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systems analysis design

Questions and Answers of Systems Analysis Design

Repeat Problem 5.53, but now assume any two line segments may be out of service.Problem 5.53Open PowerWorld Simulator case Example 5_8. If the load bus voltage is greater than or equal to 730kV730kV
Recalculate the percent voltage regulation in Problem 5.15 when identical shunt reactors are installed at both ends of the line during light loads, providing \(65 \%\) total shunt compensation. The
Rework Problem 5.17 when identical shunt reactors are installed at both ends of the line, providing \(50 \%\) total shunt compensation. The reactors are removed at full load.Problem 5.17At full load,
Identical series capacitors are installed at both ends of the line in Problem 5.14, providing \(40 \%\) total series compensation. Determine the equivalent \(A B C D\) parameters of this compensated
Identical series capacitors are installed at both ends of the line in Problem 5.16, providing 30\% total series compensation.(a) Determine the equivalent \(A B C D\) parameters for this compensated
Determine the theoretical maximum real power that the seriescompensated line in Problem 5.57 can deliver when \(V_{S}=V_{R}=1.0\) per unit. Problem 5.57Identical series capacitors are installed at
What is the minimum amount of series capacitive compensation \(N_{\mathrm{C}}\) in percent of the positive-sequence line reactance needed to reduce the number of \(765-\mathrm{kV}\) lines in Example
Determine the equivalent \(A B C D\) parameters for the line in Problem 5.14 if it has \(70 \%\) shunt reactive (inductors) compensation and \(40 \%\) series capacitive compensation. Half of this
Consider the transmission line of Problem 5.18. (a) Find the \(A B C D\) parameters of the line when uncompensated. (b) For a series capacitive compensation of \(70 \%(35 \%\) at the sending end and
Given the uncompensated line of Problem 5.18, let a three-phase shunt reactor (inductor) that compensates for \(70 \%\) of the total shunt admittance of the line be connected at the receiving end of
Let the three-phase lossless transmission line of Problem 5.31 supply a load of 1000 MVA at 0.8 power factor lagging and at \(500 \mathrm{kV}\).(a) Determine the capacitance/phase and total
Open PowerWorld Simulator case Example 5_10 with the series capacitive compensation at both ends of the line in service. Graph the load bus voltage as a function of load real power (assuming unity
Open PowerWorld Simulator case Example 5_10 with the series capacitive compensation at both ends of the line in service. With the reactive power load fixed at 400 Mvar, graph the load bus voltage as
Transform the following sinusoids into phasor form and draw a phasor diagram. Use the additive property of phasors to find \(v_{1}(t)+v_{2}(t)\).(a) \(v_{1}(t)=240 \cos (\omega t+43) \mathrm{V}\)(b)
Transform the following sinusoids into phasor form and draw a phasor diagram. Use the additive property of phasors to find \(i_{1}(t)+i_{2}(t)\).(a) \(i_{1}(t)=-10 \sin (\omega t) \mathrm{mA}\)(b)
Transform the following sinusoids into phasor form and draw a phasor diagram. Use the additive property of phasors to find \(v_{1}(t)+v_{2}(t)+v_{3}(t)\).(a) \(v_{1}(t)=480 \cos \left(\omega
Figure P8-4 shows two phasor diagrams.(a) Add the voltage phasors into a new phasor \(\mathbf{V}_{3}\). Draw the sum of this new phasor on a phasor diagram.(b) Add the current phasors into a new
Convert the following phasors into sinusoidal waveforms.(a) \(\mathbf{V}_{1}=220 e^{-j 45^{\circ}} \mathrm{V}, \omega=314.2 \mathrm{rad} / \mathrm{s}\)(b) \(\mathbf{V}_{2}=440 e^{-j 225^{\circ}}
Use the phasors below and the additive property to find the sinusoidal waveforms \(v_{3}(t)=v_{1}(t)-v_{2}(t)\) and \(i_{3}(t)=2 i\) \({ }_{1}(t)+3 i_{2}(t)\).\[\begin{aligned}& \mathbf{V}_{1}=15
Convert the following phasors into sinusoidal waveforms.(a) \(\mathbf{V}_{1}=5+j 5 \mathrm{~V}, \omega=10 \mathrm{krad} / \mathrm{s}\)(b) \(\mathbf{V}_{2}=2 j(5+j 5) \mathrm{V}, \omega=200
Thinking about the derivative property of phasors as multiplication of the phasor by \(j \omega\), the integral property of phasors should be the inverse operation. Verify that the integration
Given the sinusoids \(i_{1}(t)=250 \cos \left(\omega t-60^{\circ}ight)\) \(\mathrm{mA}\) and \(i_{2}(t)=750 \sin (\omega t) \mathrm{mA}\) use the additive property of phasors to find \(i_{3}(t)\)
Given a sinusoid \(v_{1}(t)\) whose phasor is \(\mathbf{V}_{\mathbf{1}}=4-j 3 \mathrm{~V}\) and its frequency is \(10 \mathrm{rad} / \mathrm{s}\), use phasor methods to find a voltage \(v_{2}(t)\)
A design engineer needs to know what value of \(R, L\), or \(C\) to use in circuits to achieve a certain impedance.(a) At what radian frequency will a \(0.015-\mu \mathrm{F}\) capacitor's impedance
For the circuit of Figure P8-13}(a) Find the equivalent impedance \(Z\) when \(\omega=2000 \mathrm{rad} / \mathrm{s}\). Express the result in both polar and rectangular forms.(b) Select standard
A certain \(R L C\) series load has a load impedance of \(Z=1000-j 998 \Omega\) when excited by a \(1-\mathrm{krad} / \mathrm{s}\) source and a \(Z=1000-j 80 \Omega\) when driven by a
The circuit in Figure P8-17 is operating in the sinusoidal steady state with \(\omega=10 \mathrm{krad} / \mathrm{s}\).(a) What is the equivalent impedance of the circuit?(b) If one wanted to cancel
The circuit in Figure P8-18 is operating in the sinusoidal steady state with \(\omega=100 \mathrm{krad} / \mathrm{s}\).(a) Find the equivalent impedance \(Z\).(b) What circuit element can be added in
The circuit of Figure P8-19 is operating at \(50 \mathrm{~Hz}\). Find the equivalent impedance \(Z\).
A capacitor \(C\) is connected in parallel with a resistor \(R\). Select values of \(R\) and \(C\) so that the equivalent impedance of the parallel combination is \(600-j 800 \Omega\) at \(\omega=1\)
Two impedances \(Z_{1}=100-j 50 \Omega\) and \(Z_{2}=500+j 100\) \(\Omega\) are connected in parallel. Find the equivalent impedance of the pair.
A voltage source \(\mathrm{V}_{\mathrm{S}}=100 \angle 90^{\circ} \mathrm{V}\) is connected in series to a resistor of \(10 \Omega\) and an inductor of \(j 10 \Omega\). Find the phasor current
(a) Convert the circuit in Figure P8-25 into the phasor domain.(b) Find the phasor current flowing through the circuit and the phasor voltages across the capacitor and the resistor.(c) Plot all three
A complex load is driven by a current source \(i(t)\) \(=10 \cos (2 \mathrm{k} t) \mathrm{mA}\). The voltage measured across the load is \(v(t\) )\(=100 \cos \left(2 \mathrm{k} t-85^{\circ}ight)
A current source delivering \(i(t)=120 \cos (500 t) \mathrm{mA}\) is connected across a parallel combination of a \(10-k \Omega\) resistor and a \(0.2-\mu \mathrm{F}\) capacitor. Find the
A practical voltage source can be modeled using an ideal voltage source \(v_{\mathrm{S}}(t)=120 \cos (2000 t) \mathrm{V}\) in series with a5o- \(\Omega\) resistor. Convert the source into the phasor
A circuit consisting of a resistor, capacitor, and inductor is driven by a sinusoidal voltage source \(\mathbf{V}_{S}\) with a 1 \(\mathrm{krad} / \mathrm{s}\) frequency. A phasor diagram of the
Use the unit-output method to find \(\mathbf{V}_{\mathrm{X}}\) and \(\mathbf{I}_{\mathrm{X}}\) in the circuit of Figure P8-34.
An \(R C\) series circuit is excited by a sinusoidal source \(v(t)=V_{\mathrm{A}} \cos (\omega t+\phi) \mathrm{V}\). Determine the effects on the magnitudes of the current, voltages, and impedances
The OP AMP circuit of Figure P8-41 has \(\mathbf{V}_{\mathrm{S}}=2 \angle-15^{\circ} \mathrm{V}, Z_{\mathrm{S}}=50 \angle+30^{\circ} \Omega, Z_{\mathrm{F}}=100 \angle-45^{\circ} \Omega\), and a
Design an equivalent \(Z_{\mathrm{S}}=50 \angle+30 \Omega, Z_{\mathrm{F}}=100\) \(\angle-45^{\circ} \Omega\), and \(Z_{\mathrm{L}}=500 \angle-90^{\circ} \Omega\), if the circuit of Figure P8-41 is
A load of \(Z_{\mathrm{L}}=1000+j 1000 \Omega\) is to be driven by a phasor source \(\mathbf{V}_{\mathrm{S}}=150 \angle 0^{\circ} \mathrm{V}\). The voltage across the load needs to be
Design an interface voltage \(v_{\mathrm{S}}(t)=100 \cos \left(2 \times 10^{4} tight) \mathrm{V}\) delivers a steady-state output current of \(i_{\mathrm{O}}(t)=10 \cos \left(2 \times 10^{4}
Use MATLAB and mesh-current analysis to find the branch currents \(\mathbf{I}_{1}, \mathbf{I}_{2}\), and \(\mathbf{I}_{3}\) in Figure P8-52.
Use mesh-current analysis to find the phasor branch currents \(\mathbf{I}_{1}, \mathbf{I}_{2}\), and \(\mathbf{I}_{3}\) in the circuit shown in Figure P8-53. Validate your answer using Multisim.
Use MATLAB and mesh-current analysis to find the phasor currents \(\mathbf{I}_{\mathrm{A}}\) and \(\mathbf{I}_{\mathrm{B}}\) in Figure P8-55 .
The OP AMP circuit in Figure P8-56 is operating in the sinusoidal steady state.(a) Show that Image(b) Find the value of the magnitude of \(\mathbf{V}_{\mathrm{O}} / \mathbf{V}_{\mathrm{S}}\) at
The circuit in Figure P8-57 is operating in the sinusoidal steady state.(a) If \(v_{\mathrm{S}}(t)=1 \cos (2128 t) \mathrm{V}\), find the output \(v_{\mathrm{O}}(t)\).(b) At what frequency is the
For the circuit in Figure P8-5 phasor branch currents as follows:(a) Write a set of mesh-current equations. You can reduce the number of mesh equations by doing a source transformation with the
The circuit in Figure P8-60 is operating with \(\omega=20\) \(\mathrm{krad} / \mathrm{s}\).(a) Find the phasor outputs \(\mathbf{V}_{\mathrm{O}}\) and \(\mathbf{I}_{\mathrm{O}}\) in Figure P8-60 when
For the circuit of Figure P8-61 find the Thévenin equivalent circuit seen at the output.
The two competing OP AMP circuits in Figure P8-62 are operating in the sinusoidal steady state with \(\omega=100\) \(\mathrm{krad} / \mathrm{s}\). The two manufacturers both claim that their circuit
Find the phasor gain \(K=V_{\mathrm{O}} / \mathrm{V}_{\mathrm{S}}\) and input impedance Z IN of the circuit in Figure P8-64.
A load consisting of a 3.3-k \(\mathrm{k}\) resistor in series with a 3.3\(\mu \mathrm{F}\) capacitor is connected across a voltage source \(v_{\mathrm{S}}(t)=339.4\) \(\cos (314.2 t)\) V. Find the
The circuit in Figure P8-67 is operating in the sinusoidal steady state at a frequency of \(10 \mathrm{krad} / \mathrm{s}\).(a) Use Multisim to find the average power \(P\) delivered to the
You have a task of designing a load that ensures maximum power is delivered to it. The load needs to be connected to a source circuit that is not readily observable, but that you can make
An ac voltmeter measurement indicates the amplitude of a sinusoid and not its phase angle. The magnitude and phase can be inferred by making several measurements and using KVL. For example, Figure
The circuit of Figure P8-71 emulates a typical 60-Hz residential power system. There are three wires entering the house, two are called "hot" and the remaining one is called the return or "neutral."
Use the analysis methods discussed in Example 8-30 to find the input-output relationship \(\mathbf{V}_{\mathrm{O}} / \mathbf{V}_{\mathrm{S}}\) for the active bandpass filter of Figure P8-72. Treat
Ten years after graduating with a BSEE, you decide to go to graduate school for a master's degree. In desperate need of income, you agree to sign on as a grader in the basic circuitanalysis course.
Figure P8-77. shows a three-phase power system that is used in a manufacturing plant. The three sources are shown in the phasor diagram, with \(V_{\mathrm{P}}\) given as \(339.5 \mathrm{~V}\). The
The circuit in Figure P7-4 8 is in the zero state when the step function input is applied.(a) If \(V_{\mathrm{A}}=15 \mathrm{~V}, R=1.5 \mathrm{k} \Omega, L=250 \mathrm{mH}\), and \(C=025 \mu
Derive expressions for the damping ratio and undamped natural frequency of the circuit in Figure P7-4.9 in terms of the circuit parameters \(R, L\), and \(C\). Which parameter(s) affect the damping
The circuit of Figure P7=50 is a two-stage circuit that will be studied extensively in Chapter 12 as a band-pass filter. It is a second-order circuit whose zero-state step response can be solved by
The circuit of Figure P7=51 is a two-stage, firstorder cascade circuit that will be studied extensively in Chapter 14. It is a second-order circuit whose zero-state step response can be solved by
The circuit in Figure P7-52 is in the zero state when the step function input is applied. If the input source is \(V_{\mathrm{A}}\) \(=10 \mathrm{~V}\) and \(L=0.1 \mathrm{H}\), select values of
In a series \(R L C\) circuit, the step response across the 1\(\mu \mathrm{F}\) capacitor is\[v_{\mathrm{C}}(t)=25-e^{-400 t}[15 \cos (1000 t)+3 \sin (1000 t)] \mathrm{V} \quad t \geq 0\](a) Find
In a parallel \(R L C\) circuit, the state variable responses are \[\begin{aligned}v_{\mathrm{R}}(t) & =e^{-100 t}[5 \cos (300 t)+15 \sin (300 t)] \mathrm{V}, t \geq 0 \\i_{\mathrm{L}}(t) & =20-25
There is a need for a parallel \(R L C\) circuit that exhibits the desired response shown in Figure P7=55 . A vendor's spec sheet shows the circuit in Figure P7=55 and states that they are willing to
In a parallel \(R L C\) circuit, the inductor current through a \(1.5-\mathrm{H}\) inductor is observed to be\[i_{L}(t)=20 e^{-20 t} \sin (20 t) \mathrm{mA}, t \geq 0\]Find \(v_{\mathrm{L}}(t)\) at
Design a parallel \(R L C\) circuit whose natural response has the form\[v_{\mathrm{L}}(t)=K_{1} e^{-20,000 t}+K_{2} t e^{-20,000 t} \mathrm{~V} \quad t \geq 0\]
Amplitude-modulated (AM) radios use an oscillator operating at \(455 \mathrm{kHz}\) to demodulate the received signal. This frequency is called the intermediate frequency or IM. Your task is to
Design a series \(R L C\) circuit whose output voltage resides entirely within the nonshaded region of Figure \(\mathrm{P}_{7}=5.9\). Validate your design using MATLAB or Multisim. Vo(1)(V) 7 6 5 4.5
An intern designed the circuit shown in Figure P7-60 . The intern claimed that by varying the 470-2 potentiometer the circuit could achieve all three damping cases. As a wise designer, you suggest an
A variable capacitor is used in the circuit of Figure P7-61 to vary the damping ratio. What range of damping ratios is available in the circuit? At what value of \(C\) will \(\zeta\) be 1 ? 5 1-1000
A particular parallel \(R L C\) circuit has the step response observed on an oscilloscope and shown in Figure P7-62. Four points on the waveform were measured and are shown.Determine the circuit's
A car maker needs an \(R C\) timing circuit to trigger the windshield wiper relay. The circuit should be driver selectable to trigger at \(1,2,5\), and \(10 \mathrm{~s} \pm 5 \%\). The source circuit
Design the first-order \(R C\) circuit in Figure P7-64 so an input \(v_{\mathrm{S}}\) \((t)=15 u(t)\) V produces a zero-state response \(v_{\mathrm{O}}(t)=15-5 e\) \({ }^{-1000}{ }^{t} \mathrm{~V}\).
Figure P7-65 is a simplified diagram of a sample-hold circuit. When the switch is in position \(\mathrm{A}\), the circuit is in the sample mode and the capacitor voltage must charge to at least \(99
Supercapacitors have very large capacitance (typically from 0.1 to \(135 \mathrm{kF}\) ), small sizes, and very long charge-holding times, making them useful in nonbattery backup power applications.
You are assigned a task to design a series, passive \(R L C\) circuit with a characteristic equation of \(s^{2}+2000 s+5 \times 10^{6}=0\). To save money, your supervisor wants you to use a
The switch in Figure P7-68 has been in position A for a long time and is moved to position \(\mathrm{B}\) at \(t=0\) and then to position \(\mathrm{C}\) when \(t=10 \mathrm{~ms}\). For \(010
A digital clock has become corrupted by a ringing (undesired oscillations) as shown in Figure P7-69. (a). The unwanted oscillations can cause false triggers and must be reduced to not trigger a false
There is a need to generate a \(12-\mathrm{V} \pm 10 \%, 10 \mathrm{kHz}\) triangular wave. You have a \(\pm 5-\mathrm{V}, 10 \mathrm{kHz}\) square wave. You recall from your first Circuits course
A sensitive instrument that can be modeled by the series \(R L C\) circuit shown in Figure P7=71 is to be protected by a fuse. The voltage across the capacitor is\[v_{\mathrm{C}}(t)=e^{-10 t}(-\cos
The circuit in Figure P7-72 is a simplified diagram of a pulser that delivers simulated lightning transients to the test article at the output interface. Closing the switch must produce a
Losses in real inductors can be modeled by a series resistor as shown in Figure P7-7.3 . In this problem, we include the effect of this resistor on the design of the series \(R L C\) circuit shown in
Figure P7-74 shows the step responses \(v_{\mathrm{C}}(t)\) of two competing series \(R L C\) circuits from two different vendors. The circuits are designed to switch from o to \(10 \mathrm{~V}\) and
The OP AMP circuit shown in Figure P7-17 purports to be an oscillator. Derive the differential equation for the output voltage. Then build the circuit in Multisim and validate your solution by
Find the function \(i(t)\) that satisfies the following differential equation and the initial condition:\[2000 \frac{d i(t)}{d t}+10 \mathrm{k} i(t)=0, i(0)=10 \mathrm{~mA}\]
(a) Find the function \(i\) ( \(t\) ) that satisfies the following differential equation and initial condition:\[500 \frac{d i(t)}{d t}+100000 i(t)=0, i(0)=10 \mathrm{~mA}\](b) Use MATLAB's dsolve to
Find the time constants of the circuits in Figure \(\mathrm{P} 7=3\). 100 mH_10 220 mH Cl 20 mH 100 50 C2 2k 2 52 52 10 mH 21 mH
Each of the two circuits in Figure P7-4 has a switch that affects their time constants.(a) For circuit C1, find the time constant when the switch is in position \(A\) and repeat for position
The switch in Figure P7= 5 is closed at \(t=0\). The initial voltage on the capacitor is \(v_{\mathrm{C}}(0)=100 \mathrm{~V}\).(a) Find \(v_{\mathrm{C}}(t)\) and \(i_{\mathrm{O}}(t)\) for \(t \geq
In Figure P7-6, the initial current through the inductor is \(i_{\mathrm{L}}(\mathrm{O})=6 \mathrm{~mA}\).(a) Find \(i_{\mathrm{L}}(t)\) and \(v_{\mathrm{O}}(t)\) for \(t \geq 0\).(b) Use MATLAB to
The circuit in Figure P7-7 has \(25 \mathrm{~V}\) stored across the two capacitors at \(t=0\), with the same polarity as \(v_{\mathrm{O}}(t)\). If \(C_{1}=\) \(33,000 \mathrm{pF}, C_{2}=22,000
The switch in Figure P7-8 has been in position A for a long time and is moved to position B at \(t=0\). Find \(v_{\mathrm{C}}(t)\) for \(t \geq 0\). 15 V 10 A B + vc(t): 1=0 100 0.05
The switch in the circuit in Figure P7-9. has been in position A for a long time. At \(t=0\), it switches to position B; find \(i_{\mathrm{L} 1}(t)\) and \(i_{\mathrm{L} 2}(t)\) for \(t \geq 0\).
The circuit in Figure P7-10 is in the zero state. Find the voltage \(v_{\mathrm{O}}(t)\) for \(t \geq 0\) when an input of \(i_{\mathrm{S}}(t)=I_{\mathrm{A}} u(t)\) is applied. Identify the forced
The circuit in Figure \(\mathrm{P}_{7-11}\) is in the zero state when the input \(v_{\mathrm{S}}(t)=V_{\mathrm{A}} v(t)\) is applied. Find \(v_{\mathrm{O}}(t)\) for \(t \geq 0\).Identify the forced

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