In simple terms
A friendly intro before the formal notes — no formulas yet.
Capacitors and capacitance
Cambridge 9702 Paper 4 — Capacitors and capacitance (19.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.
- 1
Capacitance is directly proportional to the plate area (A).
- 2
Capacitance is inversely proportional to the plate separation (d).
- 3
Capacitance is directly proportional to the permittivity (ε) of the dielectric material.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 19.1.1
Define capacitance, as applied to both isolated spherical conductors and to parallel plate capacitors
- 19.1.2
Recall and use
- 19.1.3
Derive, using , formulae for the combined capacitance of capacitors in series and in parallel
- 19.1.4
Use the capacitance formulae for capacitors in series and in parallel
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
Capacitance is directly proportional to the plate area (A).
12 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.
12 simulations · 4 to start with
Start herein this order — each one shows a different piece of the topic
- 3JCN PhysicsStart here · 19702 19.1 · 9702 19.2
Capacitor in Parallel
Connect capacitors in parallel and read the equivalent capacitance
Why this one: Connect capacitors in parallel: same V across each, charges add, so C adds.
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 PhysicsStart here · 29702 19.1 · 9702 19.2
Capacitor in Series
Connect capacitors in series and read the equivalent capacitance
Why this one: Connect capacitors in series: same Q on each, voltages add, so 1/C adds.
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 PhysicsStart here · 39702 19.1 · 9702 19.2
Capacitor Combination Construction Kit
Construct capacitor combinations and compute equivalent C
Why this one: Build a mixed network and reduce it step by step to one equivalent capacitance.
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 PhysicsStart here · 49702 19.1 · 9702 19.2
Equivalent Capacitance Practice
Practice finding equivalent capacitance of random networks
Why this one: Test yourself on random networks until series and parallel rules are automatic.
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
More simulations8 more on this topic — core ones first
- PhETCoreJava · 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.
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)
- oPhysicsCore9702 19.1 · 9702 19.3
Capacitor Lab
RC charging: adjust voltage, resistance, plate area and separation; open/close switch and watch charge build
Try this
- Close the switch and watch the charge build.
- Double the resistance and charge again.
- Increase the plate area or reduce the separation.
Look for Charge rises exponentially towards CV with time constant RC; larger area or smaller separation raises C.
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
- The Physics ClassroomCore9702 19.3 · 9702 19.1
RC Circuit Sim
See the current flow, voltage and current readings in a simple RC circuit as the capacitor charges and discharges
Try this
- Charge the capacitor and watch the current fall.
- Discharge it and compare.
- Change R or C and repeat.
Look for Current decays exponentially with a time constant RC.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
- 3JCN PhysicsCore9702 19.1 · 9702 19.2
Capacitor - Introduction
Introduction to a capacitor: charge plates and see Q, V and C
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
- 3JCN PhysicsCore9702 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
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 PhysicsCore9702 19.3 · 9702 19.1
Capacitor Charging/Discharging
Charge and discharge a capacitor through a resistor; read current and charge curves
Try this
- Charge through the resistor and read the current and charge curves.
- Discharge and compare the shapes.
- Note when the current is largest in each case.
Look for Current is largest at the instant of switching and decays exponentially while charge approaches its final value.
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
Full topic notes
Formal explanation with the rigour you need for the exam.
What is a Capacitor?
At its core, a capacitor is an electrical component designed to store electric charge and, by extension, electrical potential energy. The most common type is the parallel-plate capacitor, which consists of two conductive plates separated by an insulating material called a dielectric. This dielectric prevents current from flowing directly between the plates while allowing an electric field to form, storing energy.
Capacitance: Measuring Storage Ability
The ability of a capacitor to store charge is quantified by its capacitance (C). It's defined as the amount of charge (Q) it can store per unit of potential difference (V) across its plates. The higher the capacitance, the more charge it can hold for a given voltage.
The Parallel-Plate Capacitor
The capacitance of a parallel-plate capacitor depends on its physical characteristics: the area of the plates, the distance between them, and the insulating material (dielectric) used.
Here, A is the area of overlap between the two plates, d is the separation between the plates, and ε (epsilon) is the permittivity of the dielectric material. Permittivity is a measure of how well a material can store energy in an electric field. It is given by , where is the permittivity of free space () and is the relative permittivity (or dielectric constant) of the material.
Capacitance is directly proportional to the plate area (A).
Capacitance is inversely proportional to the plate separation (d).
Capacitance is directly proportional to the permittivity (ε) of the dielectric material.
Capacitors in Series Circuits
When capacitors are connected in series, they are linked end-to-end, forming a single path. In this configuration, the charge stored on each capacitor is the same, but the total potential difference applied across the combination is distributed among them. This means the overall storage ability is reduced.
Total potential difference:
Charge stored: (charge is the same on each).
Total capacitance: The reciprocal rule applies.
Overall capacitance is always less than the smallest individual capacitance.
Capacitors in Parallel Circuits
In a parallel connection, capacitors are connected side-by-side across the same two points in a circuit. This means each capacitor experiences the identical potential difference. The total charge stored is the sum of the charges on each capacitor, leading to a greater overall storage ability.
Potential difference: (voltage is the same across each).
Total charge stored:
Total capacitance: Simply sum the individual capacitances.
Overall capacitance is always greater than the largest individual capacitance.
Energy Stored in a Capacitor
When a capacitor stores charge, it also stores electrical potential energy within the electric field between its plates. This energy can be released when the capacitor discharges. The amount of energy stored can be determined from the area under a charge-voltage (Q-V) graph, which for a constant capacitance, is a triangle.
Energy is stored as electrical potential energy in the electric field.
The Q-V graph for a capacitor is a straight line through the origin.
The energy stored (E) is equal to the area under this Q-V graph.
Substitute into to derive and .
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
Two capacitors, and , are connected to a power supply. Calculate the total capacitance and the total charge stored when they are connected: (a) in series (b) in parallel
- 1
Use the series capacitance formula:
A 2200 µF capacitor is charged by a 10.0 V power supply. It is then disconnected and connected in parallel with an uncharged 4700 µF capacitor. Calculate: (a) the initial energy stored in the 2200 µF capacitor. (b) the final potential difference across the combination. (c) the total energy stored in the combination after connection. (d) the energy lost during the connection.
- 1
First, find the initial charge stored on the first capacitor. This charge is conserved.
How it all connects
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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.
- dielectric
The most common type is the parallel-plate capacitor, which consists of two conductive plates separated by an insulating material called a dielectric. This dielectric prevents current from flowing directly between the plates while allowing an electric field to form, storing energy.
- capacitance (C)
The ability of a capacitor to store charge is quantified by its capacitance (C). It's defined as the amount of charge (Q) it can store per unit of potential difference (V) across its plates.
- Capacitance
Capacitance is the charge stored per unit potential difference across a capacitor.
- SI unit of capacitance,
The Farad (F), defined as 1 Coulomb of charge stored per Volt of potential difference (1 C/V).
- Draw the standard
Two parallel lines of equal length, perpendicular to the connecting wires.
- total capacitance change
The total capacitance decreases and is always less than the smallest individual capacitance.
- increasing the distance
It decreases the capacitance, as capacitance is inversely proportional to the plate separation (d).
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.
Capacitance is directly proportional to the plate area (A).
Capacitance is inversely proportional to the plate separation (d).
Capacitance is directly proportional to the permittivity (ε) of the dielectric material.
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.
Use your answers in (b) to determine capacitance C.
Extra simulations & links
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Frequently asked
Checkpoint
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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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