Help with analyzation theory

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Original poster: "Adam R." <arabraxas@xxxxxxxxxxx>

I've been working with coils for awhile now, but am still just a 
beginner's student in EE and am working to understand the circuit of 
the coil, but am running into some bumps in the road so I am 
wondering if someone can point me in the right direction. For 
brevity's sake, I won't rattle off too much off what I'm stuck on. 
I'm just asking the "whys?" of what is going on.

First, I don't quite understand how the i(t)=C(dv/dt) can get so high 
(ie hundreds of amps). I also don't fully understand the nature of 
the 60hz to high frequency tank circuit.

What's throwing me off is how I'm looking at the circuit in the 
manner of an LC, the cap/indu reactance, and etc., I'm trying to 
piece things together, but they don't seem to fit, especially when I 
add the spark gap. The math equations keep forming odd numbers, such 
as 13269 amps! I'm not trying derive everything, but just again, see 
how things (mathematically) fit together.

I don't want the theory "spoon fed" to me, just if someone could 
start pointing me in the right direction as to what I should 
research. Thanks in advance!