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




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From:  richard hull [SMTP:rhull-at-richmond.infi-dot-net]
Sent:  Thursday, February 05, 1998 7:27 PM
To:  Tesla List
Subject:  Re: Is 0.5*C*V*V vaild?  (Was Output Voltages and  Voltage/Length)

At 12:41 AM 2/5/98 -0600, you wrote:
>
>----------
>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

Jim,

The C used in the equations is the discharge terminal's Cterm and usually
dwarfs the Cdistrib. of the resonator.  Massive terminal loadings are the
norm now and long sparks just can't be have from simple free standing
resonators.  Thus, the Cterm is a large, lumped storage capacity.  So large
that the average big system with properly proportioned terminal can have its
resonantor's natural frequency cut in half or even to one third, by this
lumped addition.

Richard Hull, TCBOR