On 03/20/2010 12:01 AM, Harvey Norris wrote:
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> Pioneering the Applications of Interphasal Resonances
> http://tech.groups.yahoo.com/group/teslafy/
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> --- On Fri, 3/19/10, Harvey Norris <[email protected]> wrote:
>
>> From: Harvey Norris <[email protected]> Subject: [Vo]:Pi factor To:
>> [email protected] Date: Friday, March 19, 2010, 11:18 PM The
>> energy transfer between L and C as stored joules by the
>> quantities; J= .5 CV^2 and J = .5 LI^2
> The quandary here is the fact when we measure either I or V by meter
> means, this displayed value is the rms or averaged, and the true peak
> value is therefore 1.4 times the reading.
I'm not quite sure where you're going with this, but I think it's worth
pointing out that RMS volts isn't the same as average volts (it's the
root of the average of the square, which may be rather different from
the simple average). Furthermore, peak volts are only 1.414... times
the RMS volts when you're dealing with perfect sine waves.
A sine wave with peaks of +/- 1 volt has a mean square value of 1/2
volt, and the square root of that, which is the RMS voltage, is
1/sqrt(2) volts. The peak voltage is, in this case, sqrt(2) times the
RMS value.
The same wave has an *average* voltage of 0 (positive and negative going
values cancel out, when averaged over time).
The average of the *absolute value* of our +/- 1 volt sine wave is
integral(sin(x))_0^pi / pi, which is (cos(0)-cos(pi))/pi, or 2/pi, which
is roughly 10% smaller than the RMS voltage.
Finally, if we're using a +/- 1 volt square wave, the RMS value is 1
volt; peak voltage is equal to RMS voltage. The average is again zero,
and the average of the absolute value is 1/2 volt, or half the RMS
voltage. This is rather different from the case of a sine wave!
> However even after making
> this corrective manipulation of indicating true values,
All these ways of measuring the voltage are equally "true"; neither peak
nor RMS voltage is "more true" or "more correct" than the other. But no
single number can capture all aspects of an AC signal.
> the
> comparison to actual energy transfer over time falls short by pi
> times the amount of supposed energy transfer. Here perhaps semantics,
> or wording of the involved process of description might explain this
> apparent discrepancy that has long bothered me. When we speak of
> energy transfer OVER TIME; the amount of energy being transferred {in
> time itself] is only at a peak at a certain instant of time, and
> therefore by using that derived peak value as the total amount of
> energy to be transferred in time itself, a different answer is
> arrived at. The true analysis should include the fact that the amount
> of energy being transferred over time is itself not constant,(we need
> calculus) and in fact it can be itself zero at certain time
> measurements of the time interval itself as a cycle being measured. I
> am now wondering if this is the explanation for the discrepancy of
> joules/sec vs wattage measurements in comparison for equal energy
> transfer resonant circuits.
>> and considering The I^2R heating loss of the inductor itself; when
>> the transfer of energy between L and C as joules/sec becomes equal
>> to the inductor heat loss wattage, by the inductor displaying a Q
>> factor of 3.14; the oscillation of energy between the fields has
>> become Pi times greater then its ordinary reactive state. HDN
>> Pioneering the Applications of Interphasal Resonances
>> http://tech.groups.yahoo.com/group/teslafy/
>>
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