2}$ factor in the formula for energy stored in a capacitor
  - Why it fails: Work done to charge a capacitor uses the average potential difference, not the final potential difference
  - Correct: Recall energy stored equals the area under the $Q-V$ graph, which gives the $\frac{1}{2}$ factor in all equivalent energy formulas

## Cheatsheet

| Concept | Key Formula |
| --- | --- |
| Capacitance definition | $C = \frac{Q}{V}$ |
| Parallel plate capacitance | $C = \frac{\varepsilon_0 A \varepsilon_r}{d}$ |
| Energy stored in capacitor | $W = \frac{1}{2}CV^2 = \frac{1}{2}QV = \frac{Q^2}{2C}$ |
| Total capacitance (series) | $\frac{1}{C_{\text{total}}} = \sum \frac{1}{C_i}$ |
| Total capacitance (parallel) | $C_{\text{total}} = \sum C_i$ |
| RC time constant | $\tau = RC$ |
| Exponential discharge | $V = V_0 e^{-t/\tau}, \quad Q = Q_0 e^{-t/\tau}, \quad I = I_0 e^{-t/\tau}$ |

## What's next

Begin your study of this unit with the first sub-topic, which covers core capacitance definitions and relationships. Once you complete all sub-topics in this unit, you will move on to the next unit covering magnetic fields.

- [Capacitance concepts (first sub-topic of this unit)](https://www.owlsprep.com/study/cie-9702-u22-capacitance-concepts/)
- [Magnetic Fields (next unit)](https://www.owlsprep.com/study/cie-9702-u23-overview/)
- [Parallel plate capacitor](https://www.owlsprep.com/study/cie-9702-u22-parallel-plate-capacitor/)

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