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[TCML] capacitor charge time?

Hey guys. 
I was explaining the tesla coil to one of my physics friends (we are both sophmores) and he asked a question that i could not answer. 

I was asked if it would be a good idea to match the time required to charge a capacitor to (1/4) of the resonant frequencies period. with the general idea that the capacitor would be completely charged when the resonant wave form was at a max or a min, thus maximizing efficiency. 

sounds like a good idea to me. 

But when we went to try and do an example calculation we realized that our standard RC capacitor charging equation would not work because our current output from the transformer was fixed and would only decrease after the cap charging current became less than or equal to our source current. 

and this spawns my question. how does one calculate the charge time of a capacitor with a fixed source voltage and current. 

does the capacitor ignore the fact that the transformer is current limited and draw that initial huge current anyway. or is there some other special equation that accounts for a limited source current and fixed source voltage. 
or are we both just missing something. 

t=-CR ln(IR/V) derived from I=V/R e^(-t/RC) 

thanks for the help 
Jay Howson 
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