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9.18

SINUSOIDAL STEADY-STATE CIRCUIT ANALYSIS

[CHAP. 9

Obtain the voltage Vx in the network of Fig. 9-28, using the mesh current method.

Fig. 9-28 One choice of mesh currents is shown on the circuit diagram, with I3 passing through the 10- resistor in a direction such that Vx ¼ I3 ð10Þ (V). The matrix equation can be written by inspection: 3 2 32 3 2 7 þ j3 j5 5 I1 10 08 6 7 4 j5 12 þ j3 ð2  j2Þ 54 I2 5 ¼ 4 5 308 5 I3 5 ð2  j2Þ 17  j2 0 Solving by determinants,    7 þ j3 j5 10 08      j5 12 þ j3 5 308     5 2 þ j2 0  667:96 169:098 ¼ 0:435 I3 ¼  ¼  7 þ j3  j5 5 1534:5 25:068    j5 12 þ j3 2 þ j2    5 2 þ j2 17  j2  and Vx ¼ I3 ð10Þ ¼ 4:35

9.19

194:158 A

194:158 V.

In the netwrok of Fig. 9-29, determine the voltage V which results in a zero current through the 2 þ j3  impedance.

Fig. 9-29

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An  
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