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P q
s
Motor:
h � Pi � � �4548.78 W � P3 Fp � 0.72 lagging
P3 � S3 cos v S3 � � �6317.75 VA
Also, v � cos �1 0.72 � 43.95°, so that
Q3 � S3 sin v � (6317.75 VA)(sin 43.95°)
� (6317.75 VA)(0.694) � 4384.71 VAR (L)
Capacitive load:
I � � � �13.87 A �53.13°
P4 � I 2 R � (13.87 A) 2 • 9 ��1731.39 W
Q4 � I 2 XC � (13.87 A) 2 • 12 ��2308.52 VAR (C)
S4 � �P� 2 4��� Q� 2 4� � �(1�7�3�1�.3�9� W�) 2 � �� (�2�3�0�8�.5�2� V�A�R�) 2 �
� 2885.65 VA
Fp � � �0.6 leading
b. PT � P1 � P2 � P3 � P4 � 720 W � 6400 W � 4548.78 W � 1731.39 W
� 13,400.17 W
QT ��Q1 � Q2 � Q3 � Q4 � 0 � 0 � 4384.71 VAR (L) � 2308.52 VAR (C)
� 2076.19 VAR (L)
ST � �P� 2 T��� Q� 2 T� � �(1�3�,4�0�0�.1�7� W�) 2 � �� (�2�0�7�6�.1�9� V�A�R�) 2 �
� 13,560.06 VA
Fp � � �0.988 lagging
v � cos �1 Po Po 5(746 W)
� � ��
Pi h 0.82
P3 4548.78 W
� ��
cos v 0.72
E 208 V �0° 208 V �0°
� �� ��
Z 9 ��j 12 � 15 � ��53.13°
P4 1731.39 W
� ��
S4 2885.65 VA
PT 13.4 kW
� ��
ST 13,560.06 VA
0.988 � 8.89°
Note Fig. 19.22.
S T = 13,560.06 VA
8.89°
PT = 13.4 kW
Q T = 2076.19 VAR (L)
FIG. 19.22
Power triangle for Example 19.3.
S T
13,559.89 VA
c. ST � EI I � � ��� � 65.19 A
E
208 V
Lagging power factor: E leads I by 8.89°, and
I � 65.19 A ��8.89°
THE TOTAL P, Q,AND S ⏐⏐⏐ 863