A04 and A05. An air-filled parallel plate capacitor has circular parallel plates

Question

A04 and A05. An air-filled parallel plate capacitor has circular parallel plates each of radius R = 100 cm. They are separated by a distance d = 0.100 cm. The capacitor is part of an RC circuit as shown in the circuit diagram below. The EMF of the battery is 50 V. R = 100 MOhm (1MW = 10^6Ohm). The switch is initially open and the capacitor is uncharged. What is the time-constant of this circuit? If the switch is closed, derive an expression for the magnitude of the E field between the capacitor plates at some time t (ignore edge effects).

Explanation / Answer

a)

first the capacitance of the capacitor is

C = e0 * A / d

C = 8.854 * 10^-12 * pie * 1^2 / 0.1 * 10^-2

C = 2.78 * 10^-8 F

then the time constant is t = R * C

t = 100 * 10^6 * 2.78 * 10^-10

t = 2.78 sec

b)

the electric field

E = V / d

the voltage across capacitor is Vc = 50 * 2.78 = 139 volts

then

E = 139 / 0.1 = 1390 N/C

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