Solved: Determine the impedance ZL for maximum average

The voltage and current at the input of a circuit are given by the expressions (t) = 170 cos (t + 30) V i(t) = 5 cos (t + 45) A Determine the average power absorbed by the circuit

The voltage and current at the input of a network are given by the expressions (t) = 6 cos t V i(t) = 4 sin t A Determine the average power absorbed by the network

The voltage and current at the input of a network are given by the expressions (t) = 6 cos t V i(t) = 4 sin t A Determine the average power absorbed by the network

The voltage and current at the input of a network are given by the expressions (t) = 6 cos t V i(t) = 4 sin t A Determine the average power absorbed by the network

Determine the instantaneous power supplied by the source in the circuit in Fig. P9.5. 4 12 60 V + 2 j2 j2 Figure P9.5

Find the expression for the instantaneous power supplied by the source in the network in Fig. P9.6. 4 2 6 45 A j2 j1 j2 Figure P9.6

Given s(t) = 100 cos 100t volts, find the average power supplied by the source and the current i2(t) in the network in Fig. P9.7. 15 1 mF 10 50 mH S(t) i 2(t) + Figure P9.7

Compute the average power absorbed by each of the elements to the right of the dashed line in the circuit shown in Fig. P9.8. 1 j1 + j1 10 0 V Figure P9.8

Given the network in Fig. P9.9, find the power supplied and the average power absorbed by each element. j2 2 2 j1 VT + 6 0A Figure P9.9

Calculate the power absorbed by each element in the circuit in Fig. P9.10. + 25 cos 20t V 5 5 0.4 H 0.02 F 0.01 F Figure P9.10

Given the network in Fig. P9.11, determine which elements are supplying power, which ones are absorbing power, and how much power is being supplied and absorbed. + + 1 2 12 0 V j2 6 0 V j1 Figure P9.11

Determine the average power supplied by each source in the network shown in Fig. P9.12. j1 j1 10 0 V + 1 2 30 A Figure P9.12

Given the circuit in Fig. P9.13, determine the amount of average power supplied to the network. j1 2 4 12 0 V 4 0 A + Figure P9.13

Determine the average power absorbed by the 4- resistor in the network shown in Fig. P9.14. 4 2 + j4 4 0 A j2 12 90 V Figure P9.14

Find the average power absorbed by the network in Fig. P9.15. + 2 1 1 j1 12 0 V j2 j2 Figure P9.15

Find the average power absorbed by the resistor in the circuit shown in Fig. P9.16 if 1(t) = 10 cos (377t + 60) V and 2(t) = 20 cos (377t + 120) V. 1(t) 1 2(t) + + Figure P9.16

If ig(t) = 0.5 cos 2000t A, find the average power absorbed by each element in the circuit in Fig. P9.17. 120 40 12.5 F i g(t) 60 mH Figure P9.17

Find the average power absorbed by the network shown in Fig. P9.18. 4 60 A 2 j2 j4 Figure P9.18

Given the network in Fig. P9.19, find the power supplied and the average power absorbed by each element. 4 30 A VT + j3 j1 4 2 Figure P9.19

Given the network in Fig. P9.20, show that the power supplied by the sources is equal to the power absorbed by the passive elements. j2 j3 2 0 A 4 + 6 45 V Figure P9.20

Calculate the average power absorbed by the 1- resistor in the network shown in Fig. P9.21. j2 j1 6 0 V + 2 1 Figure P9.21

Find the average power supplied by the current source in the network in Fig. P9.22. 1 2 4 30 A j1 j2 Figure P9.22

Find the total average power supplied and the average power absorbed by each element in the network in Fig. P9.23. 2 2 4 0 A j2 12 0 V + j2 Figure P9.23

Determine the average power supplied by each source in the network shown in Fig. P9.24. 4 j2 j1 4 0 A 2 V + Figure P9.24

Given the network in Fig. P9.25, find the average power supplied to the circuit. 2 12 0 A 4 0 V 1 + j2 j1 Figure P9.25

Determine the average power absorbed by the 4- resistor in the network shown in Fig. P9.26. + 12 0 V 2 0 A 2 4 j4 j2 Figure P9.26

Given the network in Fig. P9.27, find the average power supplied and the total average power absorbed. 1 2 12 0 V + j1 j2 j2 Figure P9.27

Determine the average power supplied to the network in Fig. P9.28. 1 0 A 1 1 j1 2 j1 j1 Figure P9.28

Determine the average power absorbed by a 2- resistor connected at the output terminals of the network shown in Fig. P9.29. 12 0 V j2 2 j1 2Ix Ix + + Figure P9.29

Find the average power absorbed by the 2- resistor in the circuit shown in Fig. P9.30. j3 12 0 V I j2 x 2Ix 2 + Figure P9.30

Determine the impedance ZL for maximum average power transfer and the value of the maximum power transferred to ZL for the circuit shown in Fig. P9.31. 1 j1 6 0 ZL A Figure P9.31

Determine the impedance ZL for maximum average power transfer and the value of the maximum average power transferred to ZL for the circuit shown in Fig. P9.32. 1 4 + 12 30 V 4 0 A ZL j1 j1 Figure P9.32

Determine the impedance ZL for maximum average power transfer and the value of the maximum average power transferred to ZL for the circuit shown in Fig. P9.33. + 12 0 V 4 90 A 4 j2 ZL j4 Figure P9.33

Determine the impedance ZL for maximum average power transfer and the value of the maximum average power absorbed by the load in the network shown in Fig. P9.34. j2 4 30 A 2 j2 ZL 6 0 V + Figure P9.34

Determine the impedance ZL for maximum average power transfer and the value of the maximum average power transferred to ZL for the circuit shown in Fig. P9.35. 4 0 ZL V 1 1 + j1 j1 Figure P9.35

In the network in Fig. P9.36, find ZL for maximum average power transfer and the maximum average power transferred. ZL 12 0 V 4 0 A 1 1 + j1 j1 j1 Figure P9.36

Determine the impedance ZL for maximum average power transfer and the value of the maximum average power absorbed by the load in the network shown in Fig. P9.37. 4 0 A 6 0 V 2 2 + ZL j2 Figure P9.37

Find the impedance ZL for maximum average power transfer and the value of the maximum average power transferred to ZL for the circuit shown in Fig. P9.38. 12 0 V 1 1 2I I ZL + j1 j1 Figure P9.38

Repeat Problem 9.38 for the network in Fig. P9.39. 4 0 A 1 1 2Vx ZL j1 + Vx + j1 Figure P9.39

Determine the impedance ZL for maximum average power transfer and the value of the maximum average power absorbed by the load in the network shown in Fig. P9.40. j1 j1 ZL 6 0 V 1 2 + Figure P9.40

Find the value of ZL in Fig. P9.41 for maximum average power transfer to the load. 2 2 j2 4 j2 12 0 V + ZL Figure P9.41

Find the value of ZL in Fig. P9.42 for maximum average power transfer to the load. 12 0 V ZL j4 j2 j2 j4 2 4 4 + Figure P9.42

In the network in Fig. P9.43, find ZL for maximum average power transfer and the maximum average power transferred. 2 0 A j2 6 0 V 2 1 + ZL Figure P9.43

Find the value of ZL in Fig. P9.44 for maximum average power transfer to the load. 2 4 2 6 4 0 A 12 0 V ZL j4 j4 + Figure P9.44

Determine the impedance ZL for maximum average power transfer and the value of the maximum average power absorbed by the load in the network shown in Fig. P9.45. 12 0 V 2 j1 1 ZL + 2Vx Vx + Figure P9.45

Find the value of ZL in the circuit in Fig. P9.46 for maximum average power transfer. 2 45 A 5 2Ix ZL j4 Ix + Figure P9.46

Determine the impedance ZL for maximum average power transfer and the value of the maximum average power absorbed by the load in the network shown in Fig. P9.47. 12 0 V 1 2 ZL Ix 2Ix + + j1 j2 Figure P9.47

Calculate the rms value of the waveform shown in Fig. P9.48. t (s) 10 0 2 4 6 8 10 12 14 i(t) (A) Figure P9.48

Calculate the rms value of the waveform shown in Fig. P9.49. t (s) 1 2 3 0 2 4 6 8 10 12 14 (t) (V) Figure P9.49

Calculate the rms value of the waveform in Fig. P9.50. t (s) 2 0 234 7 6 i(t) (A) Figure P9.50

Calculate the rms value of the waveform shown in Fig. P9.51. t (s) 4 01 2 3 4 5 6 (t) (V) Figure P9.51

The current waveform in Fig. P9.52 is flowing through a 5- resistor. Find the average power absorbed by the resistor. t (s) 2 46 8 2 0 2 4 4 i(t) (A) Figure P9.52

Calculate the rms value of the waveform shown in Fig. P9.53. t (s) 0 1 34 5 2 1 2 i(t) (A) Figure P9.53

Calculate the rms value of the waveform in Fig. P9.54. 2 2 0 23 5 1 4 t (s) i(t) (A) Figure P9.54

Find the rms value of the voltage defined by the expression (t) = cos t + cos (t + 120) V

Compute the rms value of the voltage given by the waveform shown in Fig. P9.56. t (s) 10 0 1 5 6 10 (t) (V) Figure P9.56

Calculate the rms value of the periodic current waveform shown in Fig. P9.57. 2 t (s) 3 5 7 8 10 11 2 4 2 i(t) (A) Figure P9.57

Calculate the rms value of the waveform in Fig. P9.58. t (s) 6 0 234 7 6 (t) (V) Figure P9.58

Find the rms value of the waveform shown in Fig. P9.59. 4 t (s) 3 0 1 5 8 (t) (V) Figure P9.59

Determine the average power absorbed by a 4- resistor when the current in it is given by the waveform shown in Fig. P9.60. t (s) i(t) (A) 2 4 01 2 3 4 5 6 7 8 Figure P9.60

Find the average power delivered to a 12- resistor if the current in it is given by the waveform shown in Fig. P9.61.

Find the average power absorbed by the network in Fig. P9.62a if the output of the current source is shown in Fig. P9.62b. (a) i(t) 4 2 t (s) i(t) (A) 2 4 01 2 3 4 (b) Figure P9.62

Find the average power absorbed by the network in Fig. P9.63a if the output of the current source is shown in Fig. P9.63b. (a) i(t) 6 3 (b) t (s) i(t) (A) 1 2 01 2 3 4 5 Figure P9.63

Find the average power absorbed by the network in Fig. P9.64a if the output of the current source is shown in Fig. P9.64b. (a) i(t) 3 9 18 6 t (s) i(t) (A) 01 2 3 (b) 2 Figure P9.64

A plant consumes 100 kW of power at 0.9 pf lagging. If the load current is 200 A rms, find the load voltage

A plant draws 250 A rms from a 240-V rms line to supply a load with 50 kW. What is the power factor of the load?

A transmission line with impedance of 0.08 + j0.25 is used to deliver power to a load. The load is inductive, and the load voltage is 220 0 V rms at 60 Hz. If the load requires 12 kW and the real power loss in the line is 560 W, determine the power factor angle of the load.

The power company supplies 80 kW to an industrial load. The load draws 220 A rms from the transmission line. If the load voltage is 440 V rms and the load power factor is 0.8 lagging, find the losses in the transmission line.

An industrial load that consumes 40 kW is supplied by the power company, through a transmission line with 0.1- resistance, with 44 kW. If the voltage at the load is 240 V rms, find the power factor at the load

An industrial load operates at 30 kW, 0.8 pf lagging. The load voltage is 240 0 V rms. The real and reactive power losses in the transmission-line feeder are 1.8 kW and 2.4 kvar, respectively. Find the impedance of the transmission line and the input voltage to the line

Compute the rms value of the waveform in Fig. P9.71. 0 2 4 6 8 10 t (s) 4 4 (t) (V) Figure P9.71

An industrial load consumes 100 kW at 0.8 pf lagging. If an ammeter in the transmission line indicates that the load current is 200 A rms, find the load voltage.

The industrial load in Fig. P9.73 is known to be inductive and consumes 90 kW. The ammeter reading is 260 A rms, and the voltmeter reading is 480 V rms. Determine the power factor of the load. + Voltmeter Power supply voltage Zline Ammeter Industrial load Figure P9.73

The industrial load in Fig. P9.73 consumes 110 kW at 0.88 of lagging. The ammeter reads 252 A rms. Determine the voltmeter reading.

A plant consumes 20 kW of power from a 240-V rms line. If the load power factor is 0.9 lagging, what is the angle by which the load voltage leads the load current? What is the load current phasor if the line voltage has a phasor of 240 0 V rms?

The power company must generate 100 kW to supply an industrial load with 94 kW through a transmission line with 0.09- resistance. If the load power factor is 0.83 lagging, find the load voltage.

The power company supplies 40 kW to an industrial load. The load draws 200 A rms from the transmission line. If the load voltage is 240 V rms and the load power factor is 0.8 lagging, find the losses in the transmission line.

A transmission line with impedance 0.1 + j0.2 is used to deliver power to a load. The load is capacitive and the load voltage is 2400 V rms at 60 Hz. If the load requires 15 kW and the real power loss in the line is 660 W, determine the input voltage to the line

Determine the real power, the reactive power, the complex power, and the power factor for a load having the following characteristics. (a) I = 2 40 A rms, V = 450 70 V rms. (b) I = 1.5 20 A rms, Z = 5000 15 . (c) V = 200 +35 V rms, Z = 1500 15

Find the real and reactive power absorbed by each element in the circuit in Fig. P9.80. + + 240 0 V rms 220 30 V rms j5 4 Figure P9.80

In the circuit in Fig. P9.81, the complex power supplied by source S1 is 2000 30 VA. If V1 = 200 10 V rms, find V2. 5 j10 + V1 + V2 Figure P9.81

The load in the diagram in Fig. P9.82 may be modeled by two elements connected in paralleleither a resistor and an inductor or a resistor and a capacitor. Determine which model is appropriate for this load and determine values for R and either L or C if f = 60 Hz and the source supplies 12 kW at a pf = 0.8 leading. Source V Load s + 0.5 j1 = 240 0 V rms Figure P9.82

For the network in Fig. P9.83, the complex power absorbed by the source on the right is 0 + j1582.5 VA. Find the value of R and the unknown element and its value if f = 60 Hz. (If the element is a capacitor, give its capacitance; if the element is an inductor, give its inductance.) Unknown element R + + 120 10 V rms 150 0 V rms Figure P9.83

Find the real and reactive power absorbed by each element in the circuit in Fig. P9.84. 2 j3 j5 + 125 0 V rms 95 10 V rms + Figure P9.84

Given the circuit in Fig. P9.85, find the power factor at the source and s(t) if f = 60 Hz. j0.4 VS 0.2 + 240 0 Vrms + 12 kW unity pf 10 kW 0.8 lead Figure P9.85

Given the diagram in Fig. P9.86, the source supplies 12 kW at a power factor of 0.8 lagging. Determine the complex power absorbed by the load if VS = 240 0 V rms. Source V Load S + 0.5 j1 Figure P9.86

Two industrial loads are supplied by a source through a transmission line with an impedance of ZL = 0.1 + j0.2 . Load 1: 44 kW at 0.82 pf lagging Load 2: 64 kW at 0.92 pf lagging If the voltage at the loads is 240 0 Vrms. Determine the power factor of the source

Use Kirchhoffs laws to compute the source voltage of the network shown in Fig. P9.88. j0.25 VS 0.09 + 220 0 V rms + 24 kW 0.85 pf lagging 36 kW 0.78 pf lagging Figure P9.88

Given the network in Fig. P9.89, determine the input voltage VS. j0.3 VS 0.1 240 0 V rms + + 36 kW 0.82 pf lagging 48 kW 0.88 pf lagging Figure P9.89

Given the network in Fig. P9.90, determine the input voltage VS. j0.1 VS 0.1 240 0 V rms + + 30 kVA 0.9 pf lagging 40 kW 0.795 pf lagging Figure P9.90

Given the network in Fig. P9.91, find the complex power supplied by the source, the power factor of the source, and the voltage s(t). The frequency is 60 Hz. 0.05 j0.2 240 0 V rms 20 kW 0.7 leading 12 kVA 0.9 lagging VS + + Figure P9.91

Find the complex power supplied by the source, the power factor of the source, and s(t) if f = 60 Hz in Fig. P9.92. 0.15 j0.3 480 0 V rms 40 kW 0.84 lagging 40 kVA 0.9 leading VS + + Figure P9.92

Given the circuit in Fig. P9.93, find the complex power supplied by the source and the source power factor. If f = 60 Hz, find s(t). j0.2 0.1 30 kW 0.8 leading 10 kW 0.8 lagging 20 kVA 0.9 lagging + VS 480 0 V rms + Figure P9.93

Given the network in Fig. P9.94, compute the input source voltage and the input power factor. j0.2 VS 0.08 j0.05 0.01 220 0 V rms + + 60 kW 0.86 pf lagging 20 kW 0.8 pf lagging Figure P9.94

Given the network in Fig. P9.95, compute the input source voltage and the input power factor. j0.2 VS 0.08 0.01 j0.05 220 0 V rms + + 40 kW 0.86 pf lagging 18 kW 0.8 pf lagging Figure P9.95

A particular load has a pf of 0.8 lagging. The power delivered to the load is 40 kW from a 270-V rms 60-Hz line. What value of capacitance placed in parallel with the load will raise the pf to 0.9 lagging?

What value of capacitance must be placed in parallel with the 18-kW load in Problem 9.95 to raise the power factor of this load to 0.9 lagging?

An industrial load consumes 44 kW at 0.82 pf lagging from a 2400-V rms 60-Hz line. A bank of capacitors totaling 600 F is available. If these capacitors are placed in parallel with the load, what is the new power factor of the total load?

A plant consumes 60 kW at a power factor of 0.75 lagging from a 240-V rms 60-Hz line. Determine the value of the capacitor that when placed in parallel with the load will change the load power factor to 0.9 lagging

An industrial load is supplied through a transmission line that has a line impedance of 0.1 + j0.2 . The 60-Hz line voltage at the load is 480 0 V rms. The load consumes 124 kW at 0.75 pf lagging. What value of capacitance when placed in parallel with the load will change the power factor to 0.9 lagging?

The 60-Hz line voltage for a 60-kW, 0.76-pf lagging industrial load is 240 0 V rms. Find the value of capacitance that when placed in parallel with the load will raise the power factor to 0.9 lagging.

A particular load has a pf of 0.8 lagging. The power delivered to the load is 40 kW from a 220-V rms 60-Hz line. What value of capacitance placed in parallel with the load will raise the pf to 0.9 lagging?

The load in the network in Fig. P9.103 is located in New York. It consumes 64 kW at 0.68 pf lagging. Find the value of the capacitor that when placed in parallel with the load will raise the power factor to 0.92 lagging. + 220 0 V rms Load C VS + Figure P9.103

The load in the network in Fig. P9.104 is located in Nevada. It consumes 100 kW at 0.8 pf lagging. Find the value of the capacitor that when placed in parallel with the load will raise the power factor to 0.95 lagging. 440 0 V rms Load C + Figure P9.104

The load shown in Fig. P9.105 is located in Austin, Texas. Determine the new power factor if 3300 microfarads of capacitance is placed in parallel with this load. 220 0 V rms 100 kW pf = 0.7 lagging C + Figure P9.105

An industrial load, located in San Diego, has the following characteristics: 100 kW at 0.707 pf lagging and the line voltage is 480 0 V rms. Find the value of the capacitor that when placed in parallel with the load will raise the power factor to 0.92 lagging.

An industrial load, located in Chicago, has the following characteristics: 300 kW at 0.70 pf lagging and the line voltage is 480 0 V rms. Find the value of the capacitor that when placed in parallel with the load will raise the power factor to 0.92 lagging

An industrial load, located in Memphis, has the following characteristics: 100 kW at 0.70 pf lagging and the line voltage is 220 0 V rms. Find the value of the capacitor that when placed in parallel with the load will raise the power factor to 0.92 lagging

A 5-kW load operates at 60 Hz, 240-V rms and has a power factor of 0.866 lagging. We wish to create a power factor of at least 0.975 lagging using a single capacitor. What is the smallest value of capacitance that would meet the requirement?

A 5.1-kW household range is designed to operate on a 240-V rms sinusoidal voltage, as shown in Fig. P9.110a. However, the electrician has mistakenly connected the range to 120 V rms, as shown in Fig. P9.110b. What is the effect of this error? + + 120 0 V rms a b A B (a) 120 0 V rms Range 5100 W + a n A N (b) 120 0 V rms Range Figure P9.110

A single-phase three-wire 60-Hz circuit serves three loads, as shown in Fig. P9.111. Determine IaA, InN, Ic, and the energy use over a 24-hour period in kilowatt-hours. IaA Ic InN + + 120 0 V rms A n N a b 120 0 V rms 100 W 1 kVA pf = 0.9 lagging 100 W Figure P9.111

A number of 120-V rms household fixtures are to be used to provide lighting for a large room. The total lighting load is 8 kW. The National Electric Code requires that no circuit breaker be larger than 20 A rms with a 25% safety margin. Determine the number of identical branch circuits needed for this requirement.

To test a light socket, a woman, while standing on cushions that insulate her from the ground, sticks her finger into the socket, as shown in Fig. P9.113. The tip of her finger makes contact with one side of the line, and the side of her finger makes contact with the other side of the line. Assuming that any portion of a limb has a resistance of 95 , is there any current in the body? Is there any current in the vicinity of the heart? Figure P9.113

An inexperienced mechanic is installing a 12-V battery in a car. The negative terminal has been connected. He is currently tightening the bolts on the positive terminal. With a tight grip on the wrench, he turns it so that the gold ring on his finger makes contact with the frame of the car. This situation is modeled in Fig. P9.114, where we assume that the resistance of the wrench is negligible and the resistance of the contact is as follows: R1 = Rbolt to wrench = 0.012 R2 = Rwrench to ring = 0.012 R3 = Rring = 0.012 R4 = Bring to frame = 0.012 What power is quickly dissipated in the gold ring, and what is the impact of this power dissipation? + R1 R2 R3 R4 12 V Figure P9.114

A man and his son are flying a kite. The kite becomes entangled in a 7200-V rms power line close to a power pole. The man crawls up the pole to remove the kite. While trying to remove the kite, the man accidentally touches the 7200-V rms line. Assuming that the power pole is well grounded, what is the potential current through the mans body?