Required Practicals/Edexcel/Practical 12
12A2CP12

Capacitor charge and discharge (CP12)

Investigate the exponential discharge of a capacitor and determine the time constant RC.

Apparatus

  • Electrolytic capacitor (e.g. 1000 microF)
  • Fixed resistor (e.g. 10 kOhm)
  • DC power supply (6 V)
  • High-resistance voltmeter or datalogger
  • Stopwatch and switch

Safety

  • Observe correct polarity for electrolytic capacitors.
  • Do not exceed the maximum working voltage of the capacitor.

Method

  1. Charge the capacitor to the supply voltage $V_0$.
  2. Open the switch to disconnect the supply. Allow discharge through the resistor. Record V at regular time intervals.
  3. Plot V vs t: exponential decay.
  4. Plot $\ln V$ vs t: straight line with gradient $= -1/(RC)$.
  5. Read the time constant from the graph as the time for V to fall to $V_0/e \approx 0.37V_0$.

Key Variables

Independent
Time t
Dependent
Voltage V
Controlled
Resistance R; Capacitance C; Initial voltage $V_0$

Analysis and Results

  • $V = V_0 e^{-t/RC}$. Taking logs: $\ln V = \ln V_0 - t/RC$.
  • Gradient of $\ln V$ vs t equals $-1/\tau$ where $\tau = RC$.
  • Compare measured $\tau$ with calculated $RC$.

Common Errors

  • Connecting an electrolytic capacitor with reversed polarity.
  • Using a low-resistance voltmeter that discharges the capacitor faster, reducing the time constant.
  • Missing the early data points by starting timing too late.

Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.

Q13 marks
A 680 microF capacitor is charged to 9.0 V and then discharged through a 15 k$\Omega$ resistor. Calculate the voltage after 20 s.
Q22 marks
Explain why a datalogger is preferable to a stopwatch and manual voltmeter in this experiment.