Find the average power delivered to the 5 resistor in the

The following sets of values for and i pertain to the circuit seen in Fig. 10.1. For each set of values, calculate P and Q and state whether the circuit inside the box is absorbing or delivering (1) average power and (2) magnetizing vars i = 10 cos(vt + 170) A. v = 80 cos (vt + 120) V,i = 2 cos(vt + 50 ) A. v 150 sin(vt + 25 ) V, i = 5 cos(vt - 75 ) A. v = 18 cos(vt - 30) V, i = 4 sin(vt + 60) A. v = 250

a) A college student wakes up hungry. He turns on the coffee maker, puts some oatmeal in the microwave oven to cook, puts a couple of slices of bread in the toaster, and starts making scrambled eggs in the electric frying pan. If all of these appliances in his dorm room are supplied by a 120 V branch circuit protected by a 50 A circuit breaker, will the breaker interrupt his breakfast? b) The students roommate wakes up and turns on the air conditioner. He realizes that the room is a mess, so starts to vacuum. Now does the circuit breaker interrupt breakfast?

Show that the maximum value of the instantaneous power given by Eq. 10.9 P + 2P2 + Q2 is and that the minimum value is P - 2P2 + Q2

A load consisting of a resistor in parallel with a capacitor is connected across the terminals of a sinusoidal voltage source vg, where vg = 240 cos 5000t V.a) What is the peak value of the instantaneous power delivered by the source? b) What is the peak value of the instantaneous power absorbed by the source? c) What is the average power delivered to the load? d) What is the reactive power delivered to the load? e) Does the load absorb or generate magnetizing vars? f) What is the power factor of the load? g) What is the reactive factor of the load?

Find the average power delivered by the ideal current source in the circuit in Fig. P10.5 if ig = 4 cos 5000t mA Figure P10.5

Find the average power dissipated in the resistor in the circuit seen in Fig. P10.6 if g = 6 cos 20,000t A.

The op amp in the circuit shown in Fig. P10.7 is ideal. Calculate the average power delivered to the 1 kresistor when vg = cos 1000t V.

a) Calculate the real and reactive power associated with each circuit element in the circuit in Fig. P9.63. b) Verify that the average power generated equals the average power absorbed. c) Verify that the magnetizing vars generated equal the magnetizing vars absorbed

Repeat Problem 10.8 for the circuit shown in Fig. P9.64

The load impedance in Fig. P10.10 absorbs 6 kW and generates 8 kVAR. The sinusoidal voltage source develops 8 kW. a) Find the values of inductive line reactance that will satisfy these constraints. b) For each value of line reactance found in (a), show that the magnetizing vars developed equals the magnetizing vars absorbed.

a) A personal computer with a monitor and keyboard requires 40 W at 115 V (rms). Calculate the rms value of the current carried by its power cord. b) A laser printer for the personal computer in (a) is rated at 90 W at 115 V (rms). If this printer is plugged into the same wall outlet as the computer, what is the rms value of the current drawn from the outlet?

Find the rms value of the periodic current shown in Fig. P10.12.

The periodic current shown in Fig. P10.12 dissipates an average power of 1280 W in a resistor. What is the value of the resistor?

4 a) Find the rms value of the periodic voltage shown in Fig. P10.14.b) Suppose the voltage in part (a) is applied to the terminals of a 40 resistor. Calculate the average power dissipated by the resistor. c) When the voltage in part (a) is applied to a different resistor, that resistor dissipates 10 mW of average power. What is the value of the resistor?

a) Find the rms value of the periodic voltage shown in Fig. P10.15. b) If this voltage is applied to the terminals of a 4 resistor, what is the average power dissipated in the resistor?

A dc voltage equal to V is applied to a resistor of R . A sinusoidal voltage equal to V is also applied to a resistor of R .Show that the dc voltage will deliver the same amount of energy in T seconds (where T is the period of the sinusoidal voltage) as the sinusoidal voltage provided equals the rms value of (Hint: Equate the two expressions for the energy delivered to the resistor.)

The current in the frequency-domain circuit shown in Fig. P10.17 is 50l0 mA (rms) a) Find the average and reactive power for the current source. b) Is the current source absorbing or delivering average power? c) Is the current source absorbing or delivering magnetizing vars? d) Find the average and reactive powers associated with each impedance branch in the circuit. e) Check the balance between delivered and absorbed average power. f) Check the balance between delivered and absorbed magnetizing vars.

Find the average power, the reactive power, and the apparent power absorbed by the load in the circuit in Fig. P10.18 if equals 150 cos 250t V. Figure P10.18

a) Find (rms) and for the circuit in Fig. P10.19 if the load absorbs 2500 VA at a lagging power factor of 0.8. b) Construct a phasor diagram of each solution obtained in (a).

a) Find the average power, the reactive power, and the apparent power supplied by the voltage source in the circuit in Fig. P10.20 if vg = 40 cos 106 t V b) Check your answer in (a) by showing c) Check your answer in Pdev = aPabs. (a) by showing Qdev = aQabs. Figure P10.20

Two 480 V (rms) loads are connected in parallel.The two loads draw a total average power of 40,800 W at a power factor of 0.8 lagging. One of the loads draws 20 kVA at a power factor of 0.96 leading.What is the power factor of the other load?

The two loads shown in Fig. P10.22 can be described as follows: Load 1 absorbs an average power of 10 kW and delivers 4 kVAR of reactive power; Load 2 has an impedance of (60 + j80) The voltage at the terminals of the loads is 100012 cos 100pt V a) Find the rms value of the source voltage. b) By how many microseconds is the load voltage out of phase with the source voltage? c) Does the load voltage lead or lag the source voltage?

The three loads in the circuit seen in Fig. P10.23 are S S2 = 7.5 - j4.5 kVA, 1 = 6 + j3 kVA S3 = 12 + j9 kVA a) Calculate the complex power associated with each voltage source, and b) Verify that the total real and reactive power delivered by the sources equals the total real and reactive power absorbed by the network.

The three loads in the circuit seen in Fig. P10.24 are described as follows: Load 1 is absorbing 4.8 kW and delivering 2.4 kVAR; Load 2 is absorbing 6 kVA at a power factor of 0.8 lagging; Load 3 is a 24 resistor in parallel with an inductance whose reactance is . a) Calculate the average power and the magnetizing reactive power delivered by each source if Vg1 = Vg2 = 120l0 V (rms) b) Check your calculations by showing your results are consistent with the requirements aPdev = aPab aQdev = aQabs.

Suppose the circuit shown in Fig. P10.24 represents a residential distribution circuit in which the impedances of the service conductors are negligible and Vg1 = Vg2 = 110l0 V (rms) The three loads in the circuit are L1 (a toaster, a coffee maker, and a microwave oven);L2 (a solid-state TV, a vacuum cleaner, and a portable heater); and L3 (an automatic washing machine and a clothes dryer). Assume that all of these appliances are in operation at the same time. The service conductors are protected with 50 A circuit breakers. Will the service to this residence be interrupted? Why or why not?

The three parallel loads in the circuit shown in Fig. 10.26 can be described as follows: Load 1 is absorbing an average power of 6 kW and delivering reactive power of 8 kvars; Load 2 is absorbing an average power of 9 kW and reactive power of 3 kvars; Load 3 is a resistor in parallel with a capacitor whose reactance is Find the rms magnitude and the phase angle of if Vo = 250l0 V.

Consider the circuit described in Problem 9.78. a) What is the rms magnitude of the voltage across the load impedance? b) What percentage of the average power developed by the practical source is delivered to the load impedance?

Three loads are connected in parallel across a 300 V(rms) line, as shown in Fig. P10.28. Load 1 absorbs 3 kW at unity power factor; Load 2 absorbs 5 kVA at 0.8 leading; Load 3 absorbs 5 kW and delivers 6 kvars. a) Find the impedance that is equivalent to the three parallel loads. b) Find the power factor of the equivalent load as seen from the lines input terminals.

The three loads in Problem 10.28 are fed from a line having a series impedance as shown in Fig. P10.29. a) Calculate the rms value of the voltage at the sending end of the line. b) Calculate the average and reactive powers associated with the line impedance. c) Calculate the average and reactive powers at the sending end of the line. d) Calculate the efficiency of the line if the efficiency is defined as h = (Pload>Psending end) * 100.

The three loads in the circuit in Fig. P10.30 can be described as follows: Load 1 is a 240 resistor in series with an inductive reactance of 70 ; load 2 is a capacitive reactance of 120 in series with a 160 resistor; and load 3 is a 30 resistor in series with a capacitive reactance of 40 . The frequency of the voltage source is 60 Hz. a) Give the power factor and reactive factor of each load. b) Give the power factor and reactive factor of the composite load seen by the voltage source.

a) Find the average power dissipated in the line in Fig. P10.31. b) Find the capacitive reactance that when connected in parallel with the load will make the load look purely resistive. c) What is the equivalent impedance of the load in (b)? d) Find the average power dissipated in the line when the capacitive reactance is connected across the load. e) Express the power loss in (d) as a percentage of the power loss found in (a).

The steady-state voltage drop between the load and the sending end of the line seen in Fig. P10.32 is excessive. A capacitor is placed in parallel with the 150 kVA load and is adjusted until the steady-state voltage at the sending end of the line has the same magnitude as the voltage at the load end, that is, 4800 V (rms). The 150 kVA load is operating at a power factor of 0.8 lag. Calculate the size of the capacitor in microfarads if the circuit is operating at 60 Hz. In selecting the capacitor, keep in mind the need to keep the power loss in the line at a reasonable level

A group of small appliances on a 60 Hz system requires 20 kVA at 0.85 pf lagging when operated at 125 V (rms).The impedance of the feeder supplying the appliances is 0.01 + j0.08 The voltage at the load end of the feeder is 125 V (rms). a) What is the rms magnitude of the voltage at the source end of the feeder? b) What is the average power loss in the feeder? c) What size capacitor (in microfarads) across the load end of the feeder is needed to improve the load power factor to unity? d) After the capacitor is installed, what is the rms magnitude of the voltage at the source end of the feeder if the load voltage is maintained at 125 V (rms)? e) What is the average power loss in the feeder for (d)?

A factory has an electrical load of 1600 kW at a lagging power factor of 0.8. An additional variable power factor load is to be added to the factory. The new load will add 320 kW to the real power load of the factory. The power factor of the added load is to be adjusted so that the overall power factor of the factory is 0.96 lagging. a) Specify the reactive power associated with the added load. b) Does the added load absorb or deliver magnetizing vars? c) What is the power factor of the additional load? d) Assume that the voltage at the input to the factory is 2400 V (rms). What is the rms magnitude of the current into the factory before the variable power factor load is added? e) What is the rms magnitude of the current into the factory after the variable power factor load has been added?

Assume the factory described in Problem 10.34 is fed from a line having an impedance of 0.25 + j0.1 . The voltage at the factory is maintained at 2400 V (rms). a) Find the average power loss in the line before and after the load is added. b) Find the magnitude of the voltage at the sending end of the line before and after the load is added.

a) Find the six branch currents in the circuit in Fig. P10.36. b) Find the complex power in each branch of the circuit. c) Check your calculations by verifying that the average power developed equals the average power dissipated. d) Check your calculations by verifying that the magnetizing vars generated equal the magnetizing vars absorbed.

a) Find the average power delivered to the resistor in the circuit in Fig. P10.37. b) Find the average power developed by the ideal sinusoidal voltage source. c) Find Zab d) Show that the average power developed equals the average power dissipated.

a) Find the average power delivered by the sinusoidal current source in the circuit of Fig. P10.38. b) Find the average power delivered to the 20 resistor.

a) Find the average power dissipated in each resistor in the circuit in Fig. P10.39. b) Check your answer by showing that the total power developed equals the total power absorbed.

The sinusoidal voltage source in the circuit in Fig. P10.40 is developing an rms voltage of 2000 V. The load in the circuit is absorbing four times as much average power as the load. The two loads are matched to the sinusoidal source that has an internal impedance of a) Specify the numerical values of and b) Calculate the power delivered to the load. c) Calculate the rms value of the voltage across the resistor.

a) Determine the load impedance for the circuit shown in Fig. P10.41 that will result in maximum average power being transferred to the load if = 8 krad/s b) Determine the maximum average power delivered to the load from part (a) if vg =10 cos 8000t V c) Repeat part (a) when ZL. consists of two components from Appendix H whose values yield a maximum average power closest to the value calculated in part (b).

Suppose an impedance equal to the conjugate of the Thvenin impedance is connected to the terminals c, d of the circuit shown in Fig. P9.75. a) Find the average power developed by the sinusoidal voltage source. b) What percentage of the power developed by the source is lost in the linear transformer?

The phasor voltage in the circuit shown in Fig. P10.43 is 300l0 V (rms) when no external load is connected to the terminals a, b. When a load having an impedance of 200 - j500 is connected across a, b, the value of V is156 - j42 V (rms) a) Find the impedance that should be connected across a, b for maximum average power transfer. b) Find the maximum average power transferred to the load of (a). c) Construct the impedance of part (a) using components from Appendix H if the source frequency is 50 Hz.

The load impedance for the circuit shown in Fig. P10.44 is adjusted until maximum average power is delivered to ZL a) Find the maximum average power delivered to ZL b) What percentage of the total power developed in the circuit is delivered to ZL?

Prove that if only the magnitude of the load impedance can be varied, most average power is transferred to the load when (Hint: In deriving the expression for the average load power, write the load impedance (ZL ) in the form ZL = |ZL| cos u + j|ZL| sin uand note that only [ZL] is variable

The variable resistor in the circuit shown in Fig. P10.46 is adjusted until the average power it absorbs is maximum. a) Find R. b) Find the maximum average power. c) Find a resistor in Appendix H that would have the most average power delivered to it.

The variable resistor Ro in the circuit shown in Fig. P10.47 is adjusted until maximum average power is delivered to Ro a) What is the value of Ro in ohms? b) Calculate the average power delivered to Ro. c) If R , o is replaced with a variable impedance Zo what is the maximum average power that can be delivered to Zo? d) In (c), what percentage of the circuits developed power is delivered to the load Zo ?

The peak amplitude of the sinusoidal voltage source in the circuit shown in Fig. P10.48 is and its frequency is . The load resistor can be varied from 0 to and the load capacitor can be varied from . a) Calculate the average power delivered to the load when and b) Determine the settings of and that will result in the most average power being transferred to c) What is the average power in (b)? Is it greater than the power in (a)? d) If there are no constraints on and what is the maximum average power that can be delivered to a load? e) What are the values of and for the condition of (d)? f) Is the average power calculated in (d) larger than that calculated in (c)

a) Assume that in Fig. P10.48 can be varied between 0 and Repeat (b) and (c) of Problem 10.48. b) Is the new average power calculated in (a) greater than that found in Problem 10.48(a)? c) Is the new average power calculated in (a) less than that found in 10.48(d)

The sending-end voltage in the circuit seen in Fig. P10.50 is adjusted so that the rms value of the load voltage is always 4000 V. The variable capacitor is adjusted until the average power dissipated in the line resistance is minimum. a) If the frequency of the sinusoidal source is 60 Hz, what is the value of the capacitance in microfarads? b) If the capacitor is removed from the circuit, what percentage increase in the magnitude Vs of s necessary to maintain 4000 V at the load? c) If the capacitor is removed from the circuit, what is the percentage increase in line loss?

For the frequency-domain circuit in Fig. P10.51, calculate: a) the rms magnitude of V . b) the average power dissipated in the resistor. c) the percentage of the average power generated by the ideal voltage source that is delivered to the load 9 resistor.

The 160 resistor in the circuit in Fig. P10.51 is replaced with a variable impedance Zo.Assume is Zo adjusted for maximum average power transfer to Zo. a) What is the maximum average power that can be delivered to ? b) What is the average power developed by the ideal voltage source when maximum average power is delivered to ? c) Choose single components from Appendix H to form an impedance that dissipates average power closest to the value in part (a). Assume the source frequency is 60 Hz.

Find the impedance seen by the ideal voltage source in the circuit in Fig. P10.53 when Zo is adjusted for maximum average power transfer to Zo.

The impedance in the circuit in Fig. P10.54 is adjusted for maximum average power transfer to The internal impedance of the sinusoidal voltage source is 4 + j7 a) What is the maximum average power delivered to ? b) What percentage of the average power delivered to the linear transformer is delivered to ZL ?

a) Find the steady-state expression for the currents ig and in the circuit in Fig. P10.55 when vg = 400 cos 400t V. b) Find the coefficient of coupling. c) Find the energy stored in the magnetically coupled coils t = 1.25 and t = 2.5 ms d) Find the power delivered to the 375 resistor. e) If the 375 resistor is replaced by a variable resistor RL what value of will yield maximum average power transfer to RL? f) What is the maximum average power in (e)? g) Assume the 375 resistor is replaced by a variable impedance ZL What value of ZL will result in maximum average power transfer to ZL ? h) What is the maximum average power in (g)?

The values of the parameters in the circuit shown in Fig. P10.56 are L L2 = 2 mH; 1 = 8 mH k = 0.75; g = 1 ;RL = 7 vg = 5412 cos 1000t V and If find a) the rms magnitude of b) the average power delivered to c) the percentage of the average power generated by the ideal voltage source that is delivered to

Assume the coefficient of coupling in the circuit in Fig. P10.56 is adjustable. a) Find the value of k that makes equal to zero. b) Find the power developed by the source when k has the value found in (a).

Assume the load resistor ( ) in the circuit in Fig. P10.56 is adjustable. a) What value of will result in the maximum average power being transferred to ? b) What is the value of the maximum power transferred?

The load impedance in the circuit in Fig. P10.59 is adjusted until maximum average power is transferred to a) Specify the value of ZL N1 = 3600 turns N2 = 600 turns if and b) Specify the values of IL and VL when ZL is absorbing maximum average power.

The sinusoidal voltage source in the circuit in Fig. P10.60 is operating at a frequency of . The variable capacitive reactance in the circuit is adjusted until the average power delivered to the 100 resistor is as large as possible. a) Find the value of C in microfarads. b) When C has the value found in (a), what is the average power delivered to the resistor? c) Replace the 100 resistor with a variable resistor Specify the value of so that maximum average power is delivered to d) What is the maximum average power that can be delivered to Ro.

Find the average power delivered to the 5 resistor in the circuit of Fig. P10.61.

The ideal transformer connected to the 5 k load in Problem 10.61 is replaced with an ideal transformer that has a turns ratio of 1:a. a) What value of a results in maximum average power being delivered to the 5 k resistor? b) What is the maximum average power?

a) Find the turns ratio N1/N2 for the ideal transformer in the circuit in Fig. P10.63 so that maximum average power is delivered to the 400 load. b) Find the average power delivered to the 400 load. c) Find the voltage d) What percentage of the power developed by the ideal current source is delivered to the 400 resistor?

a) If equals 1000 turns, how many turns should be placed on the winding of the ideal transformer in the circuit seen in Fig. P10.64 so that maximum average power is delivered to the 6800 load? b) Find the average power delivered to the 6800 resistor. c) What percentage of the average power delivered by the ideal voltage source is dissipated in the linear transformer?

The variable load resistor RL in the circuit shown in Fig. P10.65 is adjusted for maximum average power transfer to RL a) Find the maximum average power. b) What percentage of the average power developed by the ideal voltage source is delivered to when is absorbing maximum average power? c) Test your solution by showing that the power developed by the ideal voltage source equals the power dissipated in the circuit.

Repeat Problem 10.65 for the circuit shown in Fig. P10.66.

Use the values in Table 10.3 to calculate the number of kilowatt-hours consumed in one month by a notebook computer AC adapter if every day the computer is charging for 5 hours and sleeping for 19 hours.. b) Repeat the calculation in part (a) assuming that the computer is charging for 5 hours and off for 19 hours. c) Repeat the calculation in part (a) assuming that the computer is charging for 5 hours and disconnected from the AC adapter for 19 hours, but the AC adapter remains plugged into the wall outlet. d) Repeat the calculation in part (a) assuming that the computer is charging for 5 hours and the AC adapter is unplugged from the wall outlet for 19 hours.

a) Suppose you use your microwave oven for 12 minutes each day. The remaining time, the oven is ready with the door closed. Use the values in Table 10.3 to calculate the total number of kilowatt-hours used by the microwave oven in one month. b) What percentage of the power used by the microwave oven in one month is consumed when the oven is ready with the door closed?

Determine the amount of power, in watts, consumed by the transformer in Fig. 10.29.Assume that the voltage source is ideal (Rs=0 ), R1= 5 , and L1= 250 mH.The frequency of the 120 V(rms) source is 60 H

Repeat Problem 10.69, but assume that the linear transformer has been improved so that Rs = 50 m . All other values are unchanged.

Repeat Problem 10.69 assuming that the linear transformer in Fig. 10.29 has been replaced by an ideal transformer with a turns ratio of 30:1. (Hint you shouldnt need to make any calculations to determine the amount of power consumed.)