The earth\'s surface and atmosphere act as a capacitor, storing negative charge

Question

The earth's surface and atmosphere act as a capacitor, storing negative charge on the surface and positive charge spread throughout the atmosphere. The capacitance is on the order of 5 F. There are two balancing currents in the atmosphere: a downward 1800 A current of ions spread over clear weather areas and an upward 1800 A current produced by lightning discharges at certain points on the earth's surface. Suppose that there is no lightning. Treating the earth and the attmosphere as a discharing RC circuit, determine how long it would take to discharge 90% of the earth's charge. The atmosphere has a resistance of about 200 ohms.

A: Book indicates 2300s, however, my professor seems to disagree and says that 105s is the actual answer.

To obtain points:

a) Show all work and workup steps that lead to your answer. This includes showing formulas before computing. This includes indicating the presence of particular constants. This includes following a logical flow which can be easily intepretable as to how you got supposed answer.

b) Choose a side, that is, decide if the book is correct or if my professor is correct. Have you work serve as evidence for that position.

Explanation / Answer

Start with the time constant, T = RC = 200(5) = 1000 sec

Then apply q = Qe^-t/RC

q/Q will be .9, so...

.9 = e^-t/RC (take the naurtal log of both sides)

-.1054 = -t/RC

.1054 = t/1000

t = 105.3 sec

Therefore I agree with your professor.

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