Quick answer: Capacitance is the charge stored per unit potential difference, C = Q/ΔV, measured in farads. This AP Physics C lab on capacitance 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 does the separation of two plates change their capacitance, and what does that tell you about the paper between them? You will build a capacitor from foil and printer paper, add sheets one at a time, and use a multimeter to measure C, then analyse the straight-line graph.
Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:E&M Unit 10
Aim
Test how the capacitance of a foil-and-paper capacitor depends on plate separation, and use the data to estimate the dielectric constant of paper.
Equipment
- Two sheets of aluminium foil, each 20 cm × 10 cm, on thin card
- Printer paper, 20 cm × 10 cm sheets, up to five
- A multimeter with a capacitance range
- A heavy book or wooden board
- Ruler and micrometer or calipers (to measure a stack of 20 sheets)
Safety
No external voltage is used, only the meter. Foil edges can cut: handle the sheets by the card backing and trim any sharp corners.
Method
- Measure the thickness of 20 sheets of paper and divide by 20 to find t, the thickness of one sheet.
- Place one foil sheet flat, cover it with one sheet of paper and then the second foil sheet, leaving a tab of each foil outside the paper.
- Press the stack flat with the book and connect the meter to the two tabs.
- Read C once the display is steady, then repeat with 2, 3, 4 and 5 sheets of paper.
- Zero the meter with open leads before each reading to remove stray capacitance.
Results
Sample measurements with t = 0.10 mm per sheet and plate area A = 0.0200 m²:
| n (sheets) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| C (nF) | 4.6 | 2.4 | 1.6 | 1.2 | 0.95 |
| 1/C (nF⁻¹) | 0.217 | 0.417 | 0.625 | 0.833 | 1.053 |
Analysis questions
Question 1 Linearise the data
Explain why plotting 1/C against n should give a straight line, then plot it.
Question 2 Gradient
Calculate the gradient of the 1/C against n graph in F⁻¹ per sheet.
Question 3 Dielectric constant
Use the gradient, t and A to estimate the dielectric constant of the paper.
Question 4 Air comparison
Calculate the capacitance expected for one sheet if the gap were air, and compare it with the measured value.
Question 5 Intercept
State what the graph’s intercept should be and what a non-zero intercept would indicate.
Question 6 Uncertainty
The thickness of one sheet is 0.10 ± 0.01 mm and the gradient is known to 3 %. Estimate the uncertainty in κ.
Question 7 Reducing error
Propose two changes that would make the value of κ more reliable, and say why each helps.
