A circuit is constructed with two capacitors and an inductor as shown. The value
ID: 1400509 • Letter: A
Question
A circuit is constructed with two capacitors and an inductor as shown. The values for the capacitors are: C1 = 376 F and C2 = 129 F. The inductance is L = 336 mH. At time t =0, the current through the inductor has its maximum value IL(0) = 264 mA and it has the direction shown.
1)
What is o, the resonant frequency of this circuit?
radians/s
Your submissions:
176
Computed value:
176
Submitted:
Thursday, July 23 at 5:13 PM
Feedback:
Your answer has been judged correct; the exact answer is: 176.030236618914.
2)
What is Q1(t1), the charge on the capacitor C1 at time t = t1 = 20.8 ms? The sign of Q1 is defined to be the sameas the sign of the potential difference Vab = Va - Vb at time t = t1.
C
Your submissions:
0.00019
Computed value:
0.00019
Submitted:
Thursday, July 23 at 5:15 PM
Feedback:
3)
What is Vbc(t1)= Vb - Vc, the voltage across the inductor at time t1 = 20.8 ms? Note that this voltage is a signed number.
V
Your submissions:
0
Computed value:
0
Submitted:
Thursday, July 23 at 5:01 PM
Feedback:
The voltage across the inductor at time t1 is not zero. Think about what the current is doing at t = 0 and how it will change in time. What is the voltage across the inductor at t = 0?
4)
What is Q1,max, the magnitude of the maximum charge on capacitor C1?
C
5)
At time t = t2, the magnitude of the current through the inductor has its maximum value. What are the magnitudes of Q1, the charge on capacitor C1, and VL, the voltage across the inductor at this time?
Q1 = Qmax and VL = Vmax
Q1 = 0 and VL = Vmax
Q1 = Qmax and VL = 0
Q1 = 0 and VL = 0
Explanation / Answer
(1) First of all we have to calculate Ceq that is equivalent of capacitor and that will be
Ceq = C1C2/(C1+C2) = 96.047*10-6 F
Wo = (1/LCeq)1/2 = (1/(336*10-3*96.047*10-6)) = 176.03 rad /s
(2) Max. Charge (Qo) = Imax /W0 = 1.499*10-3 C
Q = QoCos(Wt) = 1.459*10-3 C
(3)VL = - Imax (XLSinWt) = 0.9968 V
(4) Maximum charge is already calculated = 1.499*10-3 C
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