Please show steps and answer. A circuit is constructed with a resistor, two indu

Question

Please show steps and answer.

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 = 279 ohm. The values for the inductances are: L1 = 378 mH and L2 = 161 mH. The capacitance is C = 84 muF 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 wo, 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? muC 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. muC 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

energy Stoired across Indcutor is UL   = 0.5 Li^2

where Current i = V/R

i    = 12/279

i = 0.043 Amps

UL= 0.5 * 0.378 * 0.043* 0.043

UL = 3.5 *10^-4 Joules

--------------------

Resonant frequency Wo = 1/LC

Wo = (1/(0.378 * 84 e-6)

Wo = 31494 rad/sec

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