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Is 0.5*C*V*V vaild? (Was Output Voltages and Voltage/Length)




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From:  Jim Monte [SMTP:JDM95003-at-UCONNVM.UCONN.EDU]
Sent:  Wednesday, February 04, 1998 1:27 PM
To:  tesla-at-pupman-dot-com
Subject:  Is 0.5*C*V*V vaild?  (Was Output Voltages and Voltage/Length)


Hi,

No, this doesn't belong on the "other" Tesla list.  This isn't heresy --
put the pitchforks down!! :)  I'm not going to argue with the 0.5*C*V*V
expression for energy stored in a cap.  In fact, I almost hate to
bring this up because this energy relationship seems to be such a
convenient and simple bound to disprove any Gigavolt-type claims, but
I've seen the relationship used so many times here that I just have to ask...

A Tesla secondary has distributed capacitance rather than a lumped C.
Circuit theory indicates that ac variation is with time only, not with
time and position.  For example, if a 60 Hz ideal current source is
applied to several resistors in series, they will all see the maximum
current at the same time.  This is due to the assumption that circuit
dimensions are small relative to a wavelength.  This is not true for a
Tesla coil.  Suppose that the maximum voltage distributes itself with
respect to position so that only some of the total C sees most of the
voltage.  This would seem to possibly allow a higher voltage than would
be obtained by finding the total C and solving for Vmax based on energy
considerations.  Notice how qualified this last statement is.  I don't
know if this happens, and if it does, whether it affects the results to
any great extent.  On the other hand, it doesn't seem like the possibility
can be ruled out offhand.  I would be inclined to think that it makes
very little difference, but believing something and proving it are two
different things.  Has someone taken measurements (doesn't sound too
easy directly) or done a theoretical analysis to justify that
E sec = 0.5 * Ctotal * Vsec max * Vsec max   ?

Jim Monte


>From:  Greg Leyh [SMTP:lod-at-pacbell-dot-net]
>Sent:  Tuesday, February 03, 1998 5:58 PM
>To:  Tesla List
>Subject:  Re: Output Voltages
 <snip>
>Guestimates from CST:
>
>Cpri  = 0.15uF
>Vpri  = 30,000V
>Lxtra = 20mH
>Fxtra = 86000Hz
>
>Therefore Cxtra(tot) can be calculated at 175pF.
>The coil efficiency was probably 70% or less,
>owing to the salt-water capacitors.
>
>Epri = 67.5J
>Esec = 67.5 x 70% = 47.3J
>
>Vsec = 735,000V (max, from Conservation of Energy)
>
>735kV will easily jump 30 feet and more, given that
>Tesla ran at break rates of up to 1000 BPS!
>At those break rates, 400kV would probably have
>been sufficient to produce the arcs as shown in
>the famous photographs.
>
>
>-GL
>
>