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# Complex Power

### Formulas

When a voltage V causes a current I to flow through a reactive load Z, the complex power S is:

S = VI* where I* is the conjugate of the complex current I.

Z = R + jXL

I = IP – jIQ

cosf = R / |Z| (lagging)

I* = IP + jIQ

S = P + jQ

An inductive load is a sink of lagging VArs (a source of leading VArs).

Z = R – jXC

I = IP + jIQ

cosf = R / |Z| (leading)

I* = IP – jIQ

S = P – jQ

A capacitive load is a source of lagging VArs (a sink of leading VArs).

 NOTATION The symbol font is used for some notation and formulae. If the Greek symbols for alpha beta delta do not appear here [ a b d ] the symbol font needs to be installed for correct display of notation and formulae. B C E f G h I j L P Q susceptance capacitance voltage source frequency conductance h-operator current j-operator inductance active power reactive power [siemens, S] [farads, F] [volts, V] [hertz, Hz] [siemens, S] [1Ð120°] [amps, A] [1Ð90°] [henrys, H] [watts, W] [VAreactive, VArs] Q R S t V W X Y Z f w quality factor resistance apparent power time voltage drop energy reactance admittance impedance phase angle angular frequency [number] [ohms, W] [volt-amps, VA] [seconds, s] [volts, V] [joules, J] [ohms, W] [siemens, S] [ohms, W] [degrees, °] [rad/sec]

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