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Some Equations Useful in AC Power Calculations

# Some Equations Useful in AC Power Calculations - pf = cos...

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Some Equations Useful in AC Power Calculations Notation: All bold-face letters represent complex numbers. RMS Value of a Sinusoid V rms = V p / 2 I rms = I p / 2 Impedance Z = R + j X = | Z |∠θ | Z | = (R 2 + X 2 ) 1/2 θ = tan - 1 (X/R) Note: θ is the angle of the load impedance (We have suppressed the subscript z.) Ohm’s Law in Frequency Domain V = IZ V p = I p | Z | V rms = V / 2 I rms = I / 2 V rms = I rms | Z | θ v - θ i = θ θ > 0 when X > 0 (Inductive impedance) θ < 0 when X < 0 (Capacitive impedance) Average Power (W) P = V rms I rms cos θ = I rms 2 R = (V rms 2 cos θ )/ | Z | Power Factor
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Unformatted text preview: pf = cos θ = R/(R 2 + X 2 ) 1/2 , 1 ≥ pf ≥ 0. If θ > 0 (inductive impedance), θ i < θ v , pf lagging If θ < 0 (capacitive impedance), θ i > θ v , pf leading If θ = 0 for purely resistive load and the pf is unity Reactive Power (VAR) Q = V rms I rms sin θ = I rms 2 X Apparent Power (VA) S = V rms I rms = I rms 2 | Z | = V rms 2 / | Z | Complex Power (VA) S = V rms ( I rms )* = V rms I rms ∠θ = P + j Q = I rms 2 Z = ( V rms ) 2 / Z *...
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