Fig. 10-5 (cont.) Substituting the values of pR , pL , and pC found in Examples 10.6, 10.7, and 10.8, respectively, we get V2 1 ð1 þ cos 2!tÞ þ V 2 pT ¼ C! sin 2!t R L! The average power is PT ¼ PR ¼ V 2 =R The reactive power is QT ¼ QL þ QC ¼ V 2 For ð1=L!Þ C! ¼ 0, the total reactive power is zero. factor.
1 C! L!
Figure 10-5(d) shows pT ðtÞ for a load with a leading power
COMPLEX POWER, APPARENT POWER, AND POWER TRIANGLE
The two components P and Q of power play diﬀerent roles and may not be added together. However, they may conveniently be brought together in the form of a vector quantity called complex power S pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ and deﬁned by S ¼ P þ jQ. The magnitude jSj ¼ P2 þ Q2 ¼ Veff Ieff is called the apparent power S and is expressed in units of volt-amperes (VA). The three scalar quantities S, P, and Q may be represented geometrically as the hypotenuse, horizontal and vertical legs, respectively, of a right triangle