A negatively charged thundercloud above the Earth’s surface may be modelled by a parallel plate capacitor.
The lower plate of the capacitor is the Earth’s surface and the upper plate is the base of the thundercloud.
The following data are available.
Area of thunder cloud base = 4.7 × 1012 cm2
Distance of thundercloud base from Earth’s surface = 5600 m
Permittivity of air = 8.8 pF m-1
Lightning takes place when the capacitor discharges through the air between the thundercloud and the Earth’s surface. The time constant of the system is 48 ms. A lightning strike lasts for 25 ms.
(a)
Show that the capacitance of this arrangement is C = 740 nF.
An uncharged capacitor in a vacuum is connected to a cell of emf 18 V and negligible internal resistance. A resistor of resistance R is also connected.
At t = 0 the switch is placed at position Y. The graph shows the variation with time t of the voltage V across the capacitor. The capacitor has capacitance 2.8 μF in a vacuum.
(a)
On the axes, draw a graph to show the variation with time of the voltage across the resistor when the switch is placed at position X.
The capacitors are now connected in a circuit. A two-way switch S can connect the capacitors either to a d.c. supply, of e.m.f. 14 V, or to a voltmeter.
The switch is first connected to the d.c. supply.
(b)
Explain why the energy stored in the 2 µF capacitor is greater than the energy stored by the combined 3 µF and 4 µF capacitors.
A capacitor of capacitance C1 is discharged through a resistor of 550 MΩ. The graph shows the variation with time t of the voltage V across the capacitor.
The capacitor from part (a) is now connected in series with another capacitor of capacitance, C2. They are both fully charged by a potential difference V. Their combined capacitance is 0.3 nF.
