(The absolute electric permittivity of the vacuum is 8.85 X 10-12 Fm-1)
1. A 30 mF capacitor is charged by a 9 V battery.
(i) What charge is stored on it? (2.7 X 10-4 C)
(ii) What electrical energy is stored in it? (1.2 X 10-3 J)
2. Describe a laboratory experiment to show that the capacitance of a capacitor is proportional to the area of overlap of the plates, and inversely proportional to the distance between the plates.
3. A capacitor consisting of 2 parallel plates has a capacitance of 90 pF. Its plates are of sides 1 cm by 15 cm; they are held 0.4 mm apart by waxed paper. What is the paper’s relative permittivity? (2.71)
4. How long does it take for a steady current of 500 mA to charge a 5 mF capacitor to 90 V? (9 X 10-4 s)
5. A parallel-plate capacitor consists of two plates of sides 2 cm by 10 cm, which are 0.2 mm apart, with a material of relative permittivity 5.5 between them. A voltage of 20 V is put across the plates.
(a) What is the capacitance of the capacitor? (4.9 X 10-10 F)
(b) What is the electric field between the plates? (100 kVm-1)
(c) What charge is stored on one of the plates? (9.8 nC)
(d) What is the force on an ion charged 1+ (i.e.. it has lost one orbital electron) in the material between the plates? (1.6 X 10-14 N)
6. A capacitor of capacitance 470 mF is charged to 20 V, and then connected to a resistor of resistance 3000 W.
(i) What is the voltage across the capacitor 20 s after the discharging starts? (1.4 X 10-5 V)
(ii) How long does it take the voltage to drop to 10 V? (0.98 s)
7. A capacitor of capacitance 120 pF is connected to 10 V battery and then removed. It is then connected in series with a 20 kW resistor and a switch.
(i) How long will it take, after the switch is closed, for the voltage across the capacitor to drop to 1.5 V? (4.6 ms)
(ii) At this stage, how much charge is stored on the plates of the capacitor? (1.2 nC)
8. A 10 mF capacitor is connected to a battery. Then it is removed from the battery and connected to a resistance of 400 W. How long will the capacitor take to discharge to 5 % of its original charge? (0.012 s)
9. A capacitor of value C is discharging through resistor R. It discharges for a length of time CR. Show that in this time the voltage reduces to 1/e th of its original size. What percentage is this of the original voltage.
10. If you plot a graph of LnRt against t, for radioactive decay, you get a straight descending line, of slope -l. What would be a similar graph to plot for the discharging of a capacitor? What would the slope be?
11. A capacitor is charged to 9 V and then discharged through a resistor. It takes 20 s to reduce to 4.5 V. What would happen to this time if (separately):
(i) the resistance was doubled?
(ii) the capacitance was halved?
(iii) the resistance increased X 3 and the capacitance was doubled?
12. An uncharged capacitor of capacitance 5 mF is connected to 6 V battery, in series with a 100 kW resistor and a switch. At t = 0 the switch is closed. Sketch graphs to show how the current supplied by the battery, the voltage across the capacitor, and the voltage across the resistor, vary with time. Calculate suitable values to put onto the two axes on each graph, including the time that has elapsed when the quantities have reached half their maximum values. (0.35 s)
13. (i) A laboratory demonstration capacitor consists of two metal plates, of sides 18 cm by 16 cm, which are placed 3 mm apart. The relative permittivity of air is 1.0003. Calculate the capacitance of this capacitor.
(ii) A glass sheet, of relative permittivity 3.2, is fitted between the plates. What is the new capacitance?
(ii) The previous calculated capacitances are extremely small. Explain how a real capacitor is designed so that it has a much larger capacitance, yet takes up a much smaller volume.
14*. A transistor switches on if the potential difference between two of its terminals increases above 0.63 V. You have a 1.5 V cell (of negligible internal resistance). You want the transistor to switch on 12 s after a switch is closed.
(i) Work out a pair of realistic values for the resistor and capacitor that you would use in the circuit.
(ii) Draw the circuit.
15*. A capacitor of value 150 mF is in a circuit such that it can be charged by a 20 V supply, and then discharged through a galvanometer, 450 times per second. What is the average steady current that the galvanometer would be reading? (1.35 A)
16*. A 20 mF capacitor is charged up with a 1.5 V cell. Then it is removed from its connections to the cell, and instead is connected in parallel to a second uncharged 25 mF capacitor.
(i) What is the final voltage across the two capacitors? (Hint: What is conserved during the transfer process) (0.67 V)
(ii) How much energy is now stored in total in the two capacitors? (10 mJ)
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