Required Practicals / OCR A / Practical 9
9 A2 PAG 9

Capacitor charge and discharge - time constant (PAG 9)

Measure the time constant of an RC circuit and verify the exponential nature of capacitor discharge.

Apparatus

  • Capacitor (e.g. 470 microF electrolytic)
  • Fixed resistor (e.g. 22 kOhm)
  • DC power supply
  • High-resistance voltmeter or datalogger
  • Stopwatch and switch

Safety

  • Correct polarity for electrolytic capacitors.
  • Do not exceed maximum working voltage.

Method

  1. Charge the capacitor fully. Disconnect the supply and discharge through R. Record V at regular intervals.
  2. Plot V vs t: exponential decay.
  3. Plot $\ln V$ vs t: straight line; gradient $= -1/\tau = -1/(RC)$.
  4. Determine $\tau$ from the gradient and compare with the calculated value $RC$.
  5. Verify by reading the time for V to fall to $0.37V_0$ from the graph.

Key Variables

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

Analysis and Results

  • $V = V_0 e^{-t/RC}$. $\ln V = \ln V_0 - t/RC$.
  • Gradient of $\ln V$ vs t gives $\tau = RC$.
  • Time constant: time for V to fall to $V_0/e \approx 0.37V_0$.

Common Errors

  • Reversed polarity on electrolytic capacitor.
  • Voltmeter resistance too low, providing an extra discharge path.
  • Missing early rapid discharge by starting timing too late.

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

Q1 3 marks

A $\ln V$ vs t graph has gradient $-0.040$ s$^{-1}$ and the capacitor is $560$ microF. Find the time constant and the resistance R.

Q2 2 marks

A student uses a voltmeter of resistance $100$ k$\Omega$ in parallel with R. Explain how this affects the time constant.