In simple terms
A friendly intro before the formal notes — no formulas yet.
Discharging a capacitor
Cambridge 9702 Paper 4 — Discharging a capacitor (19.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.
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19.3 Discharging a capacitor.
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When a capacitor is being charged, the electrons flow from the positive to negative plate.
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When the capacitor is being discharged through a resistor, the electrons flow back from negative plate to the positive plate until there are equal number of electrons on each plate.
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At the start of the discharge, the current is large and gradually falls to zero.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 19.3.1
Analyse graphs of the variation with time of potential difference, charge and current for a capacitor discharging through a resistor
- 19.3.2
Recall and use for the time constant for a capacitor discharging through a resistor
- 19.3.3
Use equations of the form where x could represent current, charge or potential difference for a capacitor discharging through a resistor
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.
A charged capacitor stores energy…
A charged capacitor stores energy; discharge through a resistor.
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 · 4 to start with
Start herein this order — each one shows a different piece of the topic
- 3JCN PhysicsStart here · 19702 19.3 · 9702 19.1
Capacitor Charging/Discharging
Charge and discharge a capacitor through a resistor; read current and charge curves
Why this one: Compare the charge and current curves: both decay with the same time constant RC.
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
- The Physics ClassroomStart here · 29702 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
Why this one: Watch the meters as the capacitor discharges — current and voltage fall together through the resistor.
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)
- oPhysicsStart here · 39702 19.1 · 9702 19.3
Capacitor Lab
RC charging: adjust voltage, resistance, plate area and separation; open/close switch and watch charge build
Why this one: Double R or C and see the time constant double; the curve stretches but keeps its shape.
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)
- 3JCN PhysicsStart here · 49702 19.3
RC Circuit & Square Waves
Feed a square wave into an RC circuit and view the charging/discharging output
Why this one: Feed in a square wave and watch repeated charge and discharge curves follow each edge.
Try this
- Feed the square wave in and view the charging and discharging output.
- Compare the output when the time constant is short and when it is long relative to the period.
Look for Each edge of the square wave starts a fresh exponential charge or discharge toward the new level.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
More simulations3 more on this topic — core ones first
- PhETCore9702 19.3
Circuit Construction Kit: AC
Build an RC circuit, charge the capacitor and watch the current and voltage decay.
Try this
- Battery → switch → 100 μF capacitor → 100 Ω resistor; close the switch and watch the chart.
- Open the switch and reconnect capacitor to resistor only — the discharge curve.
- Double R — the decay takes twice as long (τ = RC).
Look for Exponential decay: V falls to 37% after one time constant RC.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- 3JCN Physics9702 19.3 · 9702 21.1
RC AC Circuit & Time Constant
Drive an RC circuit from AC and relate the time constant to the output
Try this
- Drive the RC circuit from AC and look at the output.
- Relate the time constant to how the output follows the input.
Look for When RC is long compared with the AC period the output cannot follow the input fully.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN Physics9702 19.3
RC Circuit Application
Neon-lamp relaxation oscillator: a practical RC timing application
Try this
- Watch the neon lamp flash as the capacitor charges and discharges.
- Note how the flash timing relates to the RC charging.
Look for The lamp fires each time the capacitor voltage reaches the strike voltage, so the flash period is set by RC.
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.
The Discharge Process
When a charged capacitor is connected across a resistor, the stored electrical energy is released. This release drives an electric current through the resistor. Initially, the current is at its maximum, but as the capacitor loses charge, the potential difference across it drops, causing the current to decrease over time. The rate of discharge is always proportional to the amount of charge remaining.
19.3 Discharging a capacitor.
When a capacitor is being charged, the electrons flow from the positive to negative plate.
When the capacitor is being discharged through a resistor, the electrons flow back from negative plate to the positive plate until there are equal number of electrons on each plate.
At the start of the discharge, the current is large and gradually falls to zero.
As a capacitor discharges, the I, V and Q all decrease exponentially.
This is represented by an exponential decay in the graph above.
Exponential Decay
A key characteristic of capacitor discharge is that the charge (Q), voltage (Vc), and current (I) all decrease following an exponential decay pattern. This means they don't drop linearly but rather shed a constant fraction of their remaining value over equal time intervals. This pattern is crucial for predicting circuit behaviour.
The mathematical expressions for exponential decay are:
Here, , , and are the initial values at when discharge begins. The term 'e' is Euler's number (approx. 2.718).
Linearizing the Decay Equation for Analysis
To determine the time constant experimentally from a set of measurements, it's useful to rearrange the decay equation into a linear form. By taking the natural logarithm of the voltage equation, we can plot a straight-line graph.
Starting with Taking natural logs of both sides: Rearranging into the form :
A graph of (y-axis) against (x-axis) will be a straight line.
The gradient of this line is equal to .
The y-intercept is equal to , the natural log of the initial voltage.
The Time Constant (τ)
The symbol (tau) represents the time constant of the RC circuit. It's a critical parameter that tells us how quickly the capacitor will discharge. A larger time constant means a slower discharge, while a smaller one means a faster discharge. It's determined by the resistance and capacitance values in the circuit.
The time constant is calculated as:
The time constant () is the product of resistance () and capacitance ().
It measures the speed of discharge in an RC circuit.
After one time constant, fall to (approx. 37%) of their initial value.
After , a capacitor is considered almost fully discharged (less than 1% remaining).
Energy and Half-Life during Discharge
The energy stored in the capacitor is dissipated as heat in the resistor. Since energy is proportional to the square of the voltage (), it also decays exponentially, but at a faster rate.
Another useful concept is the half-life (), the time it takes for the charge (or voltage) to fall to half its initial value. It's directly related to the time constant.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
A 2200 µF capacitor is charged to 12 V and then discharged through a 1.5 kΩ resistor. Calculate the time constant () of the circuit. Also, calculate the voltage across the capacitor after 3.0 seconds.
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Convert units:
A student investigates the discharge of a capacitor. They record the potential difference, V, across the capacitor at various times, t. The data is shown in the table below.
| Time / s | Voltage / V |
|---|---|
| 0.0 | 9.0 |
| --- | --- |
| 10.0 | 5.4 |
| 20.0 | 3.3 |
| 30.0 | 2.0 |
| 40.0 | 1.2 |
Use the data to determine the time constant, τ, for the circuit.
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Linearize the data: To use the linear equation , we must first calculate the natural logarithm, ln(V), for each voltage reading.
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.
- exponential decay
A key characteristic of capacitor discharge is that the charge (Q), voltage (Vc), and current (I) all decrease following an exponential decay pattern. This means they don't drop linearly but rather shed a constant fraction of their remaining value over equal time intervals.
- time constant
The symbol (tau) represents the time constant of the RC circuit. It's a critical parameter that tells us how quickly the capacitor will discharge.
- half-life
Another useful concept is the half-life (), the time it takes for the charge (or voltage) to fall to half its initial value.
- approximate value of 1/e
0.368 (or 36.8%).
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
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Teach it back
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Revision flashcards
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Key takeaways
Review these before you close the topic — retrieval beats re-reading.
19.3 Discharging a capacitor.
When a capacitor is being charged, the electrons flow from the positive to negative plate.
When the capacitor is being discharged through a resistor, the electrons flow back from negative plate to the positive plate until there are equal number of electrons on each plate.
At the start of the discharge, the current is large and gradually falls to zero.
As a capacitor discharges, the I, V and Q all decrease exponentially.
This is represented by an exponential decay in the graph above.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
the time constant τ of the circuit.
the time constant τ of the circuit in Fig. 6.1.
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 · Q7(b)(iii) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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