Energy stored in a capacitor Cambridge International AS & A Level Physics revision
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In plain words
Charging a capacitor takes work: every extra bit of charge has to be pushed on against the charge that is already there. That work is stored, and it can be let out in a rush, which is how a camera flash gets its burst from a small battery.
Three things to know
- The energy stored is the area under a graph of p.d. against charge. The graph is a straight line through the origin, so the area is a triangle: W = ½QV.
- Using Q = CV, the same energy is W = ½CV², or W = ½Q² ÷ C.
- The battery supplies an energy QV, but only half is stored. The rest is dissipated in the resistance of the circuit while the capacitor charges.
Worked example
A 470 µF capacitor is charged to 12 V. Find the energy stored in it.
- W = ½CV².
- = ½ × 470 × 10⁻⁶ × 12².
- = 0.034 J.
Tips and tricks
- Double the p.d. and the energy stored is four times bigger.
- The half comes from the triangle under the graph: the p.d. rises as the charge goes on.
It lands in your notebook with its questions as flashcards.
Energy stored in a capacitor: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What does the area under a graph of p.d. against charge for a capacitor represent?
Each bit of charge is pushed through the p.d. at that moment.
The p.d. across a capacitor is doubled. What happens to the energy stored?
W = ½CV².
How much energy is stored in a 2.0 µF capacitor charged to 100 V?
½ × 2.0 × 10⁻⁶ × 100².
Which of these is not an expression for the energy stored in a capacitor?
QV is the energy supplied by the battery, which is twice what is stored.
A battery supplies an energy QV while charging a capacitor. How much of it ends up stored in the capacitor?
The other half is dissipated in the resistance of the circuit.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 9 marks. Write your answers on paper, then check them.
Energy stored in a capacitor
Cambridge International AS & A Level Physics 9702 · 9 marks · papermunch.org
Name ______________________________ Date ______________
Find the energy stored in a 100 µF capacitor charged to 20 V.[2]
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0.020 J.
A capacitor holds a charge of 6.0 mC at a p.d. of 12 V. Find the energy stored.[2]
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0.036 J. ½ × 6.0 × 10⁻³ × 12.
A 2200 µF capacitor charged to 9.0 V discharges through a lamp in 0.050 s. Find the energy stored, and the average power delivered to the lamp.[3]
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0.089 J, and 1.8 W.
Explain why the energy stored in a capacitor is ½QV and not QV.[2]
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The p.d. is not V the whole time: it rises from zero to V as the capacitor charges. The energy is the area under the p.d.–charge graph, which is a triangle, so it is half of Q × V.
Answers: Energy stored in a capacitor
- 1. 0.020 J.
- 2. 0.036 J. ½ × 6.0 × 10⁻³ × 12.
- 3. 0.089 J, and 1.8 W.
- 4. The p.d. is not V the whole time: it rises from zero to V as the capacitor charges. The energy is the area under the p.d.–charge graph, which is a triangle, so it is half of Q × V.