Quick answer: A capacitor stores charge on two plates, and its capacitance is C = Q / V in farads. This Physics 11-12 lab on capacitor gives the aim, the equipment, the safety points, a step-by-step method, sample results and 8 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
A capacitor discharging through a resistor loses voltage by the same fraction in equal intervals of time. In this lab you record the voltage every ten seconds, take logarithms and use the straight line to measure the time constant and test it against the value of RC.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: A Level 3.7.4
Aim
To measure how the voltage across a capacitor falls as it discharges through a resistor and to find the time constant from a straight-line graph of ln V against time.
Equipment
- electrolytic capacitor, 1000 µF, 16 V rating
- resistor, 22 kΩ
- 9 V battery or low-voltage supply
- digital voltmeter (input resistance 10 MΩ or more)
- stopwatch, switch and connecting leads
Safety
Electrolytic capacitors are polarised: connect the positive terminal to the positive side of the supply, and never exceed the voltage rating, because the capacitor can burst. Wear goggles and discharge the capacitor through the resistor before handling it.
Method
- Connect the capacitor, resistor and battery in series with the switch, with the voltmeter across the capacitor.
- Close the switch until the voltmeter shows about 9 V, then leave the capacitor fully charged.
- Disconnect the battery so that the capacitor can discharge only through the resistor, and start the stopwatch.
- Record the voltage every 10 s for 60 s.
- Calculate ln V for each reading and plot ln V (vertical axis) against t.
- Draw the line of best fit and find its gradient.
Results
Sample measurements from one group:
| Time t (s) | Voltage V (V) |
|---|---|
| 0 | 9.0 |
| 10 | 5.9 |
| 20 | 3.9 |
| 30 | 2.6 |
| 40 | 1.7 |
| 50 | 1.1 |
| 60 | 0.7 |
Analysis questions
Question 1 Shape of the curve
Describe the shape of a graph of V against t for the sample data and state what it shows about the rate of discharge.Question 2 Half the voltage
Use the data to estimate the time for the voltage to halve from 9.0 V, and relate it to the time constant using t½ = τ ln 2.Question 3 Logarithm table
Calculate ln V for each reading and state why this graph is a straight line.Question 4 Gradient and τ
Calculate the gradient of the ln V against t line using the first and last readings, and hence the time constant.Question 5 Comparing with RC
Calculate the nominal RC value and the percentage difference from your measured time constant.Question 6 Capacitor tolerance
Electrolytic capacitors have a typical tolerance of −20 % to +50 %. Explain whether your result is consistent with the nominal value.Question 7 Initial current
Calculate the current through the resistor at t = 0.Question 8 Improving the method
Suggest two changes to make the measurements of τ more precise.
