Charge and discharge of a capacitor
Investigate the exponential charge and discharge of a capacitor through a resistor and determine the time constant RC.
Apparatus
- Capacitor (e.g. 1000 microF electrolytic)
- Fixed resistor (e.g. 10 kOhm)
- DC power supply (6 V)
- High-resistance voltmeter or datalogger with voltage probe
- Stopwatch (or datalogger), switch and connecting leads
Safety
- Connect electrolytic capacitors with the correct polarity; reverse connection can cause failure or rupture.
- Do not exceed the maximum working voltage marked on the capacitor.
Method
- Charge the capacitor fully from the power supply using a switch. Confirm the voltmeter reads the supply voltage.
- Open the switch to disconnect the supply and allow the capacitor to discharge through the resistor. Record V at regular time intervals (e.g. every 10 s).
- Plot V against t: exponential decay curve.
- Plot ln(V) against t: straight line with gradient $= -1/(RC)$ and y-intercept $= \ln(V_0)$.
- Read off the time constant tau as the time for V to fall to $V_0/e \approx 0.37\,V_0$.
Key Variables
Independent
Time t
Dependent
Voltage V across capacitor
Controlled
Resistance R; Capacitance C; Initial voltage V0
Analysis and Results
- Discharge: $V = V_0\,e^{-t/RC}$. Taking logs: $\ln V = \ln V_0 - t/RC$.
- Plot $\ln V$ vs t: gradient $= -1/(RC) = -1/\tau$ and y-intercept $= \ln V_0$.
- Time constant $\tau = RC$: the time for V to fall to $1/e$ (approximately 37%) of its initial value.
- Charging curve: $V = V_0(1 - e^{-t/RC})$ - voltage approaches $V_0$ asymptotically.
Common Errors
- Connecting an electrolytic capacitor the wrong way round.
- Using a voltmeter with too low an input resistance, which provides an additional discharge path and reduces the time constant.
- Starting the stopwatch after the switch is opened, missing the early rapid discharge.
- Taking too few data points to clearly identify the exponential shape.
Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.
Q13 marks
A 470 microF capacitor discharges through a 22 k$\Omega$ resistor. Calculate the time constant and the time for the voltage to fall to 37% of its initial value.
Q24 marks
A student plots $\ln V$ against t during discharge. The gradient is $-0.050$ s$^{-1}$ and the y-intercept is 1.79. Determine $V_0$, the time constant, and the capacitance if R = 47 k$\Omega$.
Q32 marks
Explain what is meant by the time constant of an RC circuit.