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A-level Physics required practicals

Capacitor charge and discharge — determining RC

AQA 3.7.4.4 · RP9

A-level Physics (7408) · Required practical 9 — method, techniques, safety, analysis and uncertainty. Includes errors documented in examiner reports.

Board and spec code confirmed against AQA 7408 · registry checked 2026-07-11How this checking works

Record capacitor charge and discharge curves and determine the time constant RC from a log-linear graph or a 1/e measurement.

Apparatus

  • Low-voltage dc supply, capacitor and known resistors
  • Two-way switch, discharge switch and current-limiting resistor
  • Digital multimeter and connecting leads
  • Oscilloscope with a suitable time-base or voltage data logger
  • Computer or spreadsheet for logarithms and graph fitting

Apparatus & techniques (AT)

AT b · digital instruments

Use a digital multimeter and sampled voltage readings to check component values and the initial capacitor condition.

AT f · circuit construction

Construct the charge/discharge circuit with correct capacitor polarity, switching and current limitation.

AT g · circuit design/checking

Check the proposed switching circuit before energising it and confirm that the capacitor cannot be short-circuited directly.

AT h · signal generator/oscilloscope

Set the oscilloscope time-base, trigger and voltage scale to capture a resolved charge or discharge trace.

AT k · ICT/data logging/processing

Process exported trace data with logarithms and a best-fit graph to determine RC.

Safety

Hazard

A charged capacitor can deliver a large current if short-circuited or connected with incorrect polarity.

Control

Use low voltage, observe polarity, include a current-limiting resistor and discharge through a resistor before handling or altering the circuit.

Hazard

Components may heat if the resistance is too small.

Control

Check resistor power ratings, limit current and disconnect the supply if any component warms appreciably.

Method

  1. 1Check the capacitor polarity and circuit layout before connecting the low-voltage supply. Include a resistor that limits the charging and discharging current.
  2. 2Discharge the capacitor through the resistor, verify that its voltage is near zero, then switch it to the supply and record capacitor voltage against time for charging.
  3. 3Charge the capacitor to a consistent initial voltage, isolate the supply and switch the capacitor through the known resistor while the oscilloscope or data logger records the discharge trace.
  4. 4Repeat the discharge with the same initial condition, then change one of R or C while keeping the other and the supply unchanged.
  5. 5Export or tabulate the trace values, retaining units and component tolerances, and identify the trigger time used as t = 0.

CPAC focus (editorial)

This is an editorial study focus, not an AQA mapping of fixed CPAC competencies to this practical.

  • CPAC 2: Editorial focus: choose R, C, sampling interval and scale settings that produce a measurable exponential trace.
  • CPAC 4: Editorial focus: capture repeatable traces from a defined initial voltage and preserve raw time–voltage data.
  • CPAC 5: Editorial focus: compare the 1/e and log-linear methods, propagate gradient uncertainty and evaluate component tolerance.

Variables

Independent

Time, or resistor/capacitor value when comparing traces

Dependent

Capacitor voltage or circuit current

Control

  • Supply voltage and initial capacitor voltage
  • The component not being varied
  • Trigger definition, sampling rate and measurement connection
  • Capacitor polarity and temperature

Results & processing

  • For discharge, plot ln(V) against time. The gradient equals -1/RC, so RC = -1/gradient.
  • As an independent method, read the time for voltage to fall to V0/e; this time equals RC.
  • For charging, compare the trace with V = V0(1 - e−t/RC) and check that increasing R or C increases the time constant.

Analysis skills

  • Transform discharge data using ln(V) = ln(V0) - t/RC and obtain RC from the negative reciprocal gradient.
  • Determine RC from the 1/e voltage point and compare it with the graph-based value.
  • Relate changes in trace shape to separate changes in resistance and capacitance.

Uncertainty

Sources

  • Oscilloscope or logger voltage and time resolution
  • Uncertainty in trigger time and the initial capacitor voltage
  • Resistor/capacitor tolerance, leakage and the measuring device's finite input resistance

Calculations

  • Use maximum and minimum acceptable ln(V)–t gradients to estimate uncertainty in RC.
  • Propagate percentage uncertainties in R and C when comparing the nominal product RC with an experimental time constant.
  • For repeated 1/e times, use half-range as an estimate of random uncertainty where justified.

Interpretation

  • A high-resistance voltage probe reduces loading but does not remove capacitor leakage.
  • Late-time points can dominate percentage voltage uncertainty and curve away from the ideal line near the resolution floor.

Exam angles

  • Derive or use the straight-line form of the discharge equation.
  • Obtain RC from a log-linear gradient with the correct sign and unit.
  • Explain the 1/e method and compare it with a whole-graph fit.
  • Predict and justify how changing R or C alters charge and discharge traces.

Where students lose marks

Quoting the time at V0/e without explaining why it represents the time constant.

Fix: Use V = V0e−t/RC: when V/V0 = 1/e, the exponent is -1 and therefore t = RC.

  • Examiner report: P2-24 · PDF p. 4

Plotting ln(V) against time but taking RC to be the gradient itself.

Fix: The gradient is negative and equals -1/RC, so calculate RC from the negative reciprocal of the gradient.

Changing R or C without resetting the initial capacitor voltage.

Fix: Fully discharge and then recharge to the same stated initial voltage before recording each comparison trace.

Improve the method

  • Choose R and C so the decay lasts long enough for many resolved samples but remains within the apparatus limits.
  • Use a voltage-measuring device with high input resistance so it draws little current from the capacitor.
  • Fit a line to all valid ln(V) points and avoid the late trace once voltage approaches the noise or resolution floor.

Source references

  • Specification: AQA 7408 specification §3.7.4.4 · PDF p. 38

Try it — exam-style

Medium
ORIGINAL

A discharge graph of ln(V/V) against time has gradient -2.50 s−1. The resistor is 220 kΩ. Calculate the capacitance.

[3 marks]

Total for this question: 3

Easy
ORIGINAL

A capacitor discharges from 6.00 V to 2.21 V in 0.840 s through a 470 kΩ resistor. Treat 2.21 V as V0/e and calculate the capacitance.

[2 marks]

Total for this question: 2

Medium
ORIGINAL

A capacitor charges towards 9.00 V with time constant 0.800 s. Calculate its voltage after 1.20 s using V = V0(1 - e−t/RC).

[2 marks]

Total for this question: 2

Questions are written in the style of past AQA papers — never copied from them.

Drill it properly

A-level Physics spec coverage

Capacitance, exponential change and data-processing practice for 7408.

Stuck on capacitor charge and discharge — determining rc?

Turn the curve into a line, explain what the gradient means, and the capacitor questions become much less slippery.

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