Quick answer: A capacitor stores charge on two plates separated by an insulator, with capacitance C = Q/V in farads. This AP Physics 2 worksheet on capacitors gives 20 problems from easy to hard: capacitance from charge, prefixes and plate capacitor in air. The worked answers are on a separate page, and the worksheet is a free printable PDF.
These problems train capacitance, the parallel-plate formula, energy storage and the effect of dielectrics for AP Physics 2 unit 10. They begin with one-step calculations and unit conversions and move to comparisons where you must decide whether the charge or the voltage stays fixed. Use ε₀ = 8.85 × 10⁻¹² F/m and e = 1.60 × 10⁻¹⁹ C, and write units with every answer.
Level: AP Physics 2 (algebra-based) · Curriculum: AP P2 Unit 10
Problem 1 Capacitance from charge ★★★
A capacitor holds 24 μC of charge on its plates when connected to 6.0 V.1. Calculate its capacitance.
2. Then calculate the charge it would hold at 9.0 V.
3. Finally, state the unit of capacitance in terms of coulombs and volts.
Problem 2 Prefixes ★★★
Convert each value.1. 470 μF to farads
2. 22 nF to farads
3. 100 pF to microfarads
4. 0.0033 F to millifarads
Problem 3 Plate capacitor in air ★★★
Emma makes a capacitor from two metal sheets of area 0.020 m² separated by 0.50 mm of air. Take κ = 1 and ε₀ = 8.85 × 10⁻¹² F/m.1. Calculate its capacitance in pF.
2. Then state what happens to C if the sheets are moved to 1.0 mm apart.
Problem 4 Energy in a capacitor ★★★
A 100 μF capacitor is charged to 12 V.1. Calculate the charge on a plate.
2. Then calculate the energy stored.
Problem 5 Electrons on the plates ★★★
A 2.2 μF capacitor is connected to a 9.0 V battery.1. Calculate the charge on the negative plate.
2. Then calculate the number of excess electrons on it. Use e = 1.60 × 10⁻¹⁹ C.
Problem 6 Scaling capacitance ★★★
A parallel-plate capacitor has capacitance C. State the new capacitance in each case.1. The plate area is doubled.
2. The plate separation is doubled.
3. A material with κ = 3 fills the gap.
4. The area is doubled, the separation is doubled and κ = 3.
Problem 7 Finding the gap ★★★
A 1.0 nF air capacitor has plates of area 0.050 m².1. Rearrange the capacitance equation for d.
2. Then calculate d in millimetres.
Problem 8 Charging graph ★★★
A student charges a capacitor in steps and records the voltage (graph shown).2. Then calculate the energy stored at 40 μC and 10 V.
3. Finally, state what the area under the graph represents.
Problem 9 Three energy formulas ★★★
A 10 μF capacitor holds 50 μC.1. Calculate the voltage across it.
2. Then calculate the energy using U = Q²/2C.
3. Finally, check your answer using U = ½CV².
Problem 10 Dielectric with the battery connected ★★★
A 2.0 nF capacitor is connected to a 9.0 V battery. A dielectric with κ = 4.0 is slid in while the battery stays connected.1. Calculate the new capacitance.
2. Then calculate the charge before and after.
3. Next, calculate the energy before and after.
4. Finally, state whether the field between the plates changes.
Problem 11 Dielectric in an isolated capacitor ★★★
The same 2.0 nF capacitor is charged to 9.0 V, disconnected from the battery, and then the κ = 4.0 dielectric is slid in.1. State the charge afterwards.
2. Then calculate the new voltage.
3. Next, calculate the new stored energy and compare with the original 8.1 × 10⁻⁸ J.
4. Finally, explain where the missing energy has gone.
Problem 12 Supercapacitor torch ★★★
Kofi’s torch uses a 0.50 F supercapacitor charged to 5.0 V. An LED uses 0.25 W.1. Calculate the energy stored at 5.0 V.
2. Then calculate how long the LED could run if all the energy were used.
3. Finally, calculate the energy released as the voltage falls to 3.0 V.
Problem 13 Air breakdown ★★★
Air breaks down in a field above about 3.0 × 10⁶ V/m. Two plates of area 0.040 m² are 2.0 mm apart in air.1. Calculate the highest voltage the capacitor can take.
2. Then calculate its capacitance.
3. Finally, calculate the largest charge and energy it can store.
Problem 14 Inside a dielectric ★★★
A capacitor with air between its plates is charged and disconnected. A slab of glass is inserted.1. Describe what happens to the glass molecules.
2. Then explain why the field in the gap becomes smaller.
3. Finally, explain why the capacitance increases.
Problem 15 Measuring a dielectric constant ★★★
Bilal measures a capacitor with air between the plates: 52 pF. He then fills the gap with a plastic sheet and measures 190 pF.1. Calculate κ for the plastic.
2. Then state which material in a table this resembles.
3. Finally, suggest one reason why the value might be a little off.
Problem 16 Pulling the plates apart ★★★
Two identical 5.0 μF capacitors each carry 60 μC at 12 V (shown). The battery stays connected to A, while B is disconnected. The plate separation of each is then doubled.2. For A, calculate Q, V and U afterwards.
3. For B, calculate Q, V and U afterwards.
4. Finally, explain why U changes in opposite ways.
Problem 17 Partly filled capacitors ★★★
An air capacitor has plates of area 0.020 m² and gap 1.0 mm. A slab with κ = 5 is inserted in two ways (shown).2. Then calculate C when the slab fills half of the plate area (side by side).
3. Next, calculate C when the slab fills half of the gap (stacked).
4. Finally, compare your answers and comment.
Problem 18 Sharing charge ★★★
A 4.0 μF capacitor is charged to 10 V and then connected through a switch to an uncharged 6.0 μF capacitor (shown).2. Then calculate the final common voltage.
3. Next, calculate the final energy and the energy lost.
4. Finally, suggest where the lost energy goes.
Problem 19 Defibrillator capacitor ★★★
A defibrillator uses an 80 μF capacitor charged to 3.0 kV. It delivers 80 % of its energy to a patient in 5.0 ms.1. Calculate the energy stored.
2. Then calculate the energy delivered and the average power.
3. Finally, calculate the charge on the capacitor and the average current if all of it flows in 5.0 ms.
Problem 20 Doubling the voltage ★★★
Two identical capacitors of capacitance C are charged: one to voltage V and the other to 2V. Write a paragraph-style argument comparing them.1. Compare the charge on each.
2. Then compare the stored energy.
3. Next, compare the electric field between the plates.
4. Finally, explain which is more likely to suffer breakdown.
