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664 ⏐⏐⏐ SERIES AND PARALLEL ac CIRCUITS
A plot of all of the currents and the voltage appears in Fig. 15.70.
Note that e and i R are in phase and e lags i C by 90°.
–
�
2
Power:
PT � EI cos v � (10 V)(10 A) cos 53.13° � (10) 2 (0.6)
� 60 W
or PT � E 2 G � (10 V) 2 (0.6 S) � 60 W
or, finally,
PT � PR � PC � EIR cos vR � EIC cos vC � (10 V)(6 A) cos 0° � (10 V)(8 A) cos 90°
� 60 W
Power factor: The power factor of the circuit is
Fp � cos 53.13° � 0.6 leading
Using Eq. (15.32), we have
G 0.6 S
Fp � cos vT �����0.6 leading
YT 1.0 S
Impedance approach: The voltage E can also be found by first
finding the total impedance of the circuit:
Z
ZT �
RZC (1.67 � �0°)(1.25 � ��90°)
� �����
ZR � ZC 1.67 � �0° � 1.25 � ��90°
2.09 ��90°
��� �1 � ��53.19°
2.09 ��36.81°
and then, using Ohm’s law, we find
E � IZT � (10 A �0°)(1 � ��53.19°) � 10 V ��53.19°
R-L-C
14.14 A
11.31 A
8.48 A
0
90°
36.87°
Refer to Fig. 15.71.
i
�
2
i C
�
e
i R
3
�
2
2�
FIG. 15.70
Waveforms for the parallel R-C network of Fig. 15.66.
a c
�t