In simple terms
A friendly intro before the formal notes — no formulas yet.
Capacitor Energy: The Basics
Capacitors are like tiny rechargeable batteries, storing electrical energy in an electric field. The more charge and voltage, the more energy they hold, released gradually when discharged.
Think of a capacitor as a stretched spring or a compressed air tank. The more you stretch the spring or compress the air, the more potential energy it stores. Releasing it makes things move (or in our case, current flow).
- 1
Charge Up: A capacitor collects charge on its plates, building up a potential difference.
- 2
Store Energy: This charge separation creates an electric field, storing electrical potential energy.
- 3
Calculate Power: Energy stored is proportional to charge and voltage, representable by the area under a Q-V graph.
- 4
Discharge: When connected to a circuit, the stored energy is released as current, decaying exponentially.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 19.2.1
Determine the electric potential energy stored in a capacitor from the area under the potential-charge graph
- 19.2.2
Recall and use
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Step 1
Charge Up: A capacitor collects charge on its plates, building up a potential difference.
7 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
7 simulations · 3 to start with
Start herein this order — each one shows a different piece of the topic
- 3JCN PhysicsStart here · 19702 19.2 · 9702 19.1 · 9702 18.2
Capacitor - Electric Field - Energy
Insert a dielectric and vary plate area/gap; read field, capacitance and stored energy
Why this one: Pull the plates apart at fixed charge and watch the stored energy rise — the energy lives in the field.
Try this
- Increase the plate area and read the capacitance.
- Widen the gap and read the field and capacitance.
- Insert the dielectric and compare the stored energy.
Look for C = εA / d: larger area or smaller gap raises C, and a dielectric raises it by its relative permittivity.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsStart here · 29702 19.1 · 9702 19.2
Capacitor - Introduction
Introduction to a capacitor: charge plates and see Q, V and C
Why this one: Charge the plates and see Q and V grow together; the energy is the triangle ½QV under that line.
Try this
- Charge the plates and read Q, V and C.
- Double the charge and read V.
- Check that Q / V stays constant.
Look for C = Q / V is fixed by the geometry, so charge and voltage rise together.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- PhETStart here · 3Java · best on a laptop9702 19.1–19.2 · 18.2 · IB D.2
Capacitor Lab
Change the plate size, separation and dielectric of a capacitor; measure capacitance, charge, stored energy and field.
Why this one: Slide a dielectric in and watch capacitance and stored energy change for a fixed charge.
Try this
- Connect the battery and increase the plate area — capacitance and charge rise.
- Increase the separation — the capacitance falls and the field between the plates weakens.
- Slide a dielectric between the plates — the capacitance jumps.
Look for C = ε₀εᵣA/d; the stored energy ½CV² sits in the uniform field that fills the gap.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
More simulations4 more on this topic — core ones first
- 3JCN PhysicsCore9702 19.1 · 9702 19.2
Capacitor Combination Construction Kit
Construct capacitor combinations and compute equivalent C
Try this
- Build two capacitors in series and compute the equivalent C.
- Rebuild them in parallel and compare.
Look for Series capacitance is smaller than either part; parallel capacitance is the sum.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsCore9702 19.1 · 9702 19.2
Capacitor in Parallel
Connect capacitors in parallel and read the equivalent capacitance
Try this
- Connect two capacitors in parallel and read the equivalent.
- Add a third and compare.
Look for Parallel capacitors simply add, C = C1 + C2 + C3.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsCore9702 19.1 · 9702 19.2
Capacitor in Series
Connect capacitors in series and read the equivalent capacitance
Try this
- Connect two equal capacitors in series and read the equivalent.
- Add a third and compare.
Look for Series capacitors combine as 1/C = 1/C1 + 1/C2, giving less than the smallest.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsCore9702 19.1 · 9702 19.2
Equivalent Capacitance Practice
Practice finding equivalent capacitance of random networks
Try this
- Reduce the network step by step, combining series and parallel pairs.
- Compare your answer with the sim's equivalent capacitance.
Look for Series pairs reduce the capacitance and parallel pairs add it.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Full topic notes
Formal explanation with the rigour you need for the exam.
Understanding Energy Storage
A capacitor stores energy by accumulating electric charge on its plates, creating a potential difference across them. This separation of charge establishes an electric field between the plates, and it's within this electric field that the electrical potential energy is held. The greater the charge and potential difference, the more energy is stored.
19.2 Energy stored in a capacitor.
The charge (Q) on a capacitor is directly proportional to its potential difference (V).
The area under the curve of a potential-charge graph is equal to the area under a triangle .
This area is the energy stored in a capacitor.
The energy stored (W) is therefore W =1/2 QV Substituting Q = CV we get W = ½ CV 2.
Calculating Stored Energy
The energy stored in a capacitor can be visualised and calculated by looking at its charge-voltage (Q-V) graph. Since capacitance (C) is constant, the relationship is linear, resulting in a straight line passing through the origin. The energy stored is simply the area of the triangle formed under this graph.
Using , we can derive:
Alternatively, using , we get:
Discharging a Capacitor: Releasing Energy
When a charged capacitor is connected to a resistor, it begins to discharge. The stored electrical potential energy is released, driving a current through the circuit. This process isn't instant; the charge, voltage, and current all decrease gradually following an exponential decay pattern over time. This decay is characterised by a specific time constant.
Energy is released as current flows during discharge.
Charge (Q), voltage (), and current (I) all decrease exponentially.
Discharge equations: and .
and are initial charge and voltage at .
The time constant () for an RC circuit is defined as .
is the time for Q, V, or I to fall to approximately 37% () of its initial value.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A 220 . Calculate the energy stored. If it discharges through a 10 k\Omega resistor, what is the initial discharge current and the time constant of the circuit?
- 1
Energy Stored (E):
A capacitor is charged to . Calculate the energy stored using .
- 1
(2 s.f.)
How it all connects
The big idea sits in the middle — tap a linked idea to explore the link.
Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Key terms for this topic — skim now; the Check step will test them.
- exponential decay
This process isn't instant; the charge, voltage, and current all decrease gradually following an exponential decay pattern over time. This decay is characterised by a specific time constant.
- Fundamental relationship defining capacitance (C)
, where Q is charge and V is potential difference.
- shape of a capacitor's
A straight line passing through the origin.
- Write the exponential
.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
If you can explain it simply, you own it — gaps here are marks you’d lose.
Teach it back
Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.
Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
19.2 Energy stored in a capacitor.
The charge (Q) on a capacitor is directly proportional to its potential difference (V).
The area under the curve of a potential-charge graph is equal to the area under a triangle .
This area is the energy stored in a capacitor.
The energy stored (W) is therefore W =1/2 QV Substituting Q = CV we get W = ½ CV 2.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Two capacitors P and Q are connected in parallel to a power supply of voltage V. The capacitance of P is 200 μF. The capacitance C_Q of Q can be varied between 0 and 400 μF. When C_Q = 0, the total energy stored in the capacitors is 2.5mJ. (i) Show that the supply voltage V is 5.0V.
On Fig. 6.2, sketch the variation of the total energy E stored in the capacitors with C_Q, as C_Q varies from 0 to 400 μF.
Extra simulations & links
PhET, GeoGebra and other curated tools — open in a new tab.
Frequently asked
Checkpoint
One marked question is worth ten re-reads — close the loop before you move on.
Reading it isn’t knowing it — prove it.
Before you move on: do 9702/42 · Q6(b)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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