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a c
Time domain: In the time domain,
e � �2�(50) sin qt � 70.70 sin qt
vR � �2�(30) sin(qt � 53.13°) � 42.42 sin(qt � 53.13°)
vC � �2�(40) sin(qt � 36.87°) � 56.56 sin(qt � 36.87°)
A plot of all of the voltages and the current of the circuit appears
in Fig. 15.34. Note again that i and v R are in phase and that v C lags i
by 90°.
70.70 V
56.56 V
e
42.42 V
vR –
�
2
0 �
i 2
36.87°
�
3
�
2 2�
�t
90°
FIG. 15.34
Waveforms for the series R-C circuit of Fig. 15.30.
Power: The total power in watts delivered to the circuit is
PT � EI cos vT � (50 V)(5 A) cos 53.13°
� (250)(0.6) � 150 W
or PT � I 2 R � (5 A) 2 (6 �) � (25)(6)
� 150 W
or, finally,
PT � PR � PC � VRI cos vR � VCI cos vC � (30 V)(5 A) cos 0° � (40 V)(5 A) cos 90°
� 150 W � 0
� 150 W
Power factor: The power factor of the circuit is
Fp � cos v � cos 53.13° � 0.6 leading
Using Eq. (15.9), we obtain
R 6 �
Fp � cos v ���� ZT 10 �
� 0.6 leading
as determined above.
v C
SERIES CONFIGURATION ⏐⏐⏐ 641