Energy stored by a capacitorAQA A-Level Physics: Subtopic test

1. 1
   A 2200 µF capacitor is charged from a 9.0 V battery until the p.d. across it is 9.0 V.

   (a)

   Calculate the energy stored in the capacitor.

   [1 mark]

   • A1.8 × 10⁻¹ J
   • B8.9 × 10⁻² J
   • C9.9 × 10⁻³ J
   • D2.0 × 10⁻² J

   (b)

   The capacitor is charged so that Q is directly proportional to V. Which feature of a graph of charge against p.d. represents the energy stored?

   [1 mark]

   • AThe gradient of the graph
   • BThe intercept on the charge axis
   • CThe reciprocal of the gradient
   • DThe area under the graph

   (c)

   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]

   Total for question 1: 4 marks

2. 2
   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.

   (a)

   How much energy is stored in the capacitor before the flash?

   [1 mark]

   • A1.4 × 10¹ J
   • B2.4 × 10⁻² J
   • C7.2 J
   • D3.6 J

   (b)

   What is the mean power delivered to the lamp during the flash?

   [1 mark]

   • A3.6 × 10³ W
   • B1.4 × 10⁻² W
   • C1.8 × 10³ W
   • D3.6 W

   (c)

   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]

   Total for question 2: 4 marks

3. 3
   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.

   (a)

   Calculate the capacitance of the capacitor and the energy stored at 12 V.

   [3 marks]

   (b)

   The p.d. is now doubled to 24 V. Calculate the new charge stored and the additional energy that must be supplied to the capacitor, and explain why the energy does not simply double.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A defibrillator stores energy in an 80 µF capacitor charged to a p.d. of 2.0 kV. When it is used, the stored energy is delivered to the patient in 5.0 ms.

   (a)

   Calculate the charge stored, the energy stored, and the mean power delivered to the patient.

   [6 marks]

   (b)

   A clinician needs the capacitor to store 320 J. Two designs are proposed: keep the 80 µF capacitor and increase the p.d., or keep the 2.0 kV p.d. and increase the capacitance. Calculate the value needed for each design and evaluate which is more suitable for a portable device.

   [6 marks]

   Total for question 4: 12 marks

End of questions