Page 27 - Solutions Manual to accompany Electric Machinery Fundamentals



QVI  cos  240 V 24 A sin 45    4073 var

SVI  cos  240 V 24 A    5760 VA
As expected, the real and reactive power supplied by the source are equal to the sum of the
real and reactive powers consumed by the loads.
(c) With the switch closed, all three loads are connected to the source. The current in Loads 1 and 2 is
the same as before. The current in Load 3 is
I
3



I 3  240 0 V  24 90 A

10 90 A
Therefore the total current from the source is







I  I 1  I 2  I 3  24 30 A 24 45 A 24 90 A  38.08 7.5 A
The power factor supplied by the source is

PF cos  cos 7.5  0.991 lagging
The real, reactive, and apparent power supplied by the source are



PVI  cos  240 V 38.08 A cos 7.5  9061 W



QVI  cos  240 V 38.08 A sin 7.5  1193 var

  SVI  240 V 38.08 A   9140 VA
(d) The real, reactive, and apparent power consumed by Load 1 are



PVI  cos  240 V 24 A cos 30  4988 W



QVI  cos  240 V 24 A sin 30  2880 var

SVI  cos  240 V 24 A    5760 VA
The real, reactive, and apparent power consumed by Load 2 are


PVI  cos  240 V 24 A cos 45    4073 W


QVI  cos  240 V 24 A sin 45    4073 var

SVI  cos  240 V 24 A    5760 VA
The real, reactive, and apparent power consumed by Load 3 are



PVI  cos  240 V 24 A cos  90   0 W



QVI  cos  240 V 24 A sin  90     5760 var

SVI  cos  240 V 24 A    5760 VA
As expected, the real and reactive power supplied by the source are equal to the sum of the
real and reactive powers consumed by the loads.
(e) The current flowing decreased when the switch closed, because most of the reactive power being
consumed by Loads 1 and 2 is being supplied by Load 3. Since less reactive power has to be supplied by
the source, the total current flow decreases.
1-20. Demonstrate that Equation (1-59) can be derived from Equation (1-58) using simple trigonometric
identities:
pt v () ()  t i t 2VI cos t cos  t    (1-58)
( ) 
p VI cos  () t   1 cos2 t  VI sin sin2 t (1-59)
 

21