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720 ⏐⏐⏐ SERIES-PARALLEL ac NETWORKS<br />

E = 120 V ∠ 0°<br />

+<br />

–<br />

d. Current divider rule:<br />

Z2I (11.40 � ��37.87°)(9.36 A ��1.5°)<br />

I2 ������� Z2 � Z3 (9 ��j 7 �) � (8 ��j 6 �)<br />

106.7 A ��39.37° 106.7 A ��39.37°<br />

���� ����<br />

17 � j 1 17.03 ��3.37°<br />

I2 � 6.27 A ��36°<br />

Applying Kirchhoff’s current law (rather than another application of<br />

the current divider rule) yields<br />

I1 � I � I2 or I � I1 � I2 � (9.36 A ��1.5°) � (6.27 A ��36°)<br />

I � (9.36 A � j 0.25 A) � (5.07 A � j 3.69 A)<br />

I1 � 4.29 A � j 3.44 A � 5.5 A �38.72°<br />

e. PT � EI cos vT � (100 V)(9.36 A) cos 1.5°<br />

� (936)(0.99966)<br />

PT � 935.68 W<br />

16.3 LADDER NETWORKS<br />

Ladder networks were discussed in some detail in Chapter 7. This section<br />

will simply apply the first method described in Section 7.3 to the general<br />

sinusoidal ac ladder network of Fig. 16.19. The current I 6 is desired.<br />

Z 1 Z 3 Z 5<br />

Z 2<br />

FIG. 16.19<br />

Ladder network.<br />

Z 4<br />

Impedances ZT, Z′ T, and Z″ T and currents I1 and I3 are defined in<br />

Fig. 16.20:<br />

Z″ T � Z5 � Z6 and Z′ T � Z3 � Z4 � Z″ T<br />

with ZT � Z1 � Z2 � Z′ T<br />

Then I �<br />

and I3 �<br />

with I6 � Z E<br />

�<br />

ZT<br />

Z2I �<br />

Z2 � Z′ T<br />

4I3 ��<br />

Z4 � Z″ T<br />

Z 6<br />

I 6

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