3. The discharge curve for a capacitor connected in series with a resistor is sh

Question

3. The discharge curve for a capacitor connected in series with a resistor is shown below. (a) If the capacitance of the capacitor is 23.50 farads, what is the resistance of the resistor? (b) Please calculate the time constant for this circuit. (c) After two time constants what is the potential across capacitor (d) Please calculate the amount of charge on the capacitor 25.00 minutes after discharge has started. (b) Once the capacitor is fully discharged, the charging process begun. How much time, after charging begins, is required for the potential difference across the capacitor to reach 18.50 volts? (20 pts) 3500 30.00 25.00 OICICICICI 15.00 10.00 OTTTTT NOOOOOOOOOOOOOOOOOOOOOOD IDOTI 0.08 0.00 1000 20.00 30.00 0.0050.00 G0.00 70.00 Time (minutes)

Explanation / Answer

a)

Capacitance = C = 23 .5 F

T = time constant = RC = 23.5R

t = time = 2 sec

Vc = 35 Volts

Vmax = 40 volts

using the equation

Vc = Vmax e-t/T

35 = 40 e-2/(23.5R)

R = 0.64 ohm

b)

T = time constant = RC = 23.5 x 0.64 = 15.04 min

c)

t = 2T

Vc =  Vmax e-t/T

Vc = 40 e-2T/T

Vc = 5.41 Volts

d)

Vc = 40 e-25/15.04 = 7.6 Volts

Qc = charge = CV = 23.5 x 7.6 = 178.6 C

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