Quick answer: A capacitor stores charge on two plates, and its capacitance is C = Q / V in farads. This Physics 11-12 worksheet on capacitor gives 20 problems from easy to hard: charge on a capacitor, prefix conversions and energy in a small capacitor. The worked answers are on a separate page, and the worksheet is a free printable PDF.
These twenty problems start with Q = CV and unit prefixes, then move through energy, combinations of capacitors and the exponential charge and discharge equations. They suit A Level, IB Physics and CBSE Class 12 students. The last five problems link several ideas and include energy loss, timer design and a medical device.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: A Level 3.7.4
Problem 1 Charge on a capacitor ★★★
A 2200 µF capacitor in a radio is charged to 6.0 V. Calculate the charge on one plate.Problem 2 Prefix conversions ★★★
Chiamaka measures a capacitor that holds 2.4 µC at 12 V.1. Calculate its capacitance in farads.
2. Express the answer in microfarads and in nanofarads.
Problem 3 Energy in a small capacitor ★★★
A 100 µF capacitor is charged to 25 V. Calculate the energy it stores.Problem 4 Time constant ★★★
A circuit uses a 47 kΩ resistor and a 100 µF capacitor in series.1. Calculate the time constant.
2. Then estimate how long it takes the voltage to be practically zero during discharge (about 5τ).
Problem 5 Two capacitors ★★★
A 2.0 µF capacitor and a 3.0 µF capacitor are available.1. Calculate the total capacitance when they are in parallel.
2. Then calculate the total capacitance when they are in series.
Problem 6 Describing a discharge ★★★
1. Define capacitance.2. Then describe how the current and the voltage change as a capacitor discharges through a resistor.
3. Finally, state the value of the voltage after one time constant as a fraction of the initial voltage.
Problem 7 Camera flash ★★★
A flash unit stores charge on a 150 µF capacitor charged to 300 V. The flash lasts 1.0 ms.1. Calculate the charge stored.
2. Then calculate the energy stored.
3. Finally, calculate the average power during the flash, assuming all the energy is released.
Problem 8 Memory back-up ★★★
A 1000 µF capacitor charged to 9.0 V keeps a clock memory alive by supplying a constant 2.0 mA for 1.5 s.1. Calculate the charge removed from the capacitor.
2. Then calculate the fall in voltage.
3. Finally, calculate the voltage across the capacitor at the end.
Problem 9 Three in series ★★★
Three capacitors of 6.0 µF, 3.0 µF and 2.0 µF are connected in series across a 12 V supply.1. Calculate the total capacitance.
2. Then calculate the charge on each capacitor.
3. Finally, calculate the voltage across each capacitor.
Problem 10 Network of capacitors ★★★
Aarav in Pune builds the network shown, supplied by a 9.0 V battery.2. Then calculate the total capacitance of the network.
3. Finally, calculate the total charge supplied and the energy stored.
Problem 11 Discharge calculation ★★★
A 470 µF capacitor charged to 12 V discharges through a 22 kΩ resistor.1. Calculate the time constant.
2. Then calculate the voltage after 15 s.
3. Finally, calculate the initial current.
Problem 12 Finding τ from a graph ★★★
The graph shows a capacitor discharging through a 10 kΩ resistor.2. Then use the graph to find the time constant.
3. Finally, calculate the capacitance.
Problem 13 Charging a capacitor ★★★
A 2200 µF capacitor, initially uncharged, charges from a 9.0 V supply through a 4.7 kΩ resistor.1. Calculate the time constant.
2. Then calculate the voltage across the capacitor after 10 s.
3. Finally, calculate the time taken to reach 6.0 V.
Problem 14 Spot the error ★★★
A student has an RC circuit with R = 2.2 kΩ and C = 470 µF. She writes: “τ = 2.2 × 470 = 1034 s, so the capacitor is completely discharged after one time constant.”1. Identify the two mistakes.
2. Then calculate the correct time constant.
3. Finally, state the voltage after one time constant when V₀ = 6.0 V.
Problem 15 Parallel-plate capacitor ★★★
A capacitor is made from two plates with an air gap, using ε₀ = 8.85 × 10⁻¹² F/m.2. Then calculate the charge stored at 100 V.
3. Finally, state the effect on C of halving the separation.
Problem 16 Sharing charge ★★★
Mei in Singapore charges a 4.0 µF capacitor to 12 V, disconnects it from the supply, and then connects it across an uncharged 2.0 µF capacitor.1. Calculate the initial charge.
2. Then calculate the final voltage across the pair.
3. Finally, calculate the energy before and after, and explain the difference.
Problem 17 Energy and time constant ★★★
A 1000 µF capacitor charged to 10 V discharges through a 1.0 kΩ resistor.1. Calculate the initial energy stored.
2. Then show that the energy stored falls with time as E = E₀e−2t/τ.
3. Finally, calculate the time for the stored energy to fall to 25 % of its initial value, and the voltage at that time.
Problem 18 Delay timer design ★★★
Kofi in Accra wants a lamp to switch on 30 s after pressing a button. The lamp turns on when a 470 µF capacitor, charging from a 9.0 V supply through a resistor R, reaches 6.0 V.1. Show that the delay is t = RC ln 3.
2. Then calculate the resistance needed for a 30 s delay.
3. The nearest standard value is 56 kΩ. Calculate the actual delay.
Problem 19 Linearising the decay ★★★
Bilal in Lahore records the voltage on a capacitor discharging through a 40 kΩ resistor:| t (s) | 0 | 10 | 20 | 30 | 40 |
|---|---|---|---|---|---|
| V (V) | 10.00 | 6.07 | 3.68 | 2.23 | 1.35 |
2. Then explain why a graph of ln V against t is a straight line and find its gradient.
3. Finally, determine the time constant and the capacitance.
Problem 20 Defibrillator pulse ★★★
A defibrillator charges a 32 µF capacitor to 5.0 kV. During a shock it discharges through the patient, whose body has a resistance of 50 Ω.1. Calculate the energy stored.
2. Then calculate the initial current and the time constant.
3. Finally, calculate the energy delivered in the first 2.0 ms.
