# Re: Energy Equations For LC Standing Wave Resonance

• To: tesla@xxxxxxxxxx
• Subject: Re: Energy Equations For LC Standing Wave Resonance
• From: "Tesla list" <tesla@xxxxxxxxxx>
• Date: Sat, 09 Jul 2005 18:15:26 -0600
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• Resent-date: Sun, 10 Jul 2005 09:43:23 -0600 (MDT)
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`Original poster: Terry Fritz <teslalist@xxxxxxxxxxxxxxxxxxxxxxx>`

`Hi,`

At 05:23 AM 7/9/2005, you wrote:
```................
Now:```

```Let the total sum of capacitance for a series LC system be represented
by a spherical capacitor with the second plate at infinity.```

Capacitance = 4pi e R

How do you justify this? It implies that 2 coils with the same radius will always have the same capacitance regardless of coil length. I don't see how this can be proven...

`................`

``` w = n/2  2pi C/ wire length = 1/ sqrt( u (Turns/2n)sqrd Area
2n/Length  [Cap] )
where n = 1/2, 2/2, 3/2 ?.```

`Example:`

`With a quarter wave where n = 1/2  (1/2 a node represented) we get:`

`2pi C/4wire = 1/ sqrt LC   or C/ 4 wire = 1/ 2pi sqrtLC`

```This is Tesla?s classic quarter wave formulae. The rope resonance
model has allowed us to extend Tesla?s formulae to the general case.
```

Since the top of the coil is always an anti-node and the bottom is always a node in the case of a Tesla coil, we can use n = 1/2, 3/2, 5/2.... In actual practice, this only gives a rough estimation of the actual resonant frequencies.

```.......
Modeling Resonant transformers after the energy equations of rope
resonance has allowed us to develop an array of new coils, all of them
working directly from the drawing board.
```

Is there a case, where if one did not follow these rules, that the coil would not work?

`Cheers,`

`        Terry`

```Respectfully:
Jared Dwarshuis and Larry Morris
July 9, 2005
```