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SINUSOIDAL STEADY-STATE CIRCUIT ANALYSIS
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Fig. 9-40 9.42 Find Z in the parallel circuit of Fig. 9-41, if V 50:0 Ans: 5:0 308  30:08 V and I 27:9 57:88 A.
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Fig. 9-41 9.43 Obtain the conductance and susceptance corresponding to a voltage V 85:0 current I 41:2 141:08 A. Ans: 0:471 S; 0:117 S (capacitive) 2058 V and a resulting
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A practical coil contains resistance as well as inductance and can be represented by either a series or parallel circuit, as suggested in Fig. 9-42. Obtain Rp and Lp in terms of Rs and Ls . Ans: Rp Rs !Ls 2 R2 ; Lp Ls 2 s Rs ! Ls
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Fig. 9-42 9.45 In the network shown in Fig. 9-43 the 60-Hz current magnitudes are known to be: IT 29:9 A, I1 22:3 A, and I2 8:0 A. Obtain the circuit constants R and L. Ans: 5:8 ; 38:5 mH
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Fig. 9-43
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Fig. 9-44
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SINUSOIDAL STEADY-STATE CIRCUIT ANALYSIS
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[CHAP. 9
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Obtain the magnitude of the voltage VAB in the two-branch parallel network of Fig. 9-44, if XL is (a) 5 , (b) 15 , c 0 . Ans: 50 V, whatever XL
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In the network shown in Fig. 9-45, VAB 36:1 Ans: 75 908 V
3:188 V. Find the source voltage V.
Fig. 9-45
Fig. 9-46
For the network of Fig. 9-46 assign two di erent sets of mesh currents and show that for each, z 55:9 26:578 2 . For each choice, calculate the phasor voltage V. Obtain the phasor voltage across the 3 j4  impedance and compare with V. Ans: V V3 j4 22:36 10:308 V For the network of Fig. 9-47, use the mesh current method to nd the current in the 2 j3  impedance due Ans: 2:41 6:458 A; 1:36 141:458 A to each of the sources V1 and V2 .
Fig. 9-47
In the network shown in Fig. 9-48, the two equal capacitances C and the shunting resistance R are adjusted until the detector current ID is zero. Assuming a source angular frequency !, determine the values of Rx and Lx . Ans: Rx 1= !2 C 2 R ; Lx 1= 2!C
Fig. 9-48
CHAP. 9]
SINUSOIDAL STEADY-STATE CIRCUIT ANALYSIS
For the network of Fig. 9-49, obtain the current ratio I1 =I3 .
Ans:
908
Fig. 9-49
For the network of Fig. 9-49, obtain Zinput;1 and Ztransfer;13 . Ans: 1:31 21:88 ; 4:31 68:28 
Show that Ztransfer;31 Ztransfer;13 .
In the network of Fig. 9-50, obtain the voltage ratio V1 =V2 by application of the node voltage method. Ans: 11 1:61 12 29:88 Ans: 5:59 17:358 
For the network of Fig. 9-50, obtain the driving-point impedance Zinput;1 .
Fig. 9-50
Fig. 9-51
Obtain the Thevenin and Norton equivalent circuits at terminals ab for the network of Fig. 9-51. Choose the polarity such that V 0 Vab . Ans: V 0 20:0 08 V; I 0 5:56 23:068 A; Z 0 3:60 23:068 
Obtain the Thevenin and Norton equivalent circuits at terminals ab for the network of Fig. 9-52. Ans: V 0 11:5 95:88 V; I 0 1:39 80:68 A; Z 0 8:26 15:28 
Fig. 9-52
Fig. 9-53
SINUSOIDAL STEADY-STATE CIRCUIT ANALYSIS
[CHAP. 9
Obtain the Theveinin and Norton equivalent circuits at terminals ab for the network of Fig. 9-53. Ans: V 0 11:18 93:438 V; I 0 2:24 56:568 A; Z 0 5:0 36:878  In the circuit of Fig. 9-54, v1 10 V and v2 5 sin 2000t. Ans: i 1 0:35 sin 2000t 458 Find i.
Fig. 9-54
Fig. 9-55
In the circuit of Fig. 9-55, v1 6 cos !t and v2 cos !t 608). Find vA if ! 2 rad/sec. KCL at node A in the phasor domain. Ans: vA 1:11 sin 2t
Hint: Apply
In the circuit of Problem 9.59 nd phasor currents I1 and I2 drawn from the two sources. phasor KVL to the loops on the left and right sides of the circuit. Ans: I1 508 100:48; I2 1057 1458, both in mA
Hint: Apply
Find vA in the circuit of Problem 9.59 if ! 0:5 rad/s.
Ans:
Va 0
In the circuit of Fig. 9-55, v1 V1 cos 0:5t 1 and v2 V2 cos 0:5t 2 . Find the current through the 4 H inductor. Ans: i V2 =4 sin 0:5t 2 V1 =3 sin 0:5t 1
In the circuit of Fig. 9-55, v1 V1 cos t 1 and v2 V2 cos t 2 . Ans: vA 1, unless V1 V2 0, in which case vA 0
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