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systems analysis and design

The Analysis And Design Of Linear Circuits 8th Edition Roland E. Thomas, Albert J. Rosa, Gregory J. Toussaint - Solutions

Does your stuff feature multistep processes? Is the number of steps announced ahead of time or do you need to fine-tune your communications and/or design?
Are people trying to solve one specific task when you are actually trying to get them to solve an entirely different task to meet your own needs? Can you separate the two processes or at least let folks know that they need to do you a favor in order to get stuff to work properly?
Have you looked at design patterns that relate to your own designs? Are you following best practices? If not, why not?
Can you provide visible signals of some kind that will indicate possible dangers—particularly physical dangers?
If you are using social-media tools, are you making any of the 10 mistakes mentioned earlier in this chapter?
Are you relying on instructions to make your designs work? Can you eliminate traditional manuals and read-me texts by creating task-relevant messages that appear only when needed?
Is anything happening when you use your stuff that takes you slightly by surprise? Are there things that don’t entirely function as you expect them to?
16–71 Phase Converter Efficiency Three-phase motors are often used in equipment because they are more efficient and reliable than single-phase motors.Such equipment may be installed in locations where only single-phase power is available and the cost of installing threephase service is
16–67 In Figure P16–67, the source at bus 1 supplies two load buses through transmission lines with wire impedances of ZW1 = 6 + j33 Ω=phase and ZW2 = 3 + j15 Ω=phase. The load at bus 2 draws an apparent power 4MVA at a lagging power factor of 0:95. The load at bus 3 draws an apparent power
16–66 In Figure P16–66, the three buses are interconnected by transmission lines with wire impedances of ZW1 = 100 +j850 Ω=phase and ZW2 = 50 + j250 Ω=phase. The load at bus 1 draws an apparent power of j S1 j = 400 kVA at a lagging power factor of 0:8. The line voltage at bus 1 is VL1 = 138
16–64 In Figure P16–64, the three buses are interconnected by transmission lines with wire impedances of ZW1 = 100 +j600 Ω=phase and ZW2 = 120 + j800 Ω=phase. The source at bus 2 produces an apparent power of j S2 j = 300 kVA at a lagging power factor of 0:85. The load at bus 3 draws an
16–61 In Figure P16–61 the source and load buses are interconnected by a transmission line with ZW = 70 + j400 Ω=phase. The load at bus 2 draws an apparent power of j S2 j = 3MVA at a leading power factor of 0:85 and the line voltage at bus 2 is VL2 = 230 kV ðrmsÞ. Find the apparent power
16–54 In the balanced three-phase system in Figure 16–54 the line and load impedances are ZW = 2 + j12 Ω=phase and ZY = 16 + j10 Ω=phase. The line current is IL = 15AðrmsÞ. Find VL at the source and the complex power produced by the source. Zw Balanced IL three-phase Zw Balanced three-phase
16–28 In Figure P16–28, the load voltage is jVL j = 4160VðrmsÞ at 60Hz and the load ZL draws an average power of 12 kW at a lagging power factor of 0:75. Find the overall power factor of the combination if the parallel capacitance is 1 μF. Select the value of the capacitance required to
16–25 In Figure P16–25, the voltage across the two loads is jVL j = 4:8 kV ðrmsÞ. The load Z1 draws an average power of 15 kW at a lagging power factor of 0:8. The load Z2 draws an apparent power of 12 kVA at a lagging power factor of 0:85. The line has an impedance of ZW = 9 + j50
16–21 The average power delivered to the load ZL in Figure P16–21 is 46 kW at a lagging power factor of 0:8.The load voltage is 2:4 kV ðrmsÞ and the line has an impedance of ZW = 1 + j8 Ω=wire. Find the apparent power produced by the source and the magnitude of the source voltage. Vs Source
16–18 In Figure P16–18 the three load impedances are Z1 = 20 + j15 Ω, Z2 = 25 + j10 Ω, and Z3 = 75 + j50 Ω.Use MATLAB to solve for the three currents IA, IB, and IN, then the total complex power produced by the two sources, and finally, the overall circuit power factor 110 20 Vrms 110 20
16–16 In Figure P16–16 the load ZL is a 1500-Ωresistor and the source voltage is 440 V ðrmsÞ. Find the complex power produced by the source. Vs 1100 m j100 $2 =-25 2 ZL FIGURE P16-16
16–14 In Figure P16–14, the load ZL is a 60-Ω resistor in series with a capacitor whose reactance is −30 Ω. The source voltage is 440 V ðrmsÞ. Find the complex power produced by the source and the complex power delivered to the load. Vs 2002 j25 2 + -202 =12+ VL ZL FIGURE P16-14
16–3 The following voltage and current phasors apply to the circuit in Figure P16–3. Calculate the average power and reactive power delivered to the impedance Z. Find the power factor and state whether the power factor is lagging or leading.(a) V = 275ff20 V ðrmsÞ, I = 2ff−15 AðrmsÞ (b) V
16–1 The following sets of vðtÞ and iðtÞ apply to the load circuit in Figure P16–1. Find the average power, reactive power, and instantaneous power delivered to the load.(a) vðtÞ = 500 cos ðωt + 45Þ V, iðtÞ = 20 cos ðωt + 50ÞA(b) vðtÞ = 95 cos ðωt − 60Þ V, iðtÞ = 5:5 cos
In Figure 16–27, the source at bus 1 supplies two load buses through transmission lines with ZW1 =45+j250 Ω=phase and ZW2 =50+j330 Ω=phase. Line 1 connects the source bus to a load at bus 2 that draws a complex power of S2 =1:5+j0:5 MVA. Line 2 connects bus 2 to a load at bus 3 that draws a
In Figure 16–26, the load at bus 2 draws a complex power of S2 = 125 + j60 kVA. The line current is IL = 40AðrmsÞ, and the line impedance is ZW = 2 + j10 Ω=phase. Find the line voltages at bus 1 and bus 2 Bus 1 LI -VLI Zw FIGURE 16-26 Bus 2 VL2
In Figure 16–26, the source at bus 1 and the load at bus 2 are interconnected by a transmission line with ZW =1:5+j8:5 Ω=phase. The load at bus 2 draws a complex power of S2 = 70 + j35 kVA. Assuming that VL2 = 2400 VðrmsÞ, find the complex power produced by the source and the line voltage at
In Figure 16–23, the line current is IL = 5AðrmsÞ, the line impedance is ZW = 2 + j6 Ω=phase and the load absorbs SL =3+j2 kVA. Find the complex power produced by the source Zw Balanced IL three-phase Zw source Zw FIGURE 16-23 Balanced three-phase load
In Figure 16–23, the line current is IL = 10AðrmsÞ, the line impedance is ZW =0:6+j3:7 Ω=phase, and the phase impedance of the load is ZY =15+j28 Ω=phase. Find the complex power produced by the source. Zw Balanced IL three-phase Zw source Zw FIGURE 16-23 Balanced three-phase load
In Figure 16–23, the three-phase source produces an apparent power of 3:5 kVA at a power factor of 0.8 lagging and a line current of IL = 4:6AðrmsÞ. The three lines connecting the source to the load have impedances of ZW =1+ j6 Ω=phase. Find the complex power delivered to the load and the line
In Figure 16–23, the load is Y-connected with a phase impedance of ZY =15+j6 Ω=phase and the line current is IL = 10AðrmsÞ. Find the line voltage VL and the complex power delivered to the load Zw Balanced IL three-phase Zw source Zw FIGURE 16-23 Balanced three-phase load
In Figure 16–23 the load is Δ-connected with a phase impedance of ZΔ =26+j8 Ω=phase and the line voltage at the load is VL = 1:0 kVðrmsÞ. Find the line current IL and the complex power delivered to the load. Zw Balanced IL three-phase Zw source Zw FIGURE 16-23 Balanced three-phase load
The load in Figure 16–23 is Y-connected with a phase impedance of ZY =12 + j5 Ω=phase and the line voltage at the load is VL = 440 VðrmsÞ. Find the line current IL and the complex power delivered to the load. Verify your answers using Multisim. Assume 60Hz 4. Zw Balanced IL three-phase Zw
In Figure 16–21(a), the load impedance and line impedances are ZY =10+j5 Ω per phase and ZW =0:15 + j0:85 Ω per phase, respectively. The magnitude of the line voltage at the source is VL = 208 VðrmsÞ. Using ffVA = 0 as the phase reference, find the line current phasors and the line voltage
A balanced Y-Y circuit operates with VL = 4160 VðrmsÞ and phase impedances of ZY = 100 + j40 Ω per phase. Using ffVAB =0 as the phase reference, find IA and VAN for a positive phase sequence IA A Z IB B Z b VAN VBN VCN No- IN Z (a) FIGURE 16-21 Zy Zy Zy on
Two balanced Δ-connected loads are connected in parallel. Their phase impedances are ZΔ1 =50+j24 Ω and ZΔ2 =60+j25 Ω. Find the equivalent Y-connected load for the two parallel loads. A ZD Zy N ZA B ZA FIGURE 16-17 ZY C
The inductive load ZL in Figure 16–10 draws an apparent power of 2 kVA at a lagging power factor of 0.8 when the rms load voltage is 880 VðrmsÞ at 60Hz. Find the value of the capacitance C needed to raise the power factor of the combination to 0.95 lagging. Ic VL ZL FIGURE 16-10 1/jwC
The inductive load ZL in Figure 16–10 draws an apparent power of 5 kVA at a lagging power factor of 0.75 when the load voltage is 1:2 kV ðrmsÞ at 60Hz. Find the power factor of the parallel combination when C =5 μF. IL Ic VL Z FIGURE 16-10 1/jwC
The average power delivered to the load in Figure 16–9 is 20 kW at a lagging power factor of 0.8. The load voltage magnitude is 480 V ðrmsÞ and the two-wire line has an impedance of ZW =0:1+j0:6 Ω per wire. Find the required apparent power output and rms voltage of the source. Zw VL V ZL Zw
Figure 16–7 shows the residential power distribution circuit used in the United States.The circuit is called three-wire, single-phase service. The term three-wire refers to the three lines (A, B, and neutral) connecting the sources to the loads Z1, Z2, and Z3. The term single-phase means that the
In Figure 16–6 the load ZL is an 80-Ω resistor and the source voltage is 220 VðrmsÞ. Find the complex power produced by the source. Assuming 60 Hz for the source, validate your answer using Multisim. 50 w A V j402 VL ZL FIGURE 16-6
In Figure 16–6 the load ZL is a 100-Ω resistor in series with a capacitor whose reactance is −60 Ω. The source voltage is 880 VðrmsÞ. Find the complex power delivered to the load and the load power factor 50 A w j402 FIGURE 16-6 VL ZL
In Figure 16–5, the two parallel loads are connected across a 15-V ðrmsÞ source.(a) Find the complex power delivered to each load.(b) Find the complex power produced by the source. 15/0 V FIGURE 16-5 100 12 -200 15/0 V 60 2
Using the reference marks in Figure 16–1, calculate the average and reactive power for the following voltages and currents.(a) υðtÞ = 168 cosð377t + 45ÞV, i ðtÞ = 0:88 cos 377t A(b) υðtÞ = 285 cosð2500t + 68ÞV, i ðtÞ = 0:66 cos 2500t A i(t) Source v(t) Load FIGURE 16-1 A
The ac steady-state inputs to the load in Figure 16–1 areυðtÞ = 166 cos ð500t + 55Þ V i ðtÞ = 3:5 cos ð500t−25ÞA Find the average power, reactive power, and instantaneous power carried by these waveforms. i(t) Source v(t) Load FIGURE 16-1 A two-terminal interface.
If Z1 = −j20,Z2 = j10, and Z3 =10+j5, find ZEQ =Z2 +1 1=Z1 +1=Z3
Evaluate the expression TðωÞ = jω=ðjω+10Þ at ω = 5, 10, 20, 50, 100
Given z1 =1,z2 = −1,z3 = j, and z4 = −j, evaluate (a) z1=z3 (b) z1=z4 (c) z3z4(d) z3z3 (e) z4z4 (f) z2z3
Given z = x + jy =Mejθ, evaluate the following statements:(a) z + z∗ (b) z−z∗ (c) z=z∗ (d) z2 (e) ðz∗Þ2 (f) zz∗
Evaluate the following expressions using z1 =3+j4, z2 =5−j 7, z3 = −2+j3, and z4 =5ff−30:(a) z1z2 (b) z3 + z4 (c) z2z3=z4 (d) z1∗ + z3z1 (e) z2 + ðz1z4Þ∗
Evaluate the following expressions:(a) Reð12ejπÞ (b) Imð100ff60Þ (c) ffð−2+j6Þ (d) Im ð4ejπ4Þ ∗
Convert the following complex numbers into rectangular form:(a) 12ej90 (b) 3ej45 (c) 400ffπ (d) 8e−j60 (e) 15ejπ=6 (f) 25ff−120
Convert the following complex numbers into polar form:(a) 1 + j ffiffiffi p3 (b) −10 + j20 (c) −2000−j8000 (d) 60−j80
16–70 Three-Phase Line Impedance(a) A balanced three-phase source and a balanced threephase load are interconnected by a three-phase transmission line. The load draws an average power of PL = 45kWat a lagging power factor of 0.8 and the source produces a complex power of SS = ð45:2 + j35:4Þ
16–69 Three-Phase Motor kVA Rating The power factor of a 50-hp ð1 hp = 746WÞ three-phase induction motor is 0:8 when it delivers its rated mechanical output. When delivering its rated output, the motor efficiency is 90%. Find the kVA rating of the motor.
16–68 Three-Phase Line-Voltage Phasors for a Negative Phase Sequence In a balanced three-phase system VAN = VPff0. Find the three line-voltage phasors in polar form when the phase sequence is negative.
16–65 In Figure P16–64, the three buses are interconnected by transmission lines with wire impedances of ZW1 = 120 +j800 Ω=phase and ZW2 = 200 + j1200 Ω=phase. The source at bus 2 produces an apparent power of j S2 j = 400 kVA at a leading power factor of 0:9. The load at bus 3 draws an
16–63 In Figure P16–61 the source and load buses are interconnected by a transmission line with ZW = 8 + j75 Ω=phase. The load at bus 2 draws an average power of P2 = 600 kWat a lagging power factor of 0.8 and the line current is IL1 = 10AðrmsÞ. Find the source power factor and the line
16–62 In Figure P16–61, the source and load buses are interconnected by a transmission line with ZW = 1 + j9 Ω=phase. The load at bus 2 draws an average power of P2 = 45 kWat a lagging power factor of 0:8 and the line voltage at bus 2 is VL2 = 4:16 kV (rms). Find the apparent power produced by
16–60 The apparent power delivered to a balancedΔ-connected load is 30 kVA at a lagging power factor of 0:72. The line voltage at the load is VL = 2:4 kV ðrmsÞ. Find the phase impedance ZΔ of the load
16–59 The average power delivered to a balanced Y-connected load is 20 kW at a lagging power factor of 0:8. The line voltage at the load is VL = 480 V ðrmsÞ. Find the phase impedance ZY of the load.
16–58 Two balanced three-phase loads are connected in parallel.The first load absorbs 25 kW at a lagging power factor of 0:9. The second load absorbs an apparent power of 30 kVA at a leading power factor of 0:1. The line voltage at the parallel loads is VL = 880 V ðrmsÞ. Find the line current
16–57 In the balanced three-phase circuit in Figure P16–54, the line impedance is ZW = 2 + j12 Ω=phase. The source produces an average power 25 kW at a lagging power factor of 0:75. The line voltage at the source is VL = 4:16 kV ðrmsÞ.Find the line voltage at the load and complex power
16–56 In the balanced three-phase circuit in Figure P16–54, the line impedance is ZW =5+j30 Ω=phase. The apparent power delivered to the load is 25 kVA at a lagging power factor of 0:95. The line current is IL = 12AðrmsÞ. Find the line voltage at the source and complex power produced by the
16–55 In the balanced three-phase circuit in Figure P16–54, the line impedance is ZW = 1 + j5 Ω=phase and the average power delivered to the load is 15 kW at a lagging power factor of 0:85. The line voltage at the load is VL = 480 V ðrmsÞ.Find the line voltage at the source and complex power
16–53 A balanced three-phase load has a phase impedance is ZY = 20 + j15 Ω=phase. The line current at the load is IL = 12AðrmsÞ. Find VL and the complex power delivered to the load.
16–52 A balanced three-phase load has a phase impedance of ZΔ = 400 − j100 Ω=phase. The line voltage at the load is VL = 2:4 kV ðrmsÞ. Find IL and the complex power delivered to the load.
16–51 A balanced three-phase load has a phase impedance of ZY = 60 + j40 Ω=phase. The line voltage at the load is VL = 760 V ðrmsÞ. Find IL and the complex power delivered to the load.
16–50 An apparent power of 12 kVA is delivered to balanced three-phase load with a phase impedance of ZY = 120 +j90 Ω=phase. Find IL, VL, and the complex power delivered to the load.
16–49 An average power of 6 kW is delivered to a balanced three-phase load with a phase impedance of ZY = 40 + j30 Ω=phase. Find VL and the complex power delivered to the load.
16–48 In a balanced Δ-connected load, the phase current and phase impedance are IP = 12AðrmsÞ and ZΔ = 200ff −90 Ω=phase. Using ffVAB = 0 as the phase reference, find the line current IA and line voltage VAB for a positive phase sequence .
16–47 InabalancedY-connectedload, thelinecurrentandphase impedance are IL = 4:7AðrmsÞ and ZY = 20 + j16 Ω=phase. Using ffVAB = 0 as the phase reference, find the line current IA and phase voltage VAN for a positive phase sequence.
16–46 A balanced three-phase source with VAB = 220ff60 VðrmsÞ supplies a balanced Δ-connected load with a phase impedance of ZΔ = 20ff−90 Ω=phase. Find the phase current IAB and line current IA for a positive phase sequence.
16–45 In a balanced Δ–Y circuit, the line voltage and phase impedance are VL = 4:16 kV ðrmsÞ and ZY = 250ff30 Ω=phase. Using ffVAN = 0 as the phase reference, find the line voltage VBC and line current IB for a positive phase sequence. Validate your results using Multisim.Assume 60 Hz.
16–44 In a balancedY–Δ circuit, the line impedances connecting the source and load are ZW = 1:5 + j6:5 Ω=phase. The phase impedances of the delta load are ZΔ = 15 + j8 Ω=phase, and the line voltage at the source is VL = 250 VðrmsÞ. Using ffVAB = 0 as the phase reference, find the line
16–43 In a balanced Y–Δ circuit, the line voltage and phase impedance are VL = 440 V ðrmsÞ and ZΔ = 16 + j12 Ω=phase. Using ffVAB = 0 as the phase reference, find the line current and phase current phasors in polar form for a positive phase sequence.
16–42 In a balanced Y–Y circuit, the line voltage is VL = 680 V ðrmsÞ. The phase impedance is ZY = 50 + j40 Ω=phase. Using ffIA = 0 as the phase reference, find IA and VAB in polar form for a positive phase sequence.
16–41 In a balanced Y–Y circuit, the line voltage and phase impedance are VL = 480 V ðrmsÞ and ZY = 20 + j10 Ω=phase. Using ffVAN = 0 as the phase reference, find the line current and line voltage phasors in polar form for a positive phase sequence. Validate your results using
16–40 In a balanced Δ–Δ circuit, the Δ-connected source produces VAB = 2400ff45 V ðrmsÞ and a positive phase sequence. The phase impedance of the load is ZΔ =200ff45 Ω=phase. Find the three source voltages and the phase impedance in the equivalent Y–Y circuit
16–39 A balanced Y-connected load with ZY1 = 12 − j6 Ω=phase is connected in parallel with a second balanced Y-connected load with ZY2 = 24 + j6 Ω=phase. Find the phase impedance of the equivalent Y-connected load.
16–38 A balanced Y-connected load with ZY = 30 − j20 Ω=phase is connected in parallel with a balanced Δ-connected load with ZΔ = 120 + j400 Ω=phase. Find the phase impedance of an equivalent Y-connected load.
16–37 A balanced Y-connected load with ZY = 10 − j5 Ω=phase is connected in parallel with a balanced delta load with ZΔ = 60 + j15 Ω=phase. Find the phase impedance of an equivalent delta load.
16–36 In a balanced three-phase circuit VBN = 2400ff−90 VðrmsÞ. Find VCA in polar form for a positive phase sequence.
16–35 A balanced Y-connected three-phase source has VAN = 120ff−30 V ðrmsÞ and a positive phase sequence.Find the three line voltages in polar form.
16–34 In a balanced three-phase circuit VAN = 300 + j400 VðrmsÞ. Find all the line and phase voltage phasors in polar form for a positive phase sequence.
16–33 In a balanced three-phase circuit VBC = j208 V ðrmsÞ.Find all the line and phase voltage phasors in polar form for a positive phase sequence.
16–32 In a balanced three-phase circuit, the line voltage magnitude is VL = 2:4 kV ðrmsÞ. For a positive phase sequence:(a) Find all of the line and phase voltage phasors using VAB as the phase reference.(b) Sketch a phasor diagram of the line and phase voltages.
16–31 In a balanced three-phase circuit the phase voltage magnitude is VP = 277 V ðrmsÞ. For a positive phase sequence:(a) Find all of the line and phase voltage phasors using VAN as the phase reference.(b) Sketch a phasor diagram of the line and phase voltages.
16–30 A load draws 4AðrmsÞ and 5 kW at a power factor 0:8 (lagging) from a 60-Hz source. Select an appropriate capacitor to be placed in parallel with the load to raise the overall power factor to unity.
16–29 In Figure P16–28, the load voltage is jVL j =2400 V ðrmsÞ at 60Hz. The load ZL draws an apparent power of 25 kVA at a lagging power factor of 0:7. Select the value of the capacitance required to raise the overall power factor of the parallel combination to 0:95. Repeat for a power
16–27 A 60-Hz voltage source feeds a two-wire line with ZW = 0:6 + j3:4 Ω=wire. The load at the receiving end of the line draws an apparent power of 5 kVA at a leading power factor 0:8. The voltage across the load is 500 V ðrmsÞ. Find the apparent power produced by the source and the rms value
16–26 The two loads in Figure P16–25 draw apparent powers of j S1 j = 16 kVA at a lagging power factor of 0:8 and j S2 j = 25 kVA at unity power factor. The voltage across the loads is 3:8 kV and the line has an impedance of ZW = 5 + j26 Ω=wire. Find the apparent power produced by the source
16–24 The complex power delivered to the load ZL in Figure P16–21 is 20 + j15 kVA. The source produces an average power of 22 kW and the line has an impedance of ZW = 2 + j12 Ω=wire. Find the magnitude of the source and load voltages.
16–23 The complex power delivered to the load ZL in Figure P16–21 is 20 + j15 kVA. The load voltage is 2 kV ðrmsÞ and the line has an impedance of ZW = 2 +j12 Ω=wire. Find the magnitude of the source voltage and the complex power produced by the source
16–22 Repeat Problem 16–21 with the load power factor increased to 0:95.
16–20 Twoloads are connectedinparallel across an880 V ðrmsÞ line. The first load draws an average power of 20 kW at a lagging power factor of 0:77. The second load draws 15 kW at a lagging power factor of 0:85. Find the overall power factor of the circuit and the current drawn from the line
16–19 In Figure P16–18, the complex powers delivered to each load are S1 = 400 + j270 VA, S2 = 550 + j150 VA, and S3 = 1000 + j0 VA. Find the line currents IA, IN, and IB.Validate your answers using MATLAB.
16–17 Repeat Problem 16–16 when the load ZL is 100 − j100 Ωand the source voltage is 220 V ðrmsÞ.
16–15 Repeat Problem 16–14 when ZL is a 75-Ω resistor in parallel with an impedance of 60 − j60 Ω.
16–13 A load made up of a 100-kΩ resistor in series with a 0:02-μF capacitor is connected across 2400-V ðrmsÞ, 60-Hz voltage source. Find the complex power delivered to the load and the load power factor. State whether the power factor is lagging or leading. Verify your answers using Multisim.
16–12 A load made up of a 50-Ω resistor in parallel with a 10-μF capacitor is connected across a 400-Hz source that delivers 110-V ðrmsÞ. Find the complex power delivered to the load and the load power factor. State whether the power factor is lagging or leading. Verify your answers using
16–11 A load made up of a 200-Ω resistor in parallel with a 150-mH inductor is connected across a 240-V ðrmsÞ, 60-Hz voltage source. Find the complex power delivered to the load and the load power factor. State whether the power factor is lagging or leading. Verify your answers using Multisim.
16–10 Find the impedance of a load that is rated at 440 V ðrmsÞ, 5AðrmsÞ, and 2:2 kW.

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