346CHAPTER 11. POWER FACTOR• In a circuit consisting of resistance and reactance mixed, there will be more power dissipatedby the load(s) than returned, but some power will deﬁnitely be dissipated and some will merelybe absorbed and returned. Voltage and current in such a circuit will be out of phase by a valuesomewhere between 0o and 90o.11.2True, Reactive, and Apparent powerWe know that reactive loads such as inductors and capacitors dissipate zero power, yet the fact thatthey drop voltage and draw current gives the deceptive impression that they actually do dissipatepower. This “phantom power” is called reactive power, and it is measured in a unit called Volt-Amps-Reactive (VAR), rather than watts. The mathematical symbol for reactive power is (unfortunately)the capital letter Q. The actual amount of power being used, or dissipated, in a circuit is called truepower, and it is measured in watts (symbolized by the capital letter P, as always). The combinationof reactive power and true power is called apparent power, and it is the product of a circuit’s voltageand current, without reference to phase angle. Apparent power is measured in the unit of Volt-Amps(VA) and is symbolized by the capital letter S.As a rule, true power is a function of a circuit’s dissipative elements, usually resistances (R).Reactive power is a function of a circuit’s reactance (X). Apparent power is a function of a circuit’stotal impedance (Z). Since we’re dealing with scalar quantities for power calculation, any complexstarting quantities such as voltage, current, and impedance must be represented by their polarmagnitudes, not by real or imaginary rectangular components. For instance, if I’m calculating truepower from current and resistance, I must use the polar magnitude for current, and not merely the“real” or “imaginary” portion of the current. If I’m calculating apparent power from voltage andimpedance, both of these formerly complex quantities must be reduced to their polar magnitudesfor the scalar arithmetic.There are several power equations relating the three types of power to resistance, reactance, andimpedance (all using scalar quantities):