Hi everyone
I know that for an LC circuit to resonate, the L must equal the C.  I also know that both L and C are functions of frequency.  The question is, with a wide enough frequency range, can any LC circuit be put into resonance by the right frequency?  Or do the coil and capacitor need to be closely matched...

The next questions regard the choke coil
A) Do the coils need to be wound around each other, i.e. overlapping / intertwined?  Or can they be on opposite ends of the same core, wrapped separately?
B) Given the latter setup (separately wound on opposite ends) would it be possible to create a variable choke coil by using a hollow air core that a magnet bar could slide inside of?  My theory is that sliding the magnet in one direction or the other would alter the choke value.
Thanks!

Think of it this way perhaps. All matter has a resonance point or multiples of points. Some forms resonate easier or with less input than others due to shape or type of material or both. Electrical resonance is very much the same way. The whole circuit will have a distributed capacitance and inductance which should be accounted for for the closest approximation of a resonant frequency. Harmonics can also play a role in resonance. An easy way to practice is by using a single piece of wire and make it a coil. By doing that you are adding capacitance and inductance to the wire and it will act either as a series or parallel LC circuit when properly excited. You may even notice the the length of the leads to components will have strange effects to the circuit. A rule of thumb is to have the leads of a coil no longer than half the length of the coil but in some cases you have to find an optimum length.

Ok I think the best way to do this is bite the bullet and work out the math, instead being a wimp and relying totally on others...waterfuelcell.org has a GREAT calculator section.  Bear with me this could get ugly but it's more for me than anything, and it's a place to write it down for review.  The figures are rounded to help keep it together.  If anybody could skim this over I'd appreciate it

First, the capacitance of the cell:
K = Water dielectric constant at 20 degrees C =  80
A = Overlapping area of plates = 8" x  6" x qty. 6 =  8,915,766 mm^2
D = Distance between plates = 2mm
E= 8.854x10-12

C = Capacitance = K*E*A/D  = 0.0035663064 farads = 3556.31 uF
THAT makes sense

Next, the inductance of the primary coil:
Webers of the coil = Volts x Seconds (?)
Well, my coil is a 110V to 220V, so for every 1V in 2V come out (?)
I'll assume the max switching speed of the coil (from a UPS, iron core, about 10kg) is 20,000 Hz (?)
so Webers = 2 x .00005 = .0001 (?)
Amps = 6
L (inductance) = Webers / Amps = .00001666 H
Not so sure about this one... does the secondary winding factor in?  Are the webers right?

Finally, the resonant frequency
Fr = 1 / ( 2 * Pi * SQRT( L * C ) ) = 1 / (2 x 3.14 x sqrt ( .00001666 x .0035663)) = 2,680,078Hz.
If that's right, which it probably isn't, since I don't know WTF I'm doing and I had to redo it like 27 times, I need to build a faster PWM.... shit
God I love this