Why is the Q–V graph for a capacitor a straight line through the origin?

Because C = Q/V is constant, so Q is directly proportional to V.

Derive E = ½CV² from E = ½QV.

Substitute Q = CV: E = ½(CV)V = ½CV².

A capacitor of 100 µF is charged to 10 V. How much energy does it store?

E = ½CV² = 0.5 × 100 × 10⁻⁶ × 100 = 5.0 × 10⁻³ J.

What is a common error with E = ½CV²?

Leaving out the factor ½, or forgetting to square V.

Energy stored by a capacitorAQA A-Level Physics: Flashcards

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What does the area under a Q–V graph represent for a capacitor?

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What does the area under a Q–V graph represent for a capacitor?: The energy stored.
What does the gradient of a Q–V graph represent?: The capacitance C.
Why is the Q–V graph for a capacitor a straight line through the origin?: Because C = Q/V is constant, so Q is directly proportional to V.
Give the three equations for the energy stored in a capacitor.: E = ½QV = ½CV² = Q²/2C.
Derive E = ½CV² from E = ½QV.: Substitute Q = CV: E = ½(CV)V = ½CV².
Which energy equation do you use when you know C and V?: E = ½CV².
Which energy equation do you use when you know Q and C?: E = Q²/2C.
What happens to the energy stored if the p.d. across a capacitor doubles?: It quadruples, as E ∝ V².
What happens to the energy stored if C doubles at the same V?: It doubles, as E ∝ C.
A capacitor of 100 µF is charged to 10 V. How much energy does it store?: E = ½CV² = 0.5 × 100 × 10⁻⁶ × 100 = 5.0 × 10⁻³ J.
How do you find the mean power when the stored energy is released in a time t?: P = E / t.
What is a common error with E = ½CV²?: Leaving out the factor ½, or forgetting to square V.

Exam questions on Energy stored by a capacitor

A 2200 µF capacitor is charged from a 9.0 V battery until the p.d. across it is 9.0 V.
Explain why a graph of charge against p.d. for this capacitor is a straight line through the origin, and show that the energy stored is ½QV.2 marks
A camera flash unit uses a 160 µF capacitor charged to 300 V. When the flash is fired, the capacitor discharges completely through the flash lamp in 2.0 ms.
The unit is later charged to only 150 V. Calculate the energy now stored and state how it compares with the energy at 300 V.2 marks
A capacitor stores a charge of 3.0 mC when the p.d. across it is 12 V. A variable power supply is then used to change the p.d. across it.
Calculate the capacitance of the capacitor and the energy stored at 12 V.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).