# Question: a circuit is constructed with a resistor two inductors one...

###### Question details

A circuit is constructed with a resistor, two inductors, one
capacitor, one battery and a switch as shown. The value of the
resistance is R_{1} = 429 Ω. The values for the inductances
are: L_{1} = 203 mH and L_{2} = 111 mH. The
capacitance is C = 188 μF 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 U_{L1}(0), the magnitude of
the energy stored in inductor L_{1} just after the switch
is opened?

2) What is ω_{o}, the resonant frequency of the circuit
just after the switch is opened?

3) What is Q_{max}, the magnitude of the maximum charge
on the capacitor after the switch is opened?

4) What is Q(t_{1}), the charge on the capacitor at time
t = t_{1} = 3.38 ms. Q(t_{1}) is defined to be
positive if V(a) – V(b) is positive.

5) What is t_{2}, the first time after the switch is
opened that the energy stored in the capacitor is a maximum?

6) What is the total energy stored in the inductors plus the
capacitor at time t = t_{2}?