boylistad

a c
Phasor notation: As shown in Fig. 15.72.
E = 100 V ∠ 53.13°
Y T and Z T
I
YT � YR � YL � YC � G �0° � BL ��90° � BC �90°
1
1
1
�� �0° �� ��90° �� �90°
3.33 � 1.43 � 3.33 �
� 0.3 S �0° � 0.7 S ��90° � 0.3 S �90°
� 0.3 S � j 0.7 S � j 0.3 S
� 0.3 S � j 0.4 S � 0.5 S ��53.13°
1 1
ZT ����� �2 � �53.13°
YT 0.5 S��53.13°
Admittance diagram: As shown in Fig. 15.73.
E
I � �EYT � (100 V �53.13°)(0.5 S ��53.13°) � 50 A �0°
� ZT
I R, I L, and I C
e = �2(100) sin(qt + 53.13°)
+
–
I = 50 A ∠ 0°
R 3.33 �
IR � (E �v)(G �0°)
� (100 V �53.13°)(0.3 S �0°) � 30 A �53.13°
IL � (E �v)(BL ��90°)
� (100 V �53.13°)(0.7 S ��90°) � 70 A ��36.87°
IC � (E �v)(BC �90°)
� (100 V �53.13°)(0.3 S ��90°) � 30 A �143.13°
Kirchhoff’s current law: At node a,
I � IR � IL � IC � 0
IR
R 3.33 �
+
–
i = 70.7 sin qt
iR
FIG. 15.71
Parallel R-L-C ac network.
a
I L
1.43 �
FIG. 15.72
Applying phasor notation to the network of Fig. 15.71.
X L
X C
I C
3.33 �
X L
a
i L
PARALLEL ac NETWORKS ⏐⏐⏐ 665
1.43 �
B L – B C
j
X C
i C
53.13°
3.33 �
B C ∠ 90° = 0.3 S ∠ 90°
G ∠ 0° = 0.3 S ∠ 0°
B L ∠ –90° = 0.7 S ∠ –90°
+
Y T = 0.5 S ∠ –53.13°
FIG. 15.73
Admittance diagram for the parallel R-L-C
network of Fig. 15.71.