Quick answer: A capacitor stores charge on two plates separated by an insulator, with capacitance C = Q/V in farads. This AP Physics 2 lab on capacitors 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 capacitance of two parallel plates change as they are moved apart, and what does a dielectric do? You build a capacitor from aluminium sheets, measure its capacitance at several separations, plot C against 1/d, and use the gradient to find the permittivity of free space.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 10
Aim
To investigate how the capacitance of a parallel-plate capacitor depends on the plate separation, to estimate ε₀, and to find the dielectric constant of acrylic.
Equipment
- Two aluminium sheets 0.20 m × 0.20 m, stiff and flat
- Plastic or wooden spacers of thickness 1.0, 2.0, 3.0, 4.0 and 5.0 mm
- Digital multimeter with a capacitance range (or a dedicated capacitance meter)
- Acrylic sheet 3.0 mm thick, same size
- Callipers, tape and short leads
Safety
The meter supplies only a tiny test voltage, so there is no shock risk, but never connect the sheets to a mains socket or a battery with high voltage. Press the foil edges flat so that they cannot cut your fingers, and keep the sheets dry.
Method
- Measure each spacer thickness with callipers and record it as d.
- Lay one sheet flat, place spacers of thickness d at the corners, and lay the second sheet on top, aligned exactly.
- Connect the meter to the two sheets, press gently on top, and read the capacitance.
- Repeat for the other four spacer thicknesses.
- Fill the 3.0 mm gap completely with the acrylic sheet and record the capacitance.
Results
Sample readings from Chiamaka’s group in Lagos, with the area A = 0.040 m², are shown.
| d (mm) | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | 3.0 with acrylic |
|---|---|---|---|---|---|---|
| C (pF) | 362 | 185 | 126 | 97 | 79 | 410 |
Analysis questions
Question 1 Calculate 1/d
Convert d to metres and calculate 1/d for each air reading.Question 2 Graph and gradient
Plot C (vertical) against 1/d and find the gradient using the first and last points.Question 3 Value of ε₀
Use the gradient and A = 0.040 m² to calculate ε₀.Question 4 The intercept
Find the intercept on the C axis and suggest what it represents.Question 5 Dielectric constant
Use the 3.0 mm results to find κ for acrylic, correcting for stray capacitance.Question 6 Uncertainty in d
The spacers are measured with callipers to ±0.05 mm. Find the percentage uncertainty in d for the 1.0 mm and 5.0 mm spacers.Question 7 Prediction
Predict the reading for d = 10 mm using your line, and explain why the sheets must be flat.
