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a c
I
Admittance diagram: As shown in Fig. 15.64.
B L ∠ –90° = 0.4 S ∠ –90°
j
G ∠ 0° = 0.3 S ∠ 0°
53.13°
+
Y T = 0.5 S ∠ –53.13°
E
I � �EYT � (20 V �53.13°)(0.5 S ��53.13°) � 10 A �0°
I R and I L
FIG. 15.64
Admittance diagram for the parallel R-L network of Fig. 15.62.
� ZT
E �v
IR ���(E�v)(G �0°)
R �0°
� (20 V �53.13°)(0.3 S �0°) � 6 A �53.13°
E �v
IL ���(E�v)(BL ��90°)
XL �90°
� (20 V �53.13°)(0.4 S ��90°)
� 8 A ��36.87°
Kirchhoff’s current law: At node a,
I � IR � IL � 0
or
I � IR � IL 10 A �0° � 6 A �53.13° � 8 A ��36.87°
10 A �0° � (3.60 A � j 4.80 A) � (6.40 A � j 4.80 A) � 10 A � j 0
and 10 A �0° � 10 A �0° (checks)
Phasor diagram: The phasor diagram of Fig. 15.65 indicates that
the applied voltage E is in phase with the current IR and leads the current
IL by 90°.
Power: The total power in watts delivered to the circuit is
PT � EI cos vT � (20 V)(10 A) cos 53.13° � (200 W)(0.6)
� 120 W
or PT � I 2 R � �V 2 RG � (20 V) 2 V
(0.3 S) � 120 W
2 R
�
R
PARALLEL ac NETWORKS ⏐⏐⏐ 661
j
I R
53.13°
36.87°
FIG. 15.65
Phasor diagram for the parallel R-L network
of Fig. 15.62.
E
I L
I
+