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 = 261 %u03A9. The values for the inductances are: L1 = 351 mH and L2 = 143 mH. The capacitance is C = 71 %u03BCF 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? (Ans is in Joules)

2)What is %u03C9o, the resonant frequency of the circuit just after the switch is opened? (Ans is in radians/s)

3)What is Qmax, the magnitude of the maximum charge on the capacitor after the switch is opened? (Ans is in %u03BCC)

4)What is Q(t1), the charge on the capacitor at time t = t1 = 2.49 ms. Q(t1) is defined to be positive if V(a) %u2013 V(b) is positive. (Ans is in %u03BCC)

5)What is t2, the first time after the switch is opened that the energy stored in the capacitor is a maximum? (Ans is in ms)

6)What is the total energy stored in the inductors plus the capacitor at time t = t2? (Ans is in Joules)

Explanation / Answer

2.)resonant frequency = 1/sqrt(C(L1+L2))
3.) CV^2 =(L1+L2) 0.045^2
V = 3.75 V Q= 266 ucoloumb= 266.5 x 10 -6
6.) 1 joule

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