Consider the circuit below Let C = 25 Times 10^-9 F, R_1 = 80 Ohm, R_2 = 120 Ohm
ID: 1455713 • Letter: C
Question
Consider the circuit below Let C = 25 Times 10^-9 F, R_1 = 80 Ohm, R_2 = 120 Ohm R_3 = 95 Ohm and epsilon = 20 V Calculate the current supplied by the battery immediately after the switch is closed. Calculate the current supplied by the battery a very long time after the switch is closed. Calculate the energy stored in a capacitor a very long time after the switch is closed. if the switch is closed at time t = 0 Calculate how long it will take for the capacitor the charge to 50% of Its maximum charge if capacitor is allowed to fully charged and the switch is opened at new time t = 0, calculate how long it will take for the capacitor to discharge to 50% of Its maximum chargeExplanation / Answer
a)
as the switch is closed , R3 is chort circuited
i = current = 0
b)
as the switch is closed for long time , R3 is open circuited
Parallel combination of R1 and R2 is given as
R12 = R1 R2 / (R1 + R2) = 80 x 120 / (80 + 120) = 48 ohm
Current = E/R12 = 20 / 48 = 0.42 A
c)
E = Voltage across capacitor = 20 volts
after very long ,
U = (0.5) C E2 = (0.5) (25 x 10-9) (20)2 = 5 x 10-6 J
d)
T = time constant = R3C = 95 x 25 x 10-9 = 0.2375 x 10-5
t = time
Q = Qo (1 - e-t/T)
Given
Q = 0.5 Qo
(0.5) Qo = Qo (1 - e-t/(0.2375 x 10-5))
t = 1.64 x 10-6