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3.7.4.3 Energy Stored by a Capacitor
Q1. When fully charged the 2.0 mF capacitor used as a backup for a memory unit has a potential difference of 5.0 V across it. The capacitor is required to supply a constant current of 1.0 μA and can be used until the potential difference across it falls by 10%. For how long can the capacitor be used before it must be recharged? A 10 s B 100 s C 200 s D 1000 s (Total 1 mark)
Q2. A capacitor of capacitance 10 μF is charged through a resistor R to a potential difference
(pd) of 20 V using the circuit shown. When the capacitor is fully charged which one of the following statements is incorrect? A The energy stored by the capacitor is 2 mJ. B The total energy taken from the battery during the charging process is 2 mJ. C The pd across the capacitor is 20 V. D The pd across the resistor is 0 V. (Total 1 mark) Q3. The diagram shows a rigidly-clamped straight horizontal current-carrying wire held mid-way between the poles of a magnet on a top-pan balance. The wire is perpendicular to the magnetic field direction.
The balance, which was zeroed before the switch was closed, read 161 g after the switch was closed. When the current is reversed and doubled, what would be the new reading on the balance? A −322 g B −161 g C zero D 322 g (Total 1 mark) Q4. (a) The graph shows how the current varies with time as a capacitor is discharged through a 150 Ω resistor. (i) Explain how the initial charge on the capacitor could be determined from a graph of current against time.
(2) (Total 10 marks) Q5. The specification for a pacemaker requires a suitable charge to be delivered in 1.4 ms. A designer uses a circuit with a capacitor of capacitance 3.0 μF and a 2.5 V power supply to deliver the charge. The designer calculates that a suitable charge will be delivered to the heart as the capacitor discharges from a potential difference (pd) of 2.5 V to a pd of 1.2 V in 1.4 ms. (a) (i) Calculate the charge on the capacitor when it is charged to a pd of 2.5 V. charge .................................................. C (1)
(ii) Draw a graph showing how the charge, Q , on the capacitor varies with the pd,
V , as it discharges through the heart.
Include an appropriate scale on the charge axis.
(3) (b) Calculate the energy delivered to the heart in a single pulse from the pacemaker when the capacitor discharges to 1.2 V from 2.5 V. energy ................................................... J (3) (c) (i) Calculate the resistance of the heart that has been assumed in the design.
(2) (c) Calculate the energy that is now stored by the capacitor. energy stored = _____________μJ (2) (d) Explain why there is an increase in the energy stored by the capacitor when the polythene sheet is pulled out from between the plates. ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ (2) (Total 8 marks) Q7. Which of the following statements about a parallel plate capacitor is incorrect? A The capacitance of the capacitor is the amount of charge stored by the capacitor when the pd across the plates is 1 V. B A uniform electric field exists between the plates of the capacitor. C The charge stored on the capacitor is inversely proportional to the pd across the plates. D The energy stored when the capacitor is fully charged is proportional to the square of the pd across the plates. (Total 1 mark)
Q8. Initially a charged capacitor stores 1600 μJ of energy. When the pd across it decreases by 2.0 V, the energy stored by it becomes 400 μJ. What is the capacitance of this capacitor? A 100 μF B 200 μF C 400 μF D 600 μF (Total 1 mark)
Q9. Switch S in the circuit is held in position 1, so that the capacitor C becomes fully charged to
a pd V and stores energy E.
The switch is then moved quickly to position 2, allowing C to discharge through the fixed
resistor R. It takes 36 ms for the pd across C to fall to What period of time must
elapse, after the switch has moved to position 2, before the energy stored by C has fallen
to? A 51 ms B 72 ms C 432 ms D 576 ms (Total 1 mark)
Q13. The graph shows the results of an experiment which was carried out to investigate the relationship between the charge Q stored by a capacitor and the pd V across it. Which one of the following statements is not correct? A The energy stored can be calculated by finding the area under the line. B If a capacitor of smaller capacitance had been used the gradient of the graph would be steeper. C If Q were doubled, the energy stored would be quadrupled. D The gradient of the graph is equal to the capacitance of the capacitor. (Total 1 mark) Q14. A 10 μF capacitor is fully charged to a pd of 3.0 kV. The energy stored in the capacitor can be used to lift a load of 5.0 kg through a vertical height h. What is the approximate value of h? A 0.03 mm B 0.9 mm C 0.3 m D 0.9 m (Total 1 mark) Q15. A 400 μF capacitor is charged so that the voltage across its plates rises at a
constant rate from 0 V to 4.0 V in 20 s. What current is being used to charge the capacitor? A 5 μΑ B 20 μΑ C 40 μΑ D 80 μΑ (Total 1 mark) Q16. A capacitor of capacitance C stores an amount of energy E when the pd across it is V. Which line, A to D , in the table gives the correct stored energy and pd when the charge is increased by 50%? energy pd A 1.5 E 1.5 V B 1.5 E 2.25 V C 2.25 E 1.5 V D 2.25 E 2.25 V (Total 1 mark) Q17. Capacitors and rechargeable batteries are examples of electrical devices that can be used repeatedly to store energy. (a) (i) A capacitor of capacitance 70 F is used to provide the emergency back-up in a low voltage power supply. Calculate the energy stored by this capacitor when fully charged to its maximum operating voltage of 1.2 V. Express your answer to an appropriate number of significant figures.
Which line, A to D , in the table gives the capacitance and the energy stored when the potential difference is 5.0 V? capacitance/μF energy stored/μJ A 2.0 25 B 2.0 50 C 10.0 25 D 10.0 50 (Total 1 mark) Q19. A 10 mF capacitor is charged to 10 V and then discharged completely through a small motor. During the process, the motor lifts a weight of mass 0.10 kg. If 10% of the energy stored in the capacitor is used to lift the weight, through what approximate height will the weight be lifted? A 0.05 m B 0.10 m C 0.50 m D 1.00 m (Total 1 mark)
Q20. (a) A particular heart pacemaker uses a capacitor which has a capacitance of 4. μ F. Explain what is meant by a capacitance of 4.2 μF. ...................................................................................................................... ...................................................................................................................... ...................................................................................................................... ...................................................................................................................... (2) (b) Capacitor A , of capacitance 4.2 μ F, is charged to 4.0 V and then discharged through a sample of heart tissue. This capacitor is replaced by capacitor B and the charge and discharge process repeated through the same sample of tissue. The discharge curves are shown in the figure below. (i) By considering the discharge curve for capacitor A , show that the resistance of the sample of heart tissue through which the discharge occurs is approximately 150 Ω. ............................................................................................................. ............................................................................................................. .............................................................................................................
B 2 × 10–2^ J
C 4 × 10–2^ J
D 4 × 10–1^ J
(Total 1 mark) Q22. Figure 1 shows a circuit that is used in a defibrillator in which a short pulse of charge is used to revive a patient who suffers a cardiac arrest in which their heart stops beating. Figure 2 shows how the charge on the capacitor varies with time when the capacitor is charging. Figure 1 Figure 2 (a) (i) Use Figure 2 to determine the initial charging current.
initial charging current ....................... A (2) (ii) Calculate the emf of the supply used to charge the capacitor. Assume that the supply has negligible internal resistance. ............................................................................................................. ............................................................................................................. ............................................................................................................. ............................................................................................................. emf of the supply ...................................... V (2) (iii) Explain why the current that charges the capacitor falls as the capacitor charges. ............................................................................................................. ............................................................................................................. ............................................................................................................. ............................................................................................................. ............................................................................................................. ............................................................................................................. (3) (b) For the system to work successfully, the capacitor has to deliver 140 J of energy to the heart in a pulse that lasts for 10 ms.
Q23. The graph shows how the potential difference across a capacitor varies with the charge stored by it. Which one of the following statements is correct? A The gradient of the line equals the capacitance of the capacitor. B The gradient of the line equals the energy stored by the capacitor. C The reciprocal of the gradient equals the energy stored by the capacitor. D The reciprocal of the gradient equals the capacitance of the capacitor. (Total 1 mark) Q24. A 1000 μF capacitor, X, and a 100 μF capacitor, Y, are charged to the same potential difference. Which row, A to D , in the table gives correct ratios of charge stored and energy stored by the capacitors? A 1 1 B 1 10 C 10 1 D 10 10
(Total 1 mark) Q25. In experiments to pass a very high current through a gas, a bank of capacitors of total capacitance 50 μF is charged to 30 kV. If the bank of capacitors could be discharged completely in 5.0 m s what would be the mean power delivered? A 22 kW B 110 kW C 4.5 MW D 9.0 MW (Total 1 mark) Q26. A 680 μF capacitor is charged fully from a 12 V battery. At time t = 0 the capacitor begins to discharge through a resistor. When t = 25 s the energy remaining in the capacitor is one quarter of the energy it stored at 12 V. (a) Determine the pd across the capacitor when t = 25s. ...................................................................................................................... ...................................................................................................................... ...................................................................................................................... ...................................................................................................................... (2) (b) (i) Show that the time constant of the discharge circuit is 36 s. ............................................................................................................. ............................................................................................................. .............................................................................................................
