# Initial conditions in multi-state Tesla Coil circuit

Half a year ago I posted this quesion about a Tesla Coil resonant circuit which got an amazing answer that helped me understand the resonant frenquency of such circuit.

Now I've returned to that problem and I want to know what happens in the following scenario. I will not post the values of the components since I just want a theoretical answer to understand better this kind of circuits, but I can say that the relation $$L_1C_1=L_2C_2$$ is fulfilled. The circuit is shown below:

The capacitor C1 is the only one charged. It releases its energy and the circuit starts resonating. The voltage across C2 has the following form:

which can be translated in the mathematical expression: $$137898 \cdot (\cos(978300t) − \cos(1081600t))$$

Now, the switch Sw1 opens and Sw2 closes at the same time. Then, the circuit that (I think) results is:

My questions are:

1. Would the value of Vmax at Figure 3 be determined by the value of vSw2(t) at the instant when switch Sw2 closes and Sw1 opens?
2. Is it true that, as one of the coupled inductors is in an open-circuit, given that Sw1 is open, the initial conditions at inductor L2 are 0? In other words, is the circuit that I've drawn in Figure 3 accurate?
3. Since there are no resistive elements at circuit from Figure 1, mathematically it seems correct that the equation of the voltage vSw2(t) has only cosines, but in reality the voltage would converge to 0 due to the internal resistances of the components, right?
• It looks wrong, as the left side arcs open with no resonant circuit in theory and charges up the cap to some DC V after successive switches The arc is not a voltage source but rather and negative resistance to a charge dump. Current rises as voltage collapses. This is what you have tinyurl.com/unqp4ax – Tony Stewart Sunnyskyguy EE75 Dec 24 '19 at 2:17
• or here tinyurl.com/rafw3m9 as you can see, unless you define values you dont get the same thing – Tony Stewart Sunnyskyguy EE75 Dec 24 '19 at 2:23