Quick answer: Kirchhoff's junction rule conserves charge and his loop rule conserves energy, giving equations for every branch current. This AP Physics C lab on RC circuits gives the aim, the equipment, the safety points, a step-by-step method, sample results and 7 analysis questions; the answers are on a separate page and the lab sheet is a free printable PDF.
How quickly does a capacitor lose its charge through a resistor, and does the time constant equal RC? You will discharge a large capacitor through a fixed resistor, record the voltage with a stopwatch, and use a log graph to find τ and compare the capacitance with its label.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:E&M Unit 11
Aim
Measure how the voltage across a discharging capacitor falls with time, find the time constant from a logarithmic graph, and test the relation τ = RC.
Equipment
- Electrolytic capacitor, nominal 1000 μF, rated at least 10 V
- Resistor 22 kΩ
- Four 1.5 V cells and holder (6.0 V)
- Digital voltmeter and leads
- Stopwatch or phone timer
- Single-pole switch or a loose lead
Safety
Connect the electrolytic capacitor with the correct polarity (long lead to +) and never exceed its rated voltage. Use only the 6.0 V cells. Short the capacitor through the resistor after the lab so that it is fully discharged.
Method
- Connect the capacitor across the 6.0 V cells for 2 minutes so it is fully charged.
- Connect the voltmeter across the capacitor and disconnect the cells.
- Connect the resistor across the capacitor and start the stopwatch at the same moment.
- Record the voltage every 10 s for 60 s.
- Repeat the whole run and average the readings at each time.
- Calculate ln V for each reading.
Results
Sample measurements (voltmeter resistance 10 MΩ, negligible compared with 22 kΩ):
| t (s) | 0 | 10 | 20 | 30 | 40 | 50 | 60 |
|---|---|---|---|---|---|---|---|
| V (V) | 6.0 | 3.5 | 2.1 | 1.2 | 0.73 | 0.43 | 0.26 |
| ln(V/V) | 1.79 | 1.25 | 0.74 | 0.18 | −0.31 | −0.84 | −1.35 |
Analysis questions
Question 1 Plot ln V against t
Explain why ln V against t should be a straight line and plot it.
Question 2 Gradient
Calculate the gradient of the graph from the first and last points.
Question 3 Time constant
Use the gradient to find τ.
Question 4 Capacitance
Calculate the capacitance from τ and compare it with the nominal 1000 μF.
Question 5 Half-time check
Use τ to predict the time for V to halve and compare it with the table.
Question 6 Uncertainty
The voltmeter reads to ±0.01 V and the timing to ±0.5 s. State which reading affects τ most and estimate the percentage uncertainty.
Question 7 Reducing error
Suggest two ways to get a more accurate time constant.
