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
- Charge the capacitor fully. Disconnect the supply and discharge through R. Record V at regular intervals.
- Plot V vs t: exponential decay.
- Plot $\ln V$ vs t: straight line; gradient $= -1/\tau = -1/(RC)$.
- Determine $\tau$ from the gradient and compare with the calculated value $RC$.
- 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.
Q13 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.
Q22 marks
A student uses a voltmeter of resistance $100$ k$\Omega$ in parallel with R. Explain how this affects the time constant.