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physics
electricity and magnetism

Fundamentals Of Electric Circuits 3rd Edition Matthew Sadiku, Charles Alexander - Solutions

Obtain the overall impedance for the following cases: (a) P = 1000 W, pf = 0.8(leading), Vrms = 220 V (b) P = 1500 W, Q = 2000 VAR (inductive), Irms = 12 A (c) S = 4500∠60° VA, V = 120∠45° V
For the entire circuit in Fig. 11.70, calculate:(a) The power factor(b) The average power delivered by the source(c) The reactive power(d) The apparent power(e) The complex power
In the circuit of Fig. 11.71, device A receives 2 kW at 0.8 pf lagging, device B receives 3 kVA at 0.4 pf leading, while device C is inductive and consumes 1 kW and receives 500 VAR.(a) Determine the power factor of the entire system.(b) Find I given that Vi = 120ˆ 45° Vrms.
In the circuit of Fig. 11.72, load A receives 4 kVA at 0.8 pf leading. Load B receives 2.4 kVA at 0.6 pf lagging. Box C is an inductive load that consumes 1 kW and receives 500 VAR.(a) Determine I.(b) Calculate the power factor of the combination.
For the network in Fig. 11.73, find the complex power absorbed by each element.
Find the complex power absorbed by each of the five elements in the circuit of Fig. 11.74.
Obtain the complex power delivered by the source in the circuit of Fig. 11.75.
For the circuit in Fig. 11.76, find the average, reactive, and complex power delivered by the dependent current source.
Obtain the complex power delivered to the 10-k Î© resistor in Fig. 11.77 below.
Calculate the reactive power in the inductor and capacitor in the circuit of Fig. 11.78.
For the circuit in Fig. 11.38, is = 6 cos 103 t A. Find the average power absorbed by the 50- Î© resistor.
For the circuit in Fig. 11.79, find Vo and the input power factor.
Given the circuit in Fig. 11.80, find Io and the overall complex power supplied.
For the circuit in Fig. 11.81, find Vs.
Find Io in the circuit of Fig. 11.82.
Determine Is in the circuit of Fig. 11.83, if the voltage source supplies 2.5 kW and 0.4 kVAR (leading).
In the op amp circuit of Fig. 11.84, vs = 4 cos 104t V.~norm~&] Find the average power delivered to the 50-k Î© resistor.
Obtain the average power absorbed by the 6-k Î© resistor in the op amp circuit in Fig. 11.85.
For the op amp circuit in Fig. 11.86, calculate:(a) The complex power delivered by the voltage source(b) The average power dissipated in the 12- Î© resistor
Compute the complex power supplied by the current source in the series RLC circuit in Fig. 11.87.
Refer to the circuit shown in Fig. 11.88.(a) What is the power factor?(b) What is the average power dissipated?(c) What is the value of the capacitance that will give a unity power factor when connected to the load?
Given the circuit of Fig. 11.39, find the average power absorbed by the 10- Î© resistor.
An 880-VA, 220-V, 50-Hz load has a power factor of 0.8 lagging. What value of parallel capacitance will correct the load power factor to unity?
Three loads are connected in parallel to a 120∠0° V rms source. Load 1 absorbs 60 kVAR at pf = 0.85 lagging, load 2 absorbs 90 kW and 50 kVAR leading, and load 3 absorbs 100 kW at pf = 1. (a) Find the equivalent impedance. (b) Calculate the power factor of the parallel combination. (c)
Two loads connected in parallel draw a total of 2.4 kW at 0.8 pf lagging from a 120-V rms, 60-Hz line. One load absorbs 1.5 kW at a 0.707 pf lagging. Determine: (a) The pf of the second load, (b) The parallel element required to correct the pf to 0.9 lagging for the two loads.
A 240-V rms 60-Hz supply serves a load that is 10 kW (resistive), 15 kVAR (capacitive), and 22 kVAR (inductive). Find: (a) The apparent power (b) The current drawn from the supply (c) The kVAR rating and capacitance required to improve the power factor to 0.96 lagging (d) The current drawn from the
A 120-V rms 60-Hz source supplies two loads connected in parallel, as shown in Fig. 11.89.(a) Find the power factor of the parallel combination.(b) Calculate the value of the capacitance connected in parallel that will raise the power factor to unity.
Consider the power system shown in Fig. 11.90. Calculate:(a) The total complex power(b) The power factor
Obtain the wattmeter reading of the circuit in Fig. 11.91.
What is the reading of the wattmeter in the network of Fig. 11.92?
Find the wattmeter reading of the circuit shown in Fig. 11.93.
Determine the wattmeter reading of the circuit in Fig. 11.94.
In the circuit of Fig. 11.40, determine the average power absorbed by the 40- Î© resistor.
The circuit of Fig. 11.95 portrays a wattmeter connected into an ac network.(a) Find the load current.(b) Calculate the wattmeter reading.
A 120-V rms, 60-Hz electric hair dryer consumes 600 W at a lagging pf of 0.92. Calculate the rms-valued current drawn by the dryer.
A 240-V rms 60-Hz source supplies a parallel combination of a 5-kW heater and a 30- kVA induction motor whose power factor is 0.82. Determine: (a) The system apparent power (b) The system reactive power (c) The kVA rating of a capacitor required to adjust the system power factor to 0.9 lagging (d)
Oscilloscope measurements indicate that the voltage across a load and the current through it are, respectively, 210∠60° V and 8∠25° A. Determine: (a) The real power (b) The apparent power (c) The reactive power (d) The power factor
A consumer has an annual consumption of 1200 MWh with a maximum demand of 2.4 MVA. The maximum demand charge is $30 per kVA per annum, and the energy charge per kWh is 4 cents. (a) Determine the annual cost of energy. (b) Calculate the charge per kWh with a flat-rate tariff if the revenue to the
A regular household system of a single-phase three-wire circuit allows the operation of both 120-V and 240-V, 60-Hz appliances. The household circuit is modeled as shown in Fig. 11.96. Calculate:(a) The currents I1, I2, and In(b) The total complex power supplied(c) The overall power factor of the
A transmitter delivers maximum power to an antenna when the antenna is adjusted to represent a load of 75- Ω resistance in series with an inductance of 4μ H. If the transmitter operates at 4.12 MHz, find its internal impedance.
In a TV transmitter, a series circuit has an impedance of 3k Ω and a total current of 50 mA. If the voltage across the resistor is 80 V, what is the power factor of the circuit?
A certain electronic circuit is connected to a 110-V ac line. The root-mean-square value of the current drawn is 2 A, with a phase angle of 55º. (a) Find the true power drawn by the circuit. (b) Calculate the apparent power.
An industrial heater has a nameplate that reads: 210 V 60 Hz 12 kVA 0.78 pf lagging Determine: (a) The apparent and the complex power (b) The impedance of the heater
For the op amp circuit in Fig. 11.41, Vs =10ˆ 30°V rms. Find the average power absorbed by the 20-k Î© resistor.
A 2000-kW turbine-generator of 0.85 power factor operates at the rated load. An additional load of 300 kW at 0.8 power factor is added. What kVAR of capacitors is required to operate the turbine-generator but keep it from being overloaded?
The nameplate of an electric motor has the following information: Line voltage: 220 V rms Line current: 15 A rms Line frequency: 60 Hz Power: 2700 W Determine the power factor (lagging) of the motor. Find the value of the capacitance C that must be connected across the motor to raise the pf to
As shown in Fig. 11.97, a 550-V feeder line supplies an industrial plant consisting of a motor drawing 60 kW at 0.75 pf (inductive), a capacitor with a rating of 20 kVAR, and lighting drawing 20 kW.(a) Calculate the total reactive power and apparent power absorbed by the plant.(b) Determine the
A factory has the following four major loads: • A motor rated at 5 hp, 0.8 pf lagging (1 hp = 0.7457 kW). • A heater rated at 1.2 kW, 1.0 pf. • Ten 120-W lightbulbs. • A synchronous motor rated at 1.6 kVAR, 0.6 pf leading. (a) Calculate the total real and reactive power. (b) Find the
A 1-MVA substation operates at full load at 0.7 power factor. It is desired to improve the power factor to 0.95 by installing capacitors. Assume that new substation and distribution facilities cost $120 per kVA installed, and capacitors cost $30 per kVA installed. (a) Calculate the cost of
A coupling capacitor is used to block dc current from an amplifier as shown in Fig. 11.98(a). The amplifier and the capacitor act as the source, while the speaker is the load as in Fig. 11.98(b).(a) At what frequency is maximum power transferred to the speaker?(b) If Vs = 4.6 V rms, how much power
A power amplifier has an output impedance of 40 + j8 Ω It produces a no-load output voltage of 146 V at 300 Hz. (a) Determine the impedance of the load that achieves maximum power transfer. (b) Calculate the load power under this matching condition.
A power transmission system is modeled as shown in Fig. 11.99. If Vs = 240 ˆ 0º rms, find the average power absorbed by the load.
If Vab = 400 V in a balanced Y-connected three-phase generator, find the phase voltages, assuming the phase sequence is: (a) abc (b) acb
For the circuit in Fig. 12.43, determine the current in the neutral line.
In the Y - Î” system shown in Fig. 12.44, the source is a positive sequence with V an = 120 ˆ 0° V and phase impedance Z p = 2 - j3 Î©. Calculate the line voltage VL and the line current IL.
Solve for the line currents in the Y-Î” circuit of Fig. 12.45. Take ZÎ” = 60 ˆ 45°Î©.
In the balanced three-phase Y-Î” system in Fig. 12.46, find the line current I L and the average power delivered to the load.
Obtain the line currents in the three-phase circuit of Fig. 12.47 on the next page.
The circuit in Fig. 12.48 is excited by a balanced three-phase source with a line voltage of 210 V. If Zl = 1 + j1 Î©, = ˆ’ Î© ZÎ” 24 j30, and ZY = 12 + j5 Î©, determine the magnitude of the line current of the combined loads.
A balanced delta-connected load has a phase current IAC = 10 ∠ − 30° A. (a) Determine the three line currents assuming that the circuit operates in the positive phase sequence. (b) Calculate the load impedance if the line voltage is VAB = 110 ∠0° V.
A balanced delta-connected load has line current Ia = 10 ∠ − 25° A. Find the phase currents IAB, IBC, and ICA.
If Van = 440 ˆ 60° V in the network of Fig. 12.49, find the load phase currents IAB, IBC, and ICA.
For the Î” - Î” circuit of Fig. 12.50, calculate the phase and line currents.
Refer to the Î” - Î” circuit in Fig. 12.51. Find the line and phase currents. Assume that the load impedance is ZL = 12 + j9 Î© per phase.
Three 230-V generators form a delta-connected source that is connected to a balanced delta-connected load of ZL = 10 + j8 Î© per phase as shown in Fig. 12.52.(a) Determine the value of IAC.(b) What is the value of Ib?
Find the line currents Ia, Ib, and Ic in the three-phase network of Fig. 12.53 below. Take ZÎ” = ˆ’ 12 - j15 Î©, Zr = 4 + j6 Î©, and Zj = 2Î©.
A three-phase balanced system with a line voltage of 202 V rms feeds a delta-connected load with Zp = 25 ∠60°Ω. (a) Find the line current. (b) Determine the total power supplied to the load using two wattmeters connected to the A and C lines.
A balanced delta-connected source has phase voltage Vab = 416 ∠30° V and a positive phase sequence. If this is connected to a balanced delta-connected load, find the line and phase currents. Take the load impedance per phase as 60 ∠30°Ω and line impedance per phase as 1 + j1 Ω.
In the circuit of Fig. 12.54, if Vab = 440 ˆ 10°, Vbc = 440 ˆ 250°, Vca = 440 ˆ 130° V, find the line currents.
For the balanced circuit in Fig. 12.55, Vab = 125 ˆ 0° V. Find the line currents IaA, IbB, and IcC.
A Δ-connected source supplies power to a Y-connected load in a three-phase balanced system. Given that the line impedance is 2 + j1 Ω per phase while the load impedance is 6 + j4 Ω per phase, find the magnitude of the line voltage at the load. Assume the source phase voltage Vab = 208 ∠0° V
The line-to-line voltages in a Y-load have a magnitude of 440 V and are in the positive sequence at 60 Hz. If the loads are balanced with Z1 = Z2 = Z3 = 25∠30°, find all line currents and phase voltages.
A balanced three-phase Y-Δ system has Van = 120 ∠0° V rms and = ZΔ = 51 + j45Ω. If the line impedance per phase is 0.4 + j1.2 Ω, find the total complex power delivered to the load.
In Fig. 12.56, the rms value of the line voltage is 208 V. Find the average power delivered to the load.
A balanced delta-connected load is supplied by a 60-Hz three-phase source with a line voltage of 240 V. Each load phase draws 6 kW at a lagging power factor of 0.8. Find: (a) The load impedance per phase (b) The line current (c) The value of capacitance needed to be connected in parallel with each
A balanced Y-load is connected to a 60-Hz three-phase source with Vab = 240 ∠0° V. The load has pf = 0.5 lagging and each phase draws 5 kW. (a) Determine the load impedance ZY. (b) Find Ia, Ib, and Ic.
A three-phase source delivers 4800 VA to a wye-connected load with a phase voltage of 208 V and a power factor of 0.9 lagging. Calculate the source line current and the source line voltage.
A balanced wye-connected load with a phase impedance of 10 - j16 Ω is connected to a balanced three-phase generator with a line voltage of 220 V. Determine the line current and the complex power absorbed by the load.
Three equal impedances, 60 + j30 Ω each, are delta-connected to a 230-V rms, three-phase circuit. Another three equal impedances, 40 + j10 Ω each, are wyeconnected across the same circuit at the same points. Determine: (a) The line current (b) The total complex power supplied to the two loads (c)
A 4200-V, three-phase transmission line has an impedance of 4 + j10 Ω per phase. If it supplies a load of 1 MVA at 0.75 power factor (lagging), find: (a) The complex power (b) The power loss in the line (c) The voltage at the sending end
The total power measured in a three-phase system feeding a balanced wye-connected load is 12 kW at a power factor of 0.6 leading. If the line voltage is 208 V, calculate the line current IL and the load impedance ZY.
Given the circuit in Fig. 12.57 below, find the total complex power absorbed by the load.
Find the real power absorbed by the load in Fig. 12.58.
A three-phase system with abc sequence and VL = 200 V feeds a Y-connected load with ZL = 40∠30°Ω. Find the line currents.
For the three-phase circuit in Fig. 12.59, find the average power absorbed by the delta-connected load with ZÎ” = 21 + j24Î©.
A balanced delta-connected load draws 5 kW at a power factor of 0.8 lagging. If the three-phase system has an effective line voltage of 400 V, find the line current.
A balanced three-phase generator delivers 7.2 kW to a wye-connected load with impedance 30 - j40 Ω per phase. Find the line current IL and the line voltage VL.
Refer to Fig. 12.48. Obtain the complex power absorbed by the combined loads.
A three-phase line has an impedance of 1 + j3 Ω per phase. The line feeds a balanced delta-connected load, which absorbs a total complex power of 12 + j5 k VA. If the line voltage at the load end has a magnitude of 240 V, calculate the magnitude of the line voltage at the source end and the source
A balanced wye-connected load is connected to the generator by a balanced transmission line with an impedance of 0.5 + j2 Ω per phase. If the load is rated at 450 kW, 0.708 power factor lagging, 440-V line voltage, find the line voltage at the generator.
A three-phase load consists of three 100- Ω resistors that can be wye- or delta-connected. Determine which connection will absorb the most average power from a three-phase source with a line voltage of 110 V. Assume zero line impedance.
The following three parallel-connected three-phase loads are fed by a balanced three-phase source: Load 1: 250 kVA, 0.8 pf lagging Load 2: 300 kVA, 0.95 pf leading Load 3: 450 kVA, unity pf If the line voltage is 13.8 kV, calculate the line current and the power factor of the source. Assume that
A balanced, positive-sequence wye-connected source has Van = 240 ∠ 0° V rms and supplies an unbalanced delta-connected load via a transmission line with impedance 2 + j3 Ω per phase. (a) Calculate the line currents if ZAB = 40 + j15 Ω, ZBC = 60 Ω, ZCA = 18 - j12Ω. (b) Find the complex power
Each phase load consists of a 20- Ω resistor and a 10- Ω inductive reactance. With a line voltage of 220 V rms, calculate the average power taken by the load if: (a) The three-phase loads are delta-connected (b) The loads are wye-connected
For a Y-connected load, the time-domain expressions for three line-to-neutral voltages at the terminals are: vAN = 150 cos (ω t + 32º) V vBN = 150 cos (ω t - 88º) V vCN = 150 cos (ω t + 152º) V Write the time-domain expressions for the line-to-line voltages vAN, vBC, and vCA.
A balanced three-phase source with VL = 240 V rms is supplying 8 kVA at 0.6 power factor lagging to two wye-connected parallel loads. If one load draws 3 kW at unity power factor, calculate the impedance per phase of the second load.
Consider the Î” - Î” system shown in Fig. 12.60. Take Zi = 8 + j6 Î©, Z2 = 4.2 - j2.2 Î©, Z3 = 10 + j0Î©.(a) Find the phase current IAB, IBC, ICA.(b) Calculate line currents IaA, IbB, and IcC.
A four-wire wye-wye circuit has Van = 120∠120°, Vbn = 120 ∠0° Vcn = 120 ∠−120° V If the impedances are ZAN = 20 ∠60°, ZBN = 30 ∠0° Zcn = 40 ∠30°Ω find the current in the neutral line.
In the Y-Y system shown in Fig. 12.61, loads connected to the source are unbalanced.(a) Calculate Ia, Ib, and Ic.(b) Find the total power delivered to the load. Take Vp = 240 V rms.
A balanced three-phase Y-source with VP = 210 V rms drives a Y-connected three-phase load with phase impedance ZA = 80 Ω, ZB = 60 + j90 Ω, and ZC = j80 Ω. Calculate the line currents and total complex power delivered to the load. Assume that the neutrals are connected.

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