Determine the energy stored in the coupled inductors in

Given the network in Fig. P10.1, (a) write the equations for a (t) and b (t). (b) write the equations for c (t) and d (t). M i 1(t) i 2(t) L2 L1 + a(t) + c(t) + b(t) + d(t) Figure P10.1

Given the network in Fig. P10.2, (a) find the equations for a (t) and b (t). (b) find the equations for c (t) and d (t). M i 1(t) i 2(t) L2 L1 + a(t) + c(t) + b(t) + d(t) Figure P10.2

Given the network in Fig. P10.3, (a) find the equations for a (t) and b (t). (b) find the equations for c (t) and d (t). M i 1(t) i 2(t) L2 L1 + a(t) + d(t) + c(t) + b(t) Figure P10.3

Given the network in Fig. P10.4, (a) write the equations for a (t) and b (t). (b) write the equations for c (t) and d (t). M i 1(t) i 2(t) L2 L1 + a(t) + c(t) + b(t) + d(t) Figure P10.4

Find Io in the network in Fig. P10.5. j1 j4 j2 1 2 + 10 0 V Io Figure P10.5

Find Vo in the network in Fig. P10.6. j1 j2 j1 1 1 + 2 Vo + 12 0 V j1 Figure P10.6

Find Vo in the circuit in Fig. P10.7. j1 j2 j2 2 1 + 1 Vo + 10 0 V Figure P10.7

Write the mesh equations for the network in Fig. P10.8 and determine Vo / V1. j4 I1 j2 2 2 2 j1 + I2 V1 j2 Vo + Figure P10.8

Find Vo in the circuit in Fig. P10.9. j1 j1 j2 j2 1 2 + 1 Vo + 10 0 V Figure P10.9

Find Vo in the network in Fig. P10.10. j4 j1 j6 2 1 2 1 j1 + 24 0 V j2 Vo + Figure P10.10

Find Vo in the circuit in Fig. P10.11. j4 j2 2 j8 24 0 V + 6 8 4 j2 Vo + Figure P10.11

Find Vo in the circuit in Fig. P10.12. Vo + + 2 12 4 4 j4 j3 2 j2 j1 j1 12 0 V 24 0 V + Figure P10.12

Find Vo in the network in Fig. P10.13. j2 j1 2 1 1 j1 j1 + Vo + 10 0 V Figure P10.13

Find Io in the circuit in Fig. P10.14. + 4 4 6 + 12 j1 j3 j1 j2 j2 12 0 V 6 0 V Io Figure P10.14

Find Vo in the network in Fig. P10.15. 2 j2 1 j1 + 10 0 V 1 2 j2 j2 j2 Vo + Figure P10.15

Determine Io in the network in Fig. P10.16. 1 1 j1 j1 j1 j1 2 2 0 V + Io j2 Figure P10.16

Find Vo in the network in Fig. P10.17. + 6 6 4 6 j2 j4 j1 24 0 V 2 0 A 2 2 j4 Vo 3 0 A + Figure P10.17

Find Vo in the network in Fig. P10.18. 3 3 6 1 24 0 V j2 j2 1 4 0 A 2 0 A + + Vo j1 j4 j1 Figure P10.18

Determine the impedance seen by the source in the network shown in Fig. P10.19. 120 60 V j4 j2 j2 1 1 3 2 + j2 j1 j1 Figure P10.19

Compute the input impedance of the network in Fig. P10.20. j2 j4 Zin 2 2 j2 j1 Figure P10.20

Find Io in the circuit in Fig. P10.21. 2 2 + 32 0 V Io j4 j2 3 j2 j2 j1 Figure P10.21

Find Vo in the network in Fig. P10.22. + 6 0 A 4 0 A Vo j1 j1 j1 j1 1 1 2 Figure P10.22

Find Io in the circuit in Fig. P10.23. 1 Io 4 0 A 1 j1 j1 j2 j1 j2 j2 Figure P10.23

Find Vo in the network in Fig. P10.24. 4 0 A j2 j1 Vo + 2 j2 j2 j2 Figure P10.24

Determine the impedance seen by the source in the network shown in Fig. P10.25. 32 0 V 1 1 + j1 j1 j2 j2 j2 j2 j2 Figure P10.25

Find Vo in the network in Fig. P10.26. j1 j2 j2 1 1 j1 j2 Vo + + 24 0 V Figure P10.26

Find Vo in the network in Fig. P10.27. Vo + 10 30 V 10 0 V j1 j1 j1 j2 2 1 + + j1 j2 Figure P10.27

Find Vo in the network in Fig. P10.28. + + Vo + 100 0 V 200 0 V j5 10 j2 j2 2 j10 Figure P10.28

Find Vo in the network in Fig. P10.29. Vo + 3 2 2 2 0 A 12 0 V + j1 j2 j2 j1 Figure P10.29

Find Vo in the network in Fig. P10.30. 1 1 1 1 Vo + + 24 0 V j1 j1 j1 j2 j2 Figure P10.30

Find Vo in the circuit in Fig. P10.31. 1 1 1 j2 j1 j1 Vo + 6 0 V 4 30 A + j2 Figure P10.31

Determine the input impedance Zin of the circuit in Fig. P10.32. j2 j2 j1 j1 2 Zin 1 1 Figure P10.32

Determine the input impedance of the network shown in Fig. P10.33. 2 6 1 3 Zin j2 j4 j1 j1 j3 j2 j1 Figure P10.33

Two coils are positioned such that there is 90% coupling between them. If the inductances of the coils are 10 mH and 20 mH, respectively, find the mutual inductance.

Two coils in a network are positioned such that there is 100% coupling between them. If the inductance of one coil is 10 mH and the mutual inductance is 6 mH, compute the inductance of the other coil

Determine the input impedance Zin in the network in Fig. P10.36. j2 j1 Zin j4 j4 1 3 j1 Figure P10.36

Analyze the network in Fig. P10.37 and determine whether a value of XC can be found such that the output voltage is equal to twice the input voltage. j2 1 j2 jXC j1 + Vo V I1 + I2 Figure P10.37

Given the network shown in Fig. P10.38, determine the value of the capacitor C that will cause the impedance seen by the 24 0 V voltage source to be purely resistive, f = 60 Hz. 1 jC 12 4 10 + 24 0 V jM = j6 j50 j6 j1 Figure P10.38

The currents in the magnetically coupled inductors shown in Fig. P10.39 are known to be i1(t) = 8 cos (377t 20) mA and i2(t) = 4 cos (377t 50) mA. The inductor values are L1 = 2 H, L2 = 1 H, and k = 0.6. Determine 1(t)and 2(t). L1 L2 2(t) + 1(t) i 1(t) i 2(t) + Figure P10.39

Determine the energy stored in the coupled inductors in Problem 10.39 at t = 1 ms.

The currents in the network in Fig. P10.41 are known to be i1(t) = 10 cos (377t 30) mA and i2(t) = 20 cos (377t 45) mA. The inductances are L1 = 2 H, L2 = 2 H, and k = 0.8. Determine 1(t)and 2(t). L1 L2 2(t) + 1(t) i 1(t) i 2(t) + M Figure P10.41

Determine the energy stored in the coupled inductors in the circuit in Fig. P10.41 at t = 1 ms.

Determine I1, I2, V1, and V2 in the network in Fig. P10.43. V1 I1 I2 + V2 + + 12 30 V 1 1 2:1 Ideal Figure P10.43

Find all currents and voltages in the network in Fig. P10.44. V1 + V2 + I2 I1 3 1 1:2 Ideal + 12 0 V j1 Figure P10.44

Determine Vo in the circuit in Fig. P10.45. 1:2 Ideal 1 2 + 24 45 V j1 j3 Vo + Figure P10.45

Determine Vo in the circuit in Fig. P10.46. 1:2 Ideal j1 1 1 + Vo + 10 30 V j2 Figure P10.46

Determine I1, I2, V1, and V2 in the network in Fig. P10.47. 1:2 Ideal j1 j4 2 4 + I1 I2 10 30 V V1 + V2 + Figure P10.47

Determine I1, I2, V1, and V2 in the network in Fig. P10.48. 2 1 + 1 0 V 1 0 A 1 Ideal 1:2 I1 I2 V2 + V1 + Figure P10.48

Determine I1, I2, V1, and V2 in the network in Fig. P10.49. 1 1 1 Ideal 1:2 I2 I1 + V1 + V2 + 24 30 V j1 j1 j1 Figure P10.49

Determine I1, I2, V1, and V2 in the network in Fig. P10.50. j10 3 4 1:4 Ideal 12 0 V 24 0 V I1 I2 + + V1 + V2 + Figure P10.50

Find the current I in the network in Fig. P10.51. j4 j2 120 0 V j4 12 12 12 4 1:2 + I Ideal Figure P10.51

Find Vo in the circuit in Fig. P10.52. j16 j2 j1.2 1.6 2 2 6 10 1:2 Ideal 32 0 V Vo + + Figure P10.52

Find Vo in the network in Fig. P10.53. Vo + j2 j4 j4 2 4 2:1 Ideal 36 0 V + 6 0 A Figure P10.53

Find Vo in the circuit in Fig. P10.54. 2 + 2 2 2 2:1 Ideal + 24 0 V Vo j2 j2 j2 Figure P10.54

Find Io in the network in Fig. P10.55. 12 18 6 6 6 2:1 Ideal + 36 0 V Io j8 j4 j3 Figure P10.55

Find Io in the circuit in Fig. P10.56. Io j1 j1 j1 1 1 1 1 1 1:2 Ideal 6 0 A 12 0 V 4 0 V + + Figure P10.56

Find I in the network in Fig. P10.57. 1 1 4 + 2 45 A 1 60 V 2:1 I Ideal j1 j4 Figure P10.57

Find Vo in the network in Fig. P10.58. j1 j2 2 1 2 1:1 Ideal 24 0 V + Vo + V2 + V1 + Figure P10.58

Find Vo in the network in Fig. P10.59. j8 j12 4 6 j8 6 2:1 Ideal Ideal Vo + + 32 0 V 2. . 1 Figure P10.59

Find Vo in the circuit in Fig. P10.60. j2 j1 2 2 j2 2 2 1 1 1:2 Ideal Vo + + 24 0 V Figure P10.60

Form an equivalent circuit for the transformer and primary in the network shown in Fig. P10.61, and use this circuit to find the current I2. 3 + 2 1:2 I1 I2 V1 + V2 + 24 0 V + 12 0 V Ideal j2 6 j4 Figure P10.61

Find I in the network in Fig. P10.62. j4 j1 j12 12 3 2:1 + 2 I 1:2 8 100 0 V 10 0 A Ideal Ideal Figure P10.62

Determine the input impedance seen by the source in the circuit in Fig. P10.63. j2 2 4 Ideal 1:2 + VS V1 + V2 + Figure P10.63

Determine the input impedance seen by the source in the network shown in Fig. P10.64. j1 j32 j1 48 Ideal Ideal 2:1 1:4 + 1 12 0 V Figure P10.64

Find the voltage Vo in the network in Fig. P10.65. j2 j16 j2 4 32 2:1 1:4 Ideal Ideal 32 0 V + Vo I3 + I2 I1 Figure P10.65

Determine the input impedance seen by the source in the circuit in Fig. P10.66. j1 j2 2 1 1 Ideal 4:1 + I1 VS V1 + V2 + Figure P10.66

Determine the input impedance seen by the source in the network shown in Fig. P10.67. j4 j2 4 20 4 Ideal Ideal 4:1 2:1 + VS Figure P10.67

The output stage of an amplifier in an old radio is to be matched to the impedance of a speaker, as shown in Fig. P10.68. If the impedance of the speaker is 8 and the amplifier requires a load impedance of 3.2 k, determine the turns ratio of the ideal transformer. Ideal n:1 Amplifier Figure P10.68

Given that Vo = 48 30 V in the circuit shown in Fig. P10.69, determine VS. I1 I2 Vo VS j6 24 6 1:2 Ideal + + V2 + V1 + Figure P10.69

Determine VS in the circuit in Fig. P10.70. + VS Vo = 4 30 V 1 1:2 Ideal j1 1 j1 + Figure P10.70

Determine IS in the circuit in Fig. P10.71. IS I j2 1 2 = 2 30 A 2 j1 1:2 Ideal Figure P10.71

In the network in Fig. P10.72, if I1 = 4 0 A, find VS. VS 4 j1 j4 1 2 8 2:1 Ideal 1:2 Ideal I1 + Figure P10.72

In the circuit in Fig. P10.73, if Ix = 4 30 A, find Vo. Ix VS j1 j8 2 2 1 4 8 1:2 Ideal 1:2 Ideal + Vo + Figure P10.73

In the network shown in Fig. P10.74, determine the value of the load impedance for maximum power transfer. j2 3 + I1 I2 1:2 24 0 V Ideal V1 + V2 + ZL Figure P10.74

In the network shown in Fig. P10.75, determine the value of the load impedance for maximum power transfer. ZL 3 j2 + I1 I2 1:2 12 0 V Ideal V1 + V2 + Figure P10.75

Find VS in the network in Fig. P10.76. 0.08 j0.2 220 0 V rms + 40 kW 0.8 pf lagging 50 kW 0.77 pf lagging + 1:2 Ideal 0.01 j0.02 V1 + V2 + VS Figure P10.76

Find VS in the network in Fig. P10.77. 220 0 V rms + 10 kW 0.85 pf lagging 2 kW 0.8 pf lagging + 1:2 0.1 j0.2 VS Ideal Figure P10.77