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systems analysis and design
The Analysis And Design Of Linear Circuits 7th Edition Roland E Thomas, Albert J Rosa, Gregory J Toussaint - Solutions
Show that the active filter in Figure P14–9 has a transfer function of the form TðsÞ ¼ V2ðsÞV1ðsÞ¼R1C1s R1R2C1C2s2 þ R1C2 þ R2C2 ð Þs þ 1 Using R1¼R2¼R, develop a method of selecting values for C1, C2, and R. Then select values so that the filter has a v0 of 50 krad/s and a z of
The active filter in Figure P14–10 has a transfer function of the form TðsÞ ¼ V2ðsÞV1ðsÞ¼R3C2s R1R3C1C2s2 þ ðR1C1 þ R1C2Þs þ 1 þ R1=R2 Using C1¼C2¼C and R1¼R2¼R, develop a method of selecting values for C and R. Then select values so that the filter has a v0 of 10 krad/s and a z
The active filter in Figure P14–11 has a transfer function of the form TðsÞ ¼ V2ðsÞV1ðsÞ¼ðRCsÞ2 þ 1ðRCsÞ2 þ 2RCs þ 1 Select values ofRandCso that the filter has a v0 of 377 krad/s.Use OrCAD to plot the filter’s Bode magnitude diagram.What type of filter is this? With the gain
A certain instrumentation system for a new hybrid car needs a bandpass filter to limit its output bandwidth prior to digitization. The filter must meet the following specifications:TMAX ¼ þ20 1 dB vCH ¼ 5:5 krad=s ð875:4HzÞ 10%vCL ¼ 5 krad=s ð795:8HzÞ 10%TMIN20 dB vCHMIN ¼ 55 krad=s
You are working at an aircraft manufacturing plant on an altitude sensor that eventually will be used to retrofit dozens of similar sensors on an upgrade to a current airframe.You are required to find a quality notch filter to eliminate an undesirable interference at 400 Hz. You find a vendor and
An amplified portion of the radio spectrum is shown in Figure P14–56. You need to hear all of the signals from 1.0 MHz to 2.0 MHz, but there is an interfering signal at 1.8 MHz. Design a notch filter to reduce that signal by at least 50 dB and not reduce the desired signal at 1.7 MHz by more than
Design Evaluation A need exists for a third-order Butterworth low-pass filter with a cutoff frequency of 2 krad and a dc gain of 0 dB. The design department has proposed the circuit in Figure P14–59.As a junior engineer in the manufacturing department, you have been asked to verify the design and
Modifying an Existing Circuit One of your company’s products includes the passive RLC filter and OP AMP buffer circuit in Figure P14–60. The supplier of the inductor is no longer in business and a suitable replacement is not available, even on eBay or Craig’s List.You have been asked to
What’s a High-Pass Filter Ten years after earning a BSEE, you return for a master’s degree and sign on as the laboratory instructor for the basic circuit analysis course. One experiment asks the students to build the active filter in Figure P14–61 and measure its gain response over the range
Bandpass to Bandstop Transformation The three-terminal circuit in Figure P14–62(a) has a bandpass transfer function of the form TðsÞ ¼ VOðsÞVSðsÞ¼ 2zðs=v0Þðs=v0Þ2 þ 2zðs=v0Þ þ 1 Show that the circuit in Figure P14–62(b) has a bandstop transfer function of the form TðsÞ ¼
Third-Order Butterworth Circuit Show that the circuit in Figure P14–63 produces a third-order Butterworth low-pass filter with a cutoff frequency of vC¼1/RC and a passband gain of K¼4. R R R w w C/2 HH + 2C C R FIGURE P14-63 www 3R
Notch Filter Comparison To eliminate an interfering signal at 10 krad/s on a new product design, your consulting firm needs to purchase a notch filter with the following specifications:Center frequency¼10 krad/s 0.5%Bandwidth ¼ 200 rad/s 2%Depth of notch (attenuation at v0) ¼ 50 dB min.Two
Biquad Filter Abiquad filter has the unique properties of having the ability to alter the filter’s parameters, namely, gain K,quality factor Q, and resonant frequency v0. This is done in each case by simply adjusting one of the circuit’s resistors. Furthermore, adjusting any of the three
Crystal Filters Although not an active filter, crystal (Quartz) filters are very high-Qfilters.SomecanhaveQ’s approaching 100,000. HighQ means high selectivity; hence, crystal filters are used extensively in communications where fine tuning is essential. In its simplest form, a quartz crystal is
In Figure P15–1 L1 ¼ 120 mH, L2 ¼ 400 mH,M¼ 180 mH, and v2ðtÞ ¼ 60 sin 500t V.(a) Write the i–v relationships for the coupled inductors using the reference marks in the figure.(b) Find the source voltage vSðtÞ when the output terminals are open-circuited ði2ðtÞ ¼ 0Þ. vs(t) + i1(t)
In Figure P15–4 L1 ¼ 30mH; L2 ¼ 25 mH, and M ¼25mH. The output current is observed to be i2ðtÞ ¼5sin 100t A when the output terminals are short-circuitedðv2ðtÞ ¼ 0Þ. Find v1ðtÞ and iSðtÞ, assuming that iSðtÞ has no dc component. + i1(t) M i2(t) is(t) vi(t) Li FIGURE P15-4 12 V2(t)
InFigureP15–7L1 ¼ 6H; L2 ¼ 3H; M ¼ 4H,andi1ðtÞ ¼5 sin ð1000tÞmA. Find the input voltage vXðtÞ. i1(t) M + vx(t) v1(t) Li i2(t) L2 v2(t) - FIGURE P15-7
In Figure P15–8 show that LEQ ¼ L1 1 k2, where k is the coupling coefficient. M L 12 LEQ FIGURE P15-8
In Figure P15–9 show that the indicated open-circuit voltage is vOCðtÞ ¼ k ffiffiffiffiffiffiffiffiffiffiffiffiffiffi L2=L1 pv1ðtÞ, where k is the coupling coefficient. vs(t) + I i1(t) M i2(t) v1(t) L1 el L2 FIGURE P15-9 + v2(t) voc(t)
In Figure P15–10 show that the indicated short-circuit current is iSCðtÞ ¼ k ffiffiffiffiffiffiffiffiffiffiffiffiffiffi L1=L2 pi1ðtÞ, where k is the coupling coefficient. Assume that i1ðtÞ has no dc component. + vs(t) i1(t) M i2(t) + V(t) L1 L2 FIGURE P15-10 v2(t) isc(t)
The turns ratio of the second ideal transformer in Figure P15–13 is n ¼ 5. Find the equivalent resistance indicated in the figure. REQ 1:2 IDEAL 10 ww 1:n 50 IDEAL FIGURE P15-13
Figure P15–15 shows an ideal transformer connected as an autotransformer. Find iLðtÞ and iSðtÞ when vSðtÞ ¼120 sin 400t and RL ¼ 60 V. i2(t) is(t) V2(t) vs(t) + | el N2 = 600 L(t) RL v1(t) N = 600 i1(t) FIGURE P15-15
Select the turns ratio n of an ideal transformer in the interface circuit shown in Figure P15–17 so that the input resistance RIN seen by the voltage source is 150 V. vs(t) 50 w 150 w 1:n ww Interface 200 1 Circuit RIN FIGURE P15-17 w
Find iSðtÞ in Figure P15–19 when vSðtÞ ¼ 15 sin 377t V. is(t) vs(t) in(t) + v1(t) 602 W n = 4 eee Fiz(t) + V2(t) 12 + | FIGURE P15-19
Show that the equivalent resistance in Figure P15–20 is REO = (N + N) RL. N2 000 N1 NRL 000 REQ FIGURE P15-20
In Figure P15–21 the impedances are Z1 ¼ 25j45 V; Z2 ¼ 45 þ j30V, and Z3 ¼ 360 þ j270V. Find I1, I2, and I3. Z v 200L0 VS 12 13 1:2- 1:3 Z2 Z3 Ideal FIGURE P15-21 Ideal +
The input voltage to the transformer in Figure P15–26 is a sinusoid vSðtÞ ¼ 60 cos 2500t V. With the circuit operating in the sinusoidal steady-state, use mesh-current analysis to find the phasor output voltage V2 and the input impedance ZIN. vs(t) ZIN +1 50 60 mH w + v2(t) 30 mH 120 mH 600
The circuit in Figure P15–30 is in the sinusoidal steadystate with VS ¼ 500 V and ZL ¼ 16 þ j12V. Use meshcurrent analysis to find the amplitude of the output voltage, the input impedance seen by the source, and the average power delivered to ZL. Vs + j702 50 10 ww m + 10050 ZL ZVO FIGURE
Find the phasor current I and impedance ZIN in the circuit in Figure P15–32. 200/0 V 1 + + Vi 12 100 200 j8 j4 j16 V2 ZIN FIGURE P15-32
The circuit in Figure P15–33 is in the sinusoidal steady state with VS ¼ 100ff0 V and RL ¼ 45 V. Use mesh-current analysis to find VO and the average power delivered to RL. Vs 1 + 160 10 M 00 m j40 100 -j30 2 RL Vo FIGURE P15-33
In Figure P15–34 find IA, IB, and the input impedance seen by the voltage source. 120L0 + | n = 5 V2 - 5 IB =-j5 ZIN FIGURE P15-34
The ideal transformer in Figure P15–35 is connected as an auto transformer. Find IS and the average power delivered to RL when N1 ¼ N2 ¼ 500 turns; RL ¼ 60 V, and VS ¼ 120ff0 V ell Is S Vs | + N 000 RL IL 12 FIGURE P15-35
The transformer in Figure P15–36 is operating in the ac steady-state with a voltage source connected at the input and the output shorted. Show that the input impedance is ZIN ¼ jX1 1 k2, where k is the coupling coefficient.Hint : k ¼ XM=ffiffiffiffiffiffiffiffiffiffiffiffiffi X1X2 p: Vs ZIN 11
The linear transformer in Figure P15–38 is in the sinusoidal steady-state with reactances of X1 ¼ 32 V;X2 ¼ 48 V; XM ¼ 36 V, and a load impedance of ZL ¼150 j75 V. Find the input impedance seen by the input voltage source. Vs + | V jXM 12 V2 ZL jX1 jX2 ZIN FIGURE P15-38
Transformer Sawtooth Response The linear transformer in Figure P15–41 has inductances of L1 ¼ 25mH; L2 ¼ 100 mH, and M ¼ 50 mH. The input voltage vSðtÞ has a sawtooth waveform with a peak amplitude of 5 Vand a period of 50 ms. Derive an expression for the first three terms of the Fourier
Perfectly Coupled Transformer Figure P15–43 is an equivalent circuit of a perfectly coupled transformer. This model is the basis for the transformer equivalent circuits used in the analysis of power systems.The inductance Lm is called the magnetizing inductance. The current through this
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 ¼ 1500 cos vt 45ð ÞV; iðtÞ ¼ 2 cos vt þ 50ð ÞA(b) vðtÞ ¼ 90 cos vt þ 60ð ÞV; iðtÞ ¼ 10:5 cos vt
The following sets of vðtÞ and iðtÞ apply to the load circuit in Figure P16–1. Calculate the average power and the reactive power.(a) vðtÞ ¼ 135 cosðvtÞV; iðtÞ ¼ 2 cos vt þ 30ð ÞA(b) vðtÞ ¼ 370 sinðvtÞV; iðtÞ ¼ 10 cos vt þ 20ð ÞA
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 ¼ 250ff0 VðrmsÞ; I ¼ 0:25ff 15 AðrmsÞ(b) V ¼
The following sets of Vand I apply to the circuit in Figure P16–3. Calculate the complex power and the power factor.State whether the power factor is lagging or leading.(a) V ¼ 120ff30 VðrmsÞ; I ¼ 3:3ff 15AðrmsÞ(b) V ¼ 480ff45 VðrmsÞ; I ¼ 8:5ff90 AðrmsÞ
The conditions in this problem apply to the circuit in Figure P16–3. Calculate the complex power for each condition given below.(a) V ¼ 15ff45 kVðrmsÞ; Z ¼ 500ff 15V(b) Z ¼ 40 j30V; I ¼ 10ff25 AðrmsÞ
Find the power factor under the following conditions.State whether the power factor is lagging or leading.(a) S ¼ 1000 þ j250 kVA(b) jSj ¼ 15 kVA; P ¼ 12 kW;Q < 0:
A load draws an apparent power of 30 kVA at a power factor of 0.8 lagging from a 2400-V (rms) source. Find P, Q, and the load impedance.
A load draws 8 kWat a power factor of 0.8 leading from a 880-V(rms) source. Find Q and the load impedance.
A load draws 15 A (rms), 5 kW, and 2.5 kVARS (lagging)from a 60-Hz source. Find the load power factor and impedance.
Find the impedance of a load that is rated at 440 V (rms), 5 A (rms), and 2.2 kW.
A load made up of a 100-V resistor in series with a 150-mH inductor is connected across a 240-V(rms), 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.
Aload made up of a 50-Vresistor in parallel with a 10-mF capacitor is connected across a 400-Hz source that delivers 110 V(rms). Find the complex power delivered to the load and the load power factor. State whether the power factor is lagging or leading.
A load made up of a resistor R in series with an inductor L draws a complex power of 1200 þ j800VAwhen connected across a 440-V (rms), 60-Hz voltage source. Find the value of the value of R and L.
In Figure P16–14 the load ZL, is a 60-V resistor in series with a capacitor whose reactance is 30V. The source voltage is 440 V (rms). Find the complex power produced by the source and the complex power delivered to the load. Vs +1 20 125 -120 FIGURE P16-14 IL VL ZL
Repeat Problem 16–14 when ZL is a 50-V resistor in parallel with an impedance of 40 j60 V.
In Figure P16–16 the load ZL is a 100-V resistor and the source voltage is 240 V(rms). Find the complex power produced by the source. Vs | + 100 m 100 -125 ZL FIGURE P16-16
Repeat Problem 16–16 when the load ZL, is a 50-V resistor in series with a capacitor whose reactance is 100 V.
In Figure P16–18 the three load impedances are:Z1 ¼ 20 þ j15 V, Z2 ¼ 25 þ j10 V, and Z3 ¼ 75 þ j50 V.Find the total complex power produced by the two sources and the overall circuit power factor. 110 L0 Vrms 110 L0 Vrms 1 + 1 + (A) (N) IN Z1 Z2 B IB FIGURE P16-18 Z3
In Figure P16–18 the complex powers delivered to each load are: S1 ¼ 400 þ j270 VA, S2 ¼ 550 þ j150 VA, and S3 ¼ 1000 þ j0 VA. Find the line currents IA, IN, and IB.
Two loads are connected in parallel across an 880 V(rms)line. The first load draws an average power of 20 kW at a lagging power factor of 0.8. The second load draws 16kWat a lagging power factor of 0.9. Find the overall power factor of the circuit and the rms current drawn from the line.
The apparent power delivered to the load ZL in Figure P16–21 is 46 kVA at a lagging power factor of 0.84. The load voltage is 2.4 kV(rms) and the line has an impedance of ZW ¼ 1 þ j8V=wire. Find the required apparent source power, the source power factor, and the magnitude of the source
Repeat Problem 16–21 with the load power factor increased to 0.95.
The average power delivered to the load ZL in Figure P16–21 is 250 kWat a lagging power factor of 0.85. The load voltage is 7.2 kV(rms) and the line has an impedance of ZW ¼ 2 þ j12 V=wire. Find the apparent power supplied by the source and magnitude of the source voltage.
The complex power delivered to the load ZL in Figure P16–21 is 20 þ j15 kVA. The source produces an average power of 21 kW and the line has an impedance of ZW ¼ 2:1 þ j12 V=wire. Find the magnitude of the source and load voltages.
In Figure P16–25 the voltage across the two loads is jVLj ¼ 4:8 kVðrmsÞ. The load Z1 draws an average power of 12 kWand a power factor of 0.85 lagging. The load Z2 draws an apparent power of 15 kVAand at a lagging power factor of 0.8. The line has an impedance of ZW ¼ 9 þ j50 V=wire. Find
The two loads in Figure P16–25 draw apparent powers of jS1j ¼ 16 kVA at a lagging power factor of 0.8 and jS2j ¼25 kVA at unity power factor. The voltage across the loads is 3.8 kV and the line has an impedance of ZW ¼ 5þj26 V=wire. Find the apparent power produced by the source and the rms
A 60-Hz voltage source feeds a two-wire line with ZW ¼ 0:6 þ j3:4 V=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(rms).Find the apparent power produced by the source and the rms value of the
In Figure P16–28 the load voltage is jVLj ¼4160 VðrmsÞ at 60 Hz and the load ZL draws an average power of 10 kW at a lagging power factor of 0.725. Find the overall power factor of the combination if the parallel capacitance is 1 mF. Find the value of the capacitance needed to raise the
In Figure P16–28 the load voltage is jVLj ¼2400 VðrmsÞ at 60 Hz. The load ZL draws an apparent power of 25 kVA at a lagging power factor of 0.7. Find the value of the capacitance required to raise the overall power factor of the parallel combination to 0.95. Repeat this problem for an overall
A load draws 5 A (rms) and 4 kW at a power factor 0.8 (lagging) from a 60-Hz source. Find the capacitance needed in parallel with the load to raise the overall power factor to unity.
In a balanced three-phase circuit the phase voltage magnitude is VP ¼ 277VðrmsÞ. 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.
In a balanced three-phase circuit the line voltage magnitude is VL ¼ 2:4 kVðrmsÞ. 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.
In a balanced three-phase circuit VBC ¼ j208 VðrmsÞ.Find all the line and phase voltage phasors in polar form for a positive phase sequence.
In a balanced three-phase circuit VBN ¼ 200þj150 VðrmsÞ. Find all of the line and phase voltage phasors in polar form for a positive phase sequence.
A balanced D-connected three phase source has VAB ¼208ff30 VðrmsÞ and a positive phase sequence. Find the three source voltages of the equivalent Y-connected source.
In a balanced three-phase circuit VBN ¼ VPff90 VðrmsÞ.Show that VBC ¼ffiffiffi 3p VPff120 VðrmsÞ for a positive phase sequence.
A balanced Y-connected load with ZY ¼ 10 j10 V=phase is connected in parallel with a balanced Dconnected load with ZD ¼ 60 þ j30V=phase. Find the phase impedance of an equivalent D-connected load.
A balanced Y-connected load with ZY ¼ 30 þj30 V=phase is connected in parallel with a balanced Dconnected load with ZD ¼ 60 j900 V=phase. Find the phase impedance of an equivalent Y-connected load.
AbalancedY-connectedloadwithZY1 ¼ 12 þ j6 V=phase is connected in parallel with a second Y-connected load with ZY2 ¼ 24 þ j6V=phase. Find the phase impedance of the equivalent Y-connected load.
In a balanced D-D circuit the D-connected source produces VAB ¼ 2400ff45 VðrmsÞ and a positive phase sequence.The phase impedance of the load is ZD ¼200ff45V=phase. Find the three source voltages and the phase impedance in the equivalent Y-Y circuit.
In a balancedD-Ycircuit the line voltage andphaseimpedance areVL ¼ 560 VðrmsÞ andZY ¼ 25 þ j10V=phase. Using ffVAB ¼ 0 as the phase reference, find the line current and phase voltage phasors in polar form for a positive phase sequence.
In a balanced Y-Y circuit the line voltage is VL ¼ 480 VðrmsÞ. The phase impedance is ZY ¼ 40þj25 V=phase. Using ffIA ¼ 0 as the phase reference, find IAand VAB in polar form for a positive phase sequence.
In a balancedY-Dcircuit the line voltage and phase impedance areVL ¼ 440 VðrmsÞ andZD ¼ 16þ j12V=phase. Using ffVAN ¼ 0 as the phase reference, find the line current and phase current phasors in polar form for a positive phase sequence.
In a balanced Y-D circuit the line impedances connecting the source and load are ZW ¼ 1:5 þ j6:5 V=phase. The phase impedances of the D-connected load are ZD ¼ 15 þj8 V=phase and the line voltage at the source is VL ¼250VðrmsÞ. Using ffVAB ¼ 0 as the phase reference, find the line current
In a balanced Y-D circuit the line voltage and phase impedance are VL ¼ 4:16 kVðrmsÞ and ZD ¼ 250ff30V=phase. Using ffVAB ¼ 0 as the phase reference, find the phase current IAB and line current IA for a positive phase sequence.
A balanced three-phase source with VAB ¼440ff30 VðrmsÞ supplies a balanced D-connected load with a phase impedance of ZD ¼ 20ff 60V=phase. Find the phase current IAB and line current IAfor a positive phase sequence.
In a balanced Y-connected load the line current and phase impedance are IL ¼ 6AðrmsÞ and ZY ¼ 20þj15 V=phase. Using ffVAB ¼ 0 as the phase reference, find the line current IA and phase voltage VAN for a positive phase sequence.
In a balanced D-connected load the phase current and phase impedance are IP ¼ 12AðrmsÞ and ZD ¼200ff60V=phase. Using ffVAN ¼ 0 as the phase reference, find the line current IA and line voltage VAB for a positive phase sequence.
An average power of 6 kW is delivered to a balanced three-phase load with a phase impedance of ZY ¼ 40þj30 V=phase. Find VL and the complex power delivered to the load.
An apparent power of 12 kVA is delivered to balanced three-phase load with a phase impedance of ZY ¼ 120þj90 V=phase. Find IL, VL, and the complex power delivered to the load.
A balanced three-phase load has a phase impedance of ZY ¼ 60 j20 V=phase. The line voltage at the load is VL ¼ 440 VðrmsÞ. Find IL and the complex power delivered to the load.
A balanced three-phase load has a phase impedance of ZD ¼ 200 þ j100 V=phase. The line voltage at the load is VL ¼ 2:4 kVðrmsÞ. Find IL and the complex power delivered to the load.
A balanced three-phase load has a phase impedance is ZY ¼ 200 þ j100 V=phase. The line current at the load is IL ¼ 16AðrmsÞ. Find VL and the complex power delivered to the load.
The balanced three-phase source in Figure P16–54 produces an average power of 50 kW. The line impedance is ZW ¼ 1 þ j6V=phase and the balanced load has a phase impedance ZY ¼ 200 þ j100 V=phase. Find the line voltage VL at the load and complex power delivered to the load. IL Zw Balanced IL
The balance three-phase source in Figure P16–54 produces an average power of 15 kW at a power factor of 0.85 lagging. The line impedance is ZW ¼ 3 þ j15 V=phase and the balanced load has a phase impedance of ZD ¼ 250 þ j55 V=phase. Find the line voltage VL at the load and complex power
The balanced three-phase source in Figure P16–54 produces an apparent power of 25 kVA at a power of factor 0.9 lagging. The line impedance is ZW ¼ 2 þ j10 V=phase and line current is 10 A(rms). Find the line voltage VL at the load and complex power delivered to the load.
The balanced three-phase source in Figure P16–54 produces a average power of 50 kW at a power factor of 0.75 lagging. The line impedance is ZW ¼ 2 þ j12 V=phase and line voltage at the source is 4160 V(rms). Find the line voltage VL at the load and complex power delivered to the load.
Two balanced three-phase loads are connected in parallel.The first load absorbs 25 kWat a lagging power factor of 0.9. The second load absorbs an apparent power of 30 kVAat a leading power factor of 0.1. The line voltage at the parallel loads is VL ¼ 880 VðrmsÞ. Find the line current into the
The average power delivered to a balanced Y-connected load is 20kWat a lagging power factor of 0.8. The line voltage at the load is VL ¼ 480 VðrmsÞ. Find the phase impedance ZY of the load.
The apparent power delivered to a balanced D-connected load is 30 kVA at a lagging power factor of 0.72. The line voltage at the load is VL ¼ 2:4 kVðrmsÞ. Find the phase impedance ZD of the load.
In Figure P16–61 the source and load busses are interconnected by a transmission line with ZW ¼ 70 þ j400 V=phase.Theloadatbus2drawsanapparentpowerofjS2j ¼ 3MVAata lagging power factor of 0.85 and the line voltage at bus 2 is VL2 ¼ 230 kVðrmsÞ. Find the apparent power produced by the source
In Figure P16–61 the source and load busses are interconnected by a transmission line with ZW ¼ 2þj10 V=phase. The load at bus 2 draws an average power of P2 ¼ 50 kW at a lagging power factor of 0.8 and the line voltage at bus 2 is VL2 ¼ 4:16 kVðrmsÞ. Find the apparent power produced by the
In Figure P16–61 the source and load busses are interconnected by a transmission line with ZW ¼ 10þj75 V=phase. The load at bus 2 draws an average power of P2 ¼ 600 kW at a lagging power factor of 0.8 and the line current is IL1 ¼ 14AðrmsÞ. Find the source power factor and the line voltages
In Figure P16–64 the three buses are interconnected by transmission lines with wire impedances of ZW1 ¼100 þ j600 V=phase and ZW2 ¼ 120 þ j800 V=phase. The source at bus 2 produces an apparent power of jS2j ¼300 kVA at a lagging power factor of 0.85. The load at bus 3 draws an apparent power
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