It's amazing how far a thread can go with
no one having the slightest clue as to what the application is !!!
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Oh, you mean like this one? https://forum.allaboutcircuits.com/threads/electrical-power-design.191279/#post-1791182

 

RE:""Would this produce an AC signal on the coil?""
Sure will. BUT, if You misshap to take capacitor making near-resonant obstacles with L for the applied frequency, will happen the resonant Voltage multiplication. For example, set Vcc the 12 Volts and get the 12 kV on the coil. What coil will say, its not known, but what shall say the capacitor is well known. While its foil will scroll down the hat size hole in the ceiling, the stink will fill all the hose. Sorry. That sad experience. So, take always the capacitor large enough to not come near the Thomsson formula value.

 

The voltage developed across a resonant circuit depends on a lot of things, including the power level and impedance of the drive, and the actual resistance of the components.
Given that we are not presented with that information, other than that different coils will see different frequencies, an accurate prediction is difficult.