A circuit is constructed with a resistor, two inductors, one capacitor, one batt

Question

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= 357 ?. The values for the inductances are: L1 = 295 mH and L2 = 139 mH. The capacitance is C = 138 ?F and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.

I got:

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? Answer: 1.665E-4 J

2) What is ?o, the resonant frequency of the circuit just after the switch is opened? Answer: 129.22 radians/s

I still need help with:

3) What is Qmax, the magnitude of the maximum charge on the capacitor after the switch is opened?

4) What is Q(t1), the charge on the capacitor at time t = t1 = 3.56 ms. Q(t1) is defined to be positive if V(a)

Explanation / Answer

io= current in the inductor before opening the switch = V/R1 = 12/357 = 0.0336 A

1) UL1(0) = energy stored in L1 = L1 *io^2/2 = 0.295 *(0.0336)^2/ 2 = 1.66*10^-4 J

2) Wo = resonant frequency = 1/sqrt[ (L1+L2)*C ] = 1/sqrt(0.43 *138*10^-6)   = 129.8   rad/s

3) UL(0) = energy stored in inductor just before opening the switch

                = (L1+L2)*io^2/2

              = 0.43 *(0.0336)^2/2

               = 2.42*10^-4 J

    UC = energy stored in cacapacitor = Q(max)^2/(2C)

from conservation of energy ::   Q(max)^2/(2C) = 2.42*10^-4 J

                                                   Q(max) = 2.58*10^-4 C

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