Energy stored in a capacitor and the Q–V graph

Overview

Recall questions on Energy stored in a capacitor and the Q–V graph.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   State three equivalent expressions for the energy stored in a charged capacitor.

   Model answer

   The energy is given by U = ½QV, by U = ½CV² and by U = Q²/2C.

2. 2

   Show how the expression U = ½CV² follows from U = ½QV.

   Model answer

   Substituting Q = CV into ½QV gives ½CV × V. Collecting the two factors of V gives ½CV².

3. 3

   What does the area under a graph of charge against potential difference represent?

   Model answer

   It represents the energy stored in the capacitor.

4. 4

   A 470 μF capacitor is charged to 12 V. Calculate the energy it stores.

   Model answer

   Using U = ½CV² gives 0.5 × 470 × 10⁻⁶ × 12² = 3.4 × 10⁻² J.

5. 5

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

   Model answer

   The stored energy becomes four times as large, because the energy is proportional to the square of the potential difference.

6. 6

   A capacitor stores 0.20 J of energy when charged to 50 V. Calculate its capacitance.

   Model answer

   Rearranging U = ½CV² gives C = 2 × 0.20 ÷ 50² = 1.6 × 10⁻⁴ F. In more usual units that is 160 μF.

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