LC Circuit 2 1 1 3 4 5 6 7 A circuit is constructed with a resistor, two inducto
ID: 1786938 • Letter: L
Question
LC Circuit 2
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A circuit is constructed with a resistor, two inductors, one capacitor, one battery and a switch as shown. The value of the resistance is R1 = 344 . The values for the inductances are: L1 = 276 mH and L2 = 126 mH. The capacitance is C = 129 F and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.
1)
The switch has been closed for a long time when at time t = 0, the switch is opened. What is UL1(0), the magnitude of the energy stored in inductor L1 just after the switch is opened?
J
2)
What is o, the resonant frequency of the circuit just after the switch is opened?
radians/s
3)
What is Qmax, the magnitude of the maximum charge on the capacitor after the switch is opened?
C
4)
What is Q(t1), the charge on the capacitor at time t = t1 = 3.1 ms. Q(t1) is defined to be positive if V(a) – V(b) is positive.
C
5)
What is t2, the first time after the switch is opened that the energy stored in the capacitor is a maximum?
ms
6)
What is the total energy stored in the inductors plus the capacitor at time t = t2?
J
Explanation / Answer
1.
Current
I=V/R =12/344 =0.03488 A
UL1(0)=(1/2)L1I2=(1/2)*0.276*0.034882=1.68*10-4 J
2.
Resonant frequendy
Wo=1/sqrt(LeqC)=1/sqrt[(0.276+0.126)*(129*10-6)]
Wo=138.864 rad/sec
3.
UL=UC
(1/2)LeqI2=(1/2)(Qmax2/C)
Qmax=sqrt(LeqCI2)=sqrt[(0.276+0.126)(129*10-6)*0.034882]
Qmax=251.2 uC
d)
Q=Qmax sin(Wt)
Q=(251.2)sin(138.864*0.0031)=104.83 uC
e)
Q=Qmax
=>Qmax =Qmax sin(138.864t)
pi/2 =138.864t
t=11.31 ms
f)
U=(1/2)(251.2*10-6)2/(129*10-6)
U=2.4457*10-4 J
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