The next problems refer to the discharging of a capacitor as shown in the exampl

Question

The next problems refer to the discharging of a capacitor as shown in the example in the previous pages. Assume you have a resistor of 22kohm, and a capacitor of 15pF and the capacitor is initially charged with 75 x 10^-12 coulomb. Calculate how fast the capacitor will discharge (I want you to calculate the RC time constant here). Make sure you use the proper units and give the final time in seconds. What is the voltage of the capacitor before it is discharged? We discussed the full functional relationship for the voltage of the capacitor during the discharging process (U(t) = ?.). You can use that relationship to calculate the voltage after an amount of time has elapsed that equals the RC time constant. Calculate U(t=RC) and also calculate what the percentage value of U(t= RC) is compared to Uinitial.

Explanation / Answer

1. RC = 22 x 10^3 x 15 x 10-12 = 3.3 x 10-7

2. Q = CV

75 x 10-12 = 15 x 10-12 x V

   V = 5 Volt

3. V(t) = V e^ ( -t /Rc)

at t = RC

V(RC) = 5 e^(-RC / RC) = 1.84 V

I don;t know the previous value so

% compared to initial = (1.84 - initial / initial ) x 100

plug in the initial value and get answer in % .

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