Unit Overview

Capacitance

CIE A-Level Physics· 5 min read 📊 n/a

1. 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

Learn the core definition of capacitance and the relationship between charge, capacitance and potential difference.

★★⏱ 5 min

Parallel plate capacitor

Derive and use the formula for capacitance of a parallel plate capacitor including the effect of dielectric materials.

★★★⏱ 6 min

Energy stored in capacitor

Calculate energy stored in a charged capacitor using multiple equivalent formulas.

★★⏱ 4 min

Capacitors in series and parallel

Derive and apply rules for total capacitance for series and parallel combinations of multiple capacitors.

★★★⏱ 7 min

Capacitor charging and discharging

Analyze exponential charging and discharging of capacitors through resistors, including time constant calculations.

★★★★⏱ 10 min

2. Common Pitfalls

Wrong move:

Confusing series and parallel rules for capacitors and resistors

Why:

The order of combination rules is reversed for capacitors compared to resistors, leading to common calculation errors

Correct move:

Remember $1/ C_{total} = 1/ C_{1} + 1/ C_{2}$ for series, which is the opposite of the equivalent resistance rule for series resistors

Wrong move:

Forgetting the $\frac{1}{2}$ factor in the formula for energy stored in a capacitor

Why:

Work done to charge a capacitor uses the average potential difference, not the final potential difference

Correct move:

Recall energy stored equals the area under the $Q - V$ graph, which gives the $\frac{1}{2}$ factor in all equivalent energy formulas

3. Quick Reference Cheatsheet

Concept	Key Formula
Capacitance definition	$C = \frac{Q}{V}$
Parallel plate capacitance	$C = \frac{ε _{0} A ε _{r}}{d}$
Energy stored in capacitor	$W = \frac{1}{2} C V^{2} = \frac{1}{2} Q V = \frac{Q ^{2}}{2 C}$
Total capacitance (series)	$\frac{1}{C _{total}} = \sum \frac{1}{C _{i}}$
Total capacitance (parallel)	$C_{total} = \sum C_{i}$
RC time constant	$τ = R C$
Exponential discharge	$V = V_{0} e^{- t / τ}, Q = Q_{0} e^{- t / τ}, I = I_{0} e^{- t / τ}$

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.