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Energy stored on a capacitor

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on why the stored energy is not simply charge times voltage, the equivalent expressions, area under a charge–voltage graph, delivering large power briefly, and where a battery's energy goes.

What you need to know

Answer each one before you reveal it.

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Key term

Explain why the energy stored on a capacitor is less than the work done by the battery charging it.

Key term

Why is the energy stored on a capacitor ½QV rather than QV?

Key term

What are the three equivalent expressions for the energy stored on a capacitor?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Why is the energy stored on a capacitor ½QV rather than QV?

    Model answer

    The potential difference rises from zero to V as charge builds up, so the average potential difference through which the charge is moved is only ½V.

  2. 2

    What are the three equivalent expressions for the energy stored on a capacitor?

    Model answer

    The energy is E = ½QV, E = ½CV² and E = ½Q²/C.

  3. 3

    How is the energy stored on a capacitor found from a graph of charge against potential difference?

    Model answer

    It is the area under the Q–V graph, which for a straight line through the origin is the triangle of area ½QV.

  4. 4

    A 470 μF capacitor is charged to 12 V. How much energy is stored?

    Model answer

    E = ½CV² = 0.5 × 470 × 10⁻⁶ × 12² = 3.4 × 10⁻² J.

  5. 5

    A capacitor stores 6.0 mC at 9.0 V. Calculate the energy stored.

    Model answer

    E = ½QV = 0.5 × 6.0 × 10⁻³ × 9.0 = 2.7 × 10⁻² J.

  6. 6

    What happens to the energy stored on a capacitor if the potential difference across it is doubled?

    Model answer

    The energy becomes four times larger, because E = ½CV² makes the energy proportional to the square of the potential difference.

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