For the circuit shown in the figure, C = 12 F and R = 8.5 M?. Initially the swit
ID: 1320661 • Letter: F
Question
For the circuit shown in the figure, C = 12 F and R = 8.5 M?. Initially the switch S is open with the capacitor charged to a voltage of 80 V. The switch is then closed at time t = 0.00 s. What is the charge on the capacitor, when the current in the circuit is 3.3 A?
A)480 uC
B) 700 uC
C) 340 uC
D) 620 uC
E) 350 uC
For the circuit shown in the figure, C = 12 F and R = 8.5 M?. Initially the switch S is open with the capacitor charged to a voltage of 80 V. The switch is then closed at time t = 0.00 s. What is the charge on the capacitor, when the current in the circuit is 3.3 A? A)480 uC B) 700 uC C) 340 uC D) 620 uC E) 350 uCExplanation / Answer
Time constant, T = R*C
= 8.5*10^6*12*10^-6
= 102 s
Imax = Vo/R
= 80/8.5*106
= 9.4*10^-6 A
we know, I = Io*e^(-t/T)
let at t = t, I = 3.3*10^-6 A
so,
3.3*10^-6 = 9.4*10^-6*e^(-t/T)
e^(t/T) = 9.4/3.3
t/T = ln(9.4/3.3)
t = T*ln(9.4/3.3)
= 102*ln(9.4/3.3)
= 106.8 s
now use the euqtion, Q = Qmax*(1 - e^(-t/T))
= C*Vo*e^(-106.8/102))
= 12*10^-6*80*(1/2.718^(106.8/102))
= 340 micro C <<<<<-------------Answer
so, OptionC is the correct answer.