Re: Circulating Power

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

Original poster: "Jim Lux by way of Terry Fritz <teslalist-at-qwest-dot-net>" <jimlux-at-earthlink-dot-net>

I started doing a similar calcuation and came up with a couple
interpretations..
First.. energy transfer during a cycle (as Finn shows, but for the whole
cycle, not just the first half cycle)
C to L, L to C(reversed), C to L, L to C... 4 transfers in one cycle, so P =
Energy*4/period
Energy = 1/2*C*V^2
Period = 2*pi*sqrt(L*C)
So.. Power = C*V^2/(4 *pi* sqrt(L*C)) = V^2 * 1/(4*pi) * sqrt(C/L)

But, another interpretation is in the power engineering "var flow" sense...
Since current is 90 degrees out of phase with voltage in the
inductor/capacitor, all the current is circulating.
The circulating power would be Vrms*Irms
Vrms = Vpeak / sqrt(2)
Irms = Ipeak / sqrt(2)
Ipeak^2 * L  = Vpeak^2 * C >>>> Ipeak = sqrt(Vpeak^2 * C/L) =
sqrt(Vpeak^2)*sqrt(C/L) = Vpeak *sqrt(C/L)
So.. Vars = Vpeak / sqrt(2) * Ipeak / sqrt(2) = Vpeak*Ipeak/2
= Vpeak * Vpeak * sqrt(C/L)/2

Which looks remarkably like the first way, except that there's an extra
2*pi...

Too early in the morning to figure out why.




----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Sunday, April 20, 2003 9:22 AM
Subject: Re: Circulating Power


 > Original poster: "Finn Hammer by way of Terry Fritz <teslalist-at-qwest-dot-net>"
<f-h-at-c.dk>
 >
 > Zoran,
 >
 > Since you mention both the presence of a capacitor and an oscillation,
 > as well as stating that it is ideal,  I assume you have a resistively
 > lossless L C circuit in mind.
 >
 > The initial charge on the capacitor is going to be 1/2*U^2*C . This will
 > transfer into 1/2*L*I^2 and back into 1/2*U^2*C.
 > Since power is Joule/time, you could say that the power is 1/2*U^2*C/1
 >
 > Hope I am right, and that it helps.
 >
 > Cheers, Finn Hammer
 >
 > Tesla list skriver:
 >  >
 >  > Original poster: "Zoran Tukovic by way of Terry Fritz
 > <teslalist-at-qwest-dot-net>" <ztukovic-at-globalnet.hr>
 >  >
 >  > How can we calculate Circulating Power in ideal condenser discharge
 >  > oscillating circuit ?
 >  >
 >  > Regards,
 >  > Zoran
 >
 >