A parallel plate capacitor of capacitance 4 F is charged by a potential of 3 kV. (i) What is the charge on each plate? (ii) How much energy is stored in the capacitor?
SAMPLE ANSWER 16D
(i) Using the formula Q CV, making sure all values are in their standard unit: C 4 F 4 106 F and V 3 kV 3 103V Q CV (4 106)(3 103) 1.2 102
12 mC of charge is on each plate. (ii) Using the formula
W 1 2 CV2
18 J of energy is stored in the capacitor. W 1
, making sure all values are in their standard unit: 2 CV2 1
2 (4 106)(3 103)2 18
EXERCISE 16.2 CAPACITANCE
Q1 How much charge is stored on a 6 F capacitor connected to a potential difference of 24 V? Q2 The dome of a Van de Graaff generator is charged to a voltage of 20 kV, holding a charge of 0.3 C. What is the capacitance of the dome?
Q3 What is the capacitance of an air-filled parallel plate capacitor, given that the common area of the plates is 20 cm2 and the plates are positioned 3 cm apart. (Permittivity of air 8.9 1012 F m1.)
Q4 A capacitor of capacitance 200 F is charged to a potential difference of 12 V. What is the energy stored in the capacitor?
Q5 The plates of a glass-filled parallel plate capacitor have a common area of 4 mm2 and are 0.1 mm apart.The capacitor is connected to a 12 V d.c. supply. The permittivity of glass 6.23 1011 F m1. Calculate: (i) the capacitance of the capacitor (ii) the magnitude of the charge on each plate (iii) the amount of energy stored in the capacitor.
Capacitors conduct a.c. but not d.c.5
When you connect a capacitor to a battery (d.c.), the current flows to the capacitor for a very short time.The electrons flow onto one plate and off the other. This produces a potential difference across the capacitor. Once the capacitor is charged to the same voltage as the battery, there is no emf and therefore no more current flows.
When you connect a capacitor to an a.c. supply, electrons flow onto one plate and off the other. When the polarity of the applied a.c. voltage changes, this causes the electrons to flow around the circuit in the opposite direction.This happens continuously: this is the flow of electricity.
5D.c. is direct current, which is electric current that always flows in one direction; a.c. is alternating current as it is contin- uously changing direction. D.c. and a.c. will be dealt with in Chapter 17.
