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Plasma power calculation

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Fikadu

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With a given load( assume it is plasma) impedance of 6.55 - j87.906‎Ω and RF power P = 1KW, one can calculate a current I = Sqrt(P/R) = Sqrt(1000/6.55) = 12.35 Amps. V= Sqrt(P*|Z|) = Sqrt(88.15*1000) = 296Volts , Where |Z| = Sqrt( R^2 + X^2) = 88.15‎Ω. On the other hand, as to my understanding one may calculate V as V = I*|Z| = 12.35 *88.15 = 1089Volts. Here is my doubts, why a result from V= Sqrt(P*|Z|) is different from V = I*|Z| V = I*|Z| ? which one is correct in principle? I am not of the filed electronics engineering. I would extend a huge thanks for the one who may help me . Thank you
 
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JimB

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one can calculate a current I = Sqrt(P/R) = Sqrt(1000/6.55) = 12.35 Amps.
Correct.
You have used the RESISTIVE (R) part of the impedance to calculate the power.
Note that the REACTIVE (X) part of the impedance does not dissipate power.

Where |Z| = Sqrt( R^2 + X^2) = 88.15‎Ω.
Correct, assuming that the resistance and the reactance are in series.

one may calculate V as V = I*|Z| = 12.35 *88.15 = 1089Volts.
Correct.
This is the voltage across the resistive and reactive part of the impedance.

why a result from V= Sqrt(P*|Z|) is different from V = I*|Z| V = I*|Z| ? which one is correct in principle?
Both are correct in their own way !

The problem is your lack of understanding of resistive and reactive circuits.

V= Sqrt(P*|Z|) = Sqrt(88.15*1000) = 296Volts
Wrong.

You have a series circuit, the same current (12.35 Amps) flows through both the resistive and reactive part of the impedance.
For the "resistor"
V = I x R = 12.35 x 6.55 = 80.3 volts.

For the "reactor"
V = I x X = 12.35 x 87.906 = 1085.6 volts.

To find the total voltage, we cannot simply add 80.3 + 1085.6 = xxxx,
This is not correct because the voltages are 90 degrees out of phase with each other.
We must do:

V = sqrt ( 80.3 x 80.3 + 1085.6 x 1085.6) = 1088.6v (near enough the 1089v which was calculated earlier)

I hope that this makes sense to you.

JimB
 
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