Re: mathmatically challenged

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Jan Wagner by way of Terry Fritz <twftesla-at-qwest-dot-net>" <jwagner-at-cc.hut.fi>

Hi!

On Thu, 21 Nov 2002, Tesla list wrote:
 > Original poster: "Thad Howard by way of Terry Fritz 
<twftesla-at-qwest-dot-net>" <thoward-at-nhm-dot-org>
 > I'm having problems with  Xc = 1 / 2piFL, is F line frequency or res?
 > Same question for the inductive reactance formula.

That's a general formula, capacitive reactance Z_c = 1/(2*pi*f*C)
And Z_L = 2*pi*f*L. Any frequency. The reactance changes with frequency.

Where and how to use these or any other formula really depends on what you
want to do. ;o)

   http://www.bath.ac.uk/~chsacf/solartron/circp/html/acrci.htm

OTOH I wouldn't be suprised if there are much better pics than the above,
on RichieBurnett's site  http://www.richieburnett.co.uk/tesla.shtml
somewhere, Tesla coil operation maybe?

For some practical pictures and derivation of the resonant frequency, see
   http://engr.astate.edu/jdg/Circuits/Lab/12RLC-ResonantCircuit.html


 > My main problem is the resonant frequency formula, 4pi^F^LC=1, F= 1 /
 > 2piSQRTLC. What is F in the first part?

At resonance, the capacitive and inductive reactance are equal. This
means, you can set X_L = X_C. As said, this is at the resonant frequency,
so your F would be f_res (resonant freq).

Anyway, wanting to calculate f_res => set X_L=X_C, and this leads to

   2*pi*freq * L = 1/(2*pi*freq * C)

      multiply with 2*pi*freq and you get

   (2*pi*freq)^2 * L = 1/C

      divide with L

   (2*pi*freq)^2 = 1/(L*C)

      or multiply that with (L*C)

   (2*pi*freq)^2 * (L*C) = 1

Again, this applies to all frequencies, and any L and C.

If you know L and C, you can solve for the resonant frequency, i.e.

   (2*pi*freq)^2 = 1/LC

     take square root

   2*pi*freq = 1/(sqrt(LC))

     divide by 2*pi

   freq = 1/[2*pi*sqrt(LC)]

And there you have it. :o)

Hmm, maybe try to do this on paper, it should be much clearer
than on the PC monitor... :)

 > I'm trying to give specs to my secondary, so far I have:
 > C=11.7pF, is this .0000000000117 F? or am I on another planet? toroid is
 > and additional 30pF

uhh... (*counting*) yeah, seems right.
   1 pF = 10^(-12) F
   11.7 pF / (10^12 pF/Farad) = 11.7/10^12 = 0.0000000000117 F
(which is small, but because the TC secondary inductance is large, you
still get a low f_res (as L*C is of "medium" magnitude) )

 > L=37.2mH, is this .0372H ?

Yup, correct.
   37.2mH / (1000 mH/H) = 0.372H

have fun,

cheers,

  - Jan

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  Jan OH2GHR