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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

Repeat Problem 10–32 when iS(t)¼2.5 cos 2000 t u(t)mA.
The circuit in Figure P10–29 is in the zero state. Transform the circuit into the s domain and find the Thevenin equivalent circuit at the capacitor’s terminals.
The initial conditions for the circuit in Figure P10–29 are vC(0) ¼ 0 and iL(0) ¼ I0. Transform the circuit into the s domain and use superposition and voltage division to find the zero-state and zero-input components of VR(s).
The switch in Figure P10–25 has been in position B for a long time and is moved to position A at t ¼ 0.(a) Transform the circuit into the s domain and solve for Vc(s) in symbolic form.(b) Find vC(t) for R1 ¼ 50V, R2 ¼ 250 V, R3 ¼ l kV, L ¼500 mH, C ¼ 1 mF, and VA ¼ 15 V. In addition, the
Transform the circuit in Figure P10–23 into the s domain and find IL(s) and iL(t) when v1(t)¼VAe1000tu(t), R ¼200V, L ¼ 100 mH, and iL(0) ¼ 0 A.
The switch in Figure P10–21 has been in position B for a long time and is moved to position A at t ¼ 0. Transform the circuit into the s domain and solve for VC(s), vC(t), VL(s), and vO(t) in symbolic form.
The switch in Figure P10–19 has been in position B for a long time and is moved to position A at t ¼ 0. Transform the circuit into the s domain and solve for IL(s) and iL(t) in symbolic form.
For a parallel RC circuit find ZEQ(s) and then select R and C so that there is a pole at 10 krad/s.
For a seriesRCcircuit findZEQ(s) and then selectRand C so that there is a pole at zero and a zero at 1 krad/s.
Find the time constants of the circuits in Figure P7–3. 100 mH -m 150 mH 5 mH m C1 100 2100 100 2 w - 150 -100 10 mH 10 mH C2 FIGURE P7-3
Find the time constants of the circuits in Figure P7–4. 0.33 F= 3 ww w 3 1 www - 4 33 0.1 47 w 0.1 1 C1 2 FIGURE P7-4
Each of the two circuits in Figure P7–5 have a switch that affects their time constants. For circuit C1 find the time constant when the switch is in position A and repeat for position B. For circuit C2 find the time constant when the switch is closed and repeat when it is open. R1 R1 B www Aq C C
The switch in Figure P7–6 is closed at t ¼ 0. The initial voltage on the capacitor is vC(0) ¼ 250 V.(a) Find vC(t) and iO(t) for t 0.(b) Use MATLAB to plot the waveforms for vC(t) and iO(t).Simulate the problem using OrCAD and compare the results to the plots in part (b). 15 W io(t) + t=0
In Figure P7–7 the initial current through the inductor is iL(0) ¼ 3 mA. Find iL(t) and vO(t) for t 0. + 47 (1) vo(t) - 33 0.5 H FIGURE P7-7
The switch in Figure P7–8 has been in position A for a long time and is moved to position B at t ¼ 0. Find iL(t) for t 0. iL() 1-0 B 100 www A 15 mH 50 10 mA FIGURE P7-8
The circuit was in the zero state when the source in Figure P7–9 is applied. Find vC(t) for t 0. 100 ww 100 pF + vc(t) 100 25 u(t) V 50 : FIGURE P7-9
The switch in Figure P7–10 has been in positionAfor a long time and is moved to position B at t ¼ 0. Find vC(t) for t 0. A B 10 + + 5V. t=0 vc(t) 0.05 F FIGURE P7-10 50
The switch in Figure P7–11 has been open for a long time and is closed at t ¼ 0. Find iL(t) for t 0. 10 mA 15 23 15 47 w iL (1) t=0 FIGURE P7-11 10 mH
The circuit in Figure P7–12 is in the zero state. Find the voltage vO(t) for t 0 when an input of iS(t) ¼ IAu(t) applied.Identify the forced and natural components in the output. is(t) R w FIGURE P7-12 + vo(t)
The circuit in Figure P7–13 is in the zero state when the input vS(t) ¼ vAu(t) is applied. Find vO(t) for t 0. Identify the forced and natural components in the output. L 000 + + vs(t) R vo(t) FIGURE P7-13
The circuit in Figure P7–14 is in the zero state when the input vS(t)¼100 u(t) is applied. IfC¼0.01 mFandR¼100 kV, find vO(t) for t 0. Identify the forced and natural components in the output. C R ww + + vs(t) R vo(t) FIGURE P7-14
The circuit in Figure P7–15 is in the zero state when the input vS(t)¼20 u(t) is applied. IfL¼100mHandR¼1kV, findvO(t)for t 0. Identify the forced and natural components in the output. On a single set of axes, useMATLAB to plot the forced response, the natural response, and the complete
The switch in Figure P7–16 has been in position A for a long time and is moved to position B at t ¼ 0. Find vC(t) for t 0. Identify the forced and natural components in the response. t=0 A www 10 B + 24 V 10 ww + 10 ks 0.02 uF vc(t) FIGURE P7-16
Find the function that satisfies the following differential equation and the initial condition for an input vS(t) ¼ 50 cos(200t) V: dv(t) +50v(t) = vs(t), v(0) = 0V dt
The switch in Figure P7–20 has been open long enough for iLð0Þ to reach 0 A and is closed at t ¼ 0.(a) If vS(t) ¼ 10 u(t) V, find vL(t) for t 0.(b) If vS(t) ¼ 10 cos(100t) V, find vL(t) for t 0.(c) If vS(t) ¼ 10 e100t V, find vL(t) for t 0. vs (t) + 330 w t=0 + 4702VL (1) 1H FIGURE P7-20
The switch in Figure P7–23 has been in positionAfor a long time and is moved to position B at t ¼ 0. Find iL(t) for t 0. 100 B w t=0 iL(t) www A + 10 100 mH 15 V 000 FIGURE P7-23
The switch in Figure P7–25 has been in position A for a long time and is moved to position B at t ¼ 0. The switch suddenly returns to positionAafter 10 ms. Find vC(t) for t 0 and sketch its waveform. 100 V 1 + 20 w t=0 A? B + 1 F: vc(t) 80 - 20 FIGURE P7-25
Switches 1 and 2 in Figure P7–27 have both been in position A for a long time. Switch 1 is moved to position B at t ¼ 0 and Switch 2 is moved to position B at t ¼ 20 ms.Find the voltage across the 0.1-mF capacitor for t 0 and sketch its waveform. SW#1 SW#2 150 ww 50 ww B=0 B=0.02 + 0.1 F
The switch in Figure P7–28 has been open for a long time and is closed at t ¼ 0. The switch is reopened at t ¼ 3 ms. Find vC(t) for t 0. 1.5 www t=3 ms + t=0 + 24 V 15 1 F vc(t) FIGURE P7-28
Find the sinusoidal steady-state response of vC(t) in Figure P7–29 when R ¼ 100 kV, C ¼ 0.01 mF, and the input voltage is vS(t) ¼ 10 cos(100t) u(t) V. Repeat for an input voltage of vS(t) ¼ 10 cos(1000t) u(t) V, and one more time for an input voltage of vS(t) ¼ 10 cos(10kt) u(t) V. Describe
For t 0 the zero-input response of the circuit in Figure P7–31 is vC(t) ¼ 20e10kt V.(a) Find C and iC(t) when R ¼ 10 kV.(b) Find the energy stored in the capacitor at t ¼ 2 ms. + ic(t) R vc(t): C FIGURE P7-31
For t 0 the zero-input response of the circuit in Figure P7–32 is iL(t) ¼ 150e500t mA.(a) Find L and vL(t) when R ¼ 500 V.(b) Find the energy stored in the inductor at t ¼ 0.5 ms. + iL(t) R VL(t) L FIGURE P7-32
Design a series RC circuit using a dc voltage source that delivers a voltage across the capacitor for t >0 that fits entirely within the non-shaded region of Figure P7–35. vc(t) 10 9 6 2 -t (ms) 01 5 10 12 20 FIGURE P7-35
For t 0 the step response of the voltage across the capacitor in Figure P7–37 is vC(t) ¼ 5 10e-1000t V. Find the IV, FV, TC, R, and iC(t) when C ¼ 1.5 mF. vs(t) R ww ic(t) + C= vc(t) FIGURE P7-37
For t 0 the step responses of the current through and voltage across the inductor in Figure P7–39 are iL(t) ¼ 5 10e2000t mA and vL(t) ¼ e2000t V. Find IV, FV, TC, R, and L. vs(t) + I R iL(t) ww + L VL(t) FIGURE P7-39
The switch in Figure P7–41 has been in position B for a long time and is moved to position A at t ¼ 0. Design the firstorder RC interface circuit such that vO(t) ¼ 1515e5000t V. 20 V ( + 1 t=0 B + Interface circuit vo(t) 300 FIGURE P7-41
A timing circuit is required that feeds into an OP AMP’s non-inverting terminal (i.e. draws no current.) The circuit’s output response vO(t) must be vOðtÞ ¼ 5 1 e1000t uðtÞ V Figure P7–43 shows two commercial products and the vendors claim each will meet the requirement. Which will you
A product line needs an RC circuit that will meet the following response specifications 5%:Design a circuit to meet the specifications and validate your results using OrCAD. IV FV T R 10 V +5V 100 s
The switch in Figure P7–49 has been open for a long time and is closed at t ¼ 0. The circuit parameters are L ¼1H,C¼0.5 mF, R ¼ 1 kV, and vC(0) ¼ 10 V.(a) Find vC(t) and iL(t) for t 0.(b) Is the circuit overdamped, critically damped, or underdamped?(c) Use OrCAD to simulate your results. R
The switch in Figure P7–50 has been open for a long time and is closed at t ¼ 0. The circuit parameters are L ¼1H, C ¼1 mF, R ¼ 500 V, and vC(0) ¼ 60 V.(a) Find vC(t) and iL(t) for t 0.(b) Is the circuit overdamped, critically damped, or underdamped?(c) Use OrCAD to simulate your results. +
The switch in Figure P7–52 has been open for a long time and is closed at t ¼ 0. The circuit parameters are L ¼ 0.8 H, C ¼ 1.25 mF, R1 ¼ 2 kV, R2 ¼ 1 kV, and VA ¼ 12 V.(a) Find vC(t) and iL(t) for t 0.(b) Is the circuit overdamped, critically damped, or underdamped?(c) Use OrCAD to
The switch in Figure P7–53 has been open for a long time and is closed at t ¼ 0. The circuit parameters are L ¼ 1.25 H, C ¼ 0.05 mF, R1 ¼ 20 kV, R2 ¼ 20 kV, and VA ¼ 20 V.(a) Find vC(t) and iL(t) for t 0.(b) Is the circuit overdamped, critically damped, or underdamped?(c) Use OrCAD to
The switch in Figure P7–55 has been in position A for a long time. At t ¼ 0 it is moved to position B. The circuit parameters are R1 ¼ 20 kV, R2 ¼ 4 kV, L ¼ 1.6 H, C ¼ 1.25 mF, and VA ¼ 24 V.(a) Find vC(t) and iL(t) for t 0.(b) Is the circuit overdamped, critically damped, or
You have a need for an interface circuit that will connect your source to a load with a very high input as shown in Figure P7–56(a). Your interface must have a response that fits within the boundaries shown in Figure P7–56(b). A vendor offers a suitable circuit shown in Figure P7–56(a)and
The switch in Figure P7–57 has been in position A for a long timeandismovedtopositionBat t¼0.Thecircuitparametersare R1¼500V,R2¼220V,L¼250 mH,C¼3.3mF, andVA¼15V.(a) Find vC(t) and iL(t) for t 0.(b) Is the circuit overdamped, critically damped, or underdamped?(c) Use OrCAD to simulate your
The circuit in Figure P7–59 is in the zero state when the step function input is applied. The circuit parameters are L ¼250 mH, C = 1 mF, R ¼ 3.3 kV, and VA ¼ 10 V. Find vO(t) for t 0. (Hint. Find the capacitor voltage first.) + R C WH w VAu(t) L2 vo(t) FIGURE P7-59
The circuit in Figure P7–60 is in the zero state when the step function input is applied. If the input source is VA ¼70 V and L ¼ 0.5 H, select values of R and C so that the circuit’s output vO(t) for t 0 is critically damped. Use MATLAB or OrCAD to show your result for vO(t) (Hint:Find the
The circuit in Figure P7–61 is in the zero state when the step function input is applied.(a) If VA ¼ 24 V, R ¼ 1.5 kV, L ¼ 250 mH, and C ¼ 0.25 mF, derive an expression for the voltage vQ(t) for t 0.(b) Validate your solution by plotting it usingMATLAB and comparing it to an OrCAD simulation
Design a series RLC circuit whose output voltage resides entirely within the non-shaded region of Figure P7–72. Validate your design using MATLAB or OrCAD. 2 1 3 vo(t)(V) 7 6 5 5.25 4.5 14.75 4 t (ms) 0 1 2 3 FIGURE P7-72
A circuit is needed to produce the following step response vCðtÞ ¼ 10 13:3e200t þ 3:3e800t V t > 0 Avendor has proposed using the circuit shown in Figure P7–73 to produce the desired response. The vendor realizes that the proposed circuit does not exactly meet the desired response and is
What range of damping ratios is available in the circuit in Figure P7–74? 200 w 22 ww 0.01 F: 2.5 mH -000 FIGURE P7-74
Avariable capacitor is used in the circuit of P7–75 to vary the damping ratio.What range of damping ratios is available in the circuit? 50 www 1-1000 pF 1 mH FIGURE P7-75
A particular parallel RLC circuit has the step response observed on an oscilloscope and shown in Figure P7–76. Four points on the waveform were measured and are shown.Determine the circuit’s initial value, final value, the dominant exponential’s time constant, and the likely case (A, B, or C)
First-order OP AMP Circuit Step Response Find the zero-state response of the OPAMP output voltage in Figure P7–77 when the input is vS(t) ¼ VAu(t) V. R C R2 ww w + vs(t) vo(t) FIGURE P7-77
RC Circuit Design Design the first-order RC circuit in Figure P7–79 so an input vS(t) ¼ 15 u(t) V produces a zero-state response vO(t) ¼ 15 5e1000t V. Validate your design using MATLAB or OrCAD. vs(t) +1 First-order RC circuit vo(t) FIGURE P7-79
Sample Hold Circuit Figure P7–80 is a simplified diagram of a sample/hold circuit.When the switch is in position A, the circuit is in the sample mode and the capacitor voltage must charge to at least 99% of the source voltage VA in less than 1 ms. When the switch is moved to position B, the
Super Capacitor Super capacitors have very large capacitance (typically from 0.1 to 50 F), small sizes, and very long charge holding times, making them useful in non-battery backup power applications.The charge holding quality of a super capacitor is measured using the circuit in Figure P7–81.
Combined First- and Second-Order Response The switch in Figure P7–83 has been in positionAfor a long time and is moved to position B at t ¼ 0 and then to position C when t ¼ 10 ms. For 0 e100t) V. For t > 10 ms the capacitor voltage is a sinusoid vC(t) ¼ 6.321 cos [1000(t 0.01)] V.(a)
Undesired Ringing , A digital clock has become corrupted by a ringing (undesired oscillations) as shown in Figure P7–84(a). The unwanted oscillations can cause false triggers and must be reduced. The clock can be modeled as an RLC series circuit as shown in Figure P7–84(b) with the voltage
Optimum Fusing A sensitive instrument that can be modeled by the series RLC circuit shown in Figure P7–85 is to be protected by a fuse. The voltage across the capacitor is vCðtÞ ¼ e10tðcos 103t þ 0:0971sin 103tÞ uðtÞ V The peak current was found to occur at about 13 ms after t ¼
Lightning Pulser Design The circuit in Figure P7–86 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 short-circuit current of the formiSC(t) =IAeat cos(bt), with a ¼ 100 krad/s, b ¼200
RLCCircuit Design Losses in real inductors can be modeled by a series resistor as shown in Figure P7–87. In this problem, we include the effect of this resistor on the design of the series RLC circuit shown in the figure. The design requirements include a source resistance of 50V, an undamped
Competing Circuit Designs Figure P7–88 shows the step responses vC(t) of two competing series RLC circuits from two different vendors. The circuits are designed to switch from 0 to 10Vand to meet a specification for a desired circuit with the following characteristic equation:s2 þ 10s þ 100 ¼
Transform the following sinusoids into phasor form and draw a phasor diagram. Use the additive property of phasors to find v1(t)þv2(t).(a) v1(t)¼50 cos(vt 30)V(b) v2(t)¼200 cos(vtþ150)V
Transform the following sinusoids into phasor form and draw a phasor diagram. Use the additive property of phasors to find i1(t)þi2(t).(a) i1(t)¼4 sin(vt) A(b) i2(t)¼3 cos(vt26.6) A
The sum of the two voltage phasors shown in Figure P8–3 is V3. If the frequency is 100 Hz, write the sum in the time domain, v3(t). j Im 20 102 -10 10 135 V Re 10 20 FIGURE P8-3
Convert the following phasors into sinusoidal waveforms.(a) V1¼100ej60V, v¼103 rad/s(b) V2¼120e j45V, v¼103 rad/s(c) I1¼240e j26.6mA, v¼2p104 rad/s(d) I2 150ej45mA, v¼2p104 rad/s
Use the phasors in Problem 8–4 and the additive property to find the sinusoidal waveforms v3(t)¼v1(t)v2(t) and i3(t)¼2i1(t)þ3i2(t).
The phasor representation of a sinusoid with v¼500 rad/s is V¼15j10 V. Use the phasor derivative property to find the time derivative of the sinusoid.
Convert the following phasors into sinusoids:(a) V1 ¼ 4 þ j5V;v ¼ 10 Mrad/s(b) V2 ¼ 6ð8 j8Þ V;v ¼ 200 krad/s(c) I1 ¼ 12 þ j5 þ 5 j A;v ¼ 30 rad/s(d) I2 ¼ 330þj810 2200j560A;v ¼ 60 rad/s
Use phasors to find the sinusoid v2(t), where v2ðtÞ ¼ 1 100 dv1ðtÞdtþ 20 v1ðtÞ and v1ðtÞ ¼ 10 cosð100t þ 90Þ:
Given the sinusoids v1(t)¼500 cos(vt45)Vand v2 (t)¼750 sin (vt) V use the additive property of phasors to find v3(t) such that v1þv2þv3¼0.
Graphically add the following three phasors and determine their sum:V1 ¼ 9:85 þ j1:74V;V2 ¼ 10ff130V;V3 ¼ 3:42 j9:40 V:
Given a sinusoid v1(t) whose phasor is V1¼3j4 V, use phasor methods to find a voltage v2(t) that leads v1(t) by 90and has an amplitude of 10 V.
Anew parameter Z is defined as V/I. IfV¼9.85þj 1.74V and i1(t)¼4 sin(vt) A, find Z.
Complex power S is defined as VI, where I is the complex conjugate of the current phasor. If V¼1200þ j 1500V and I¼500j 250 mA, find S.
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 0.033 mF capacitor’s impedance equal j100V?(b) At what radian frequency will a 47 mH inductor’s impedance equal j100V?(c) At what radian frequency will
Find the equivalent impedance Z in Figure P8–15 when v¼2000 rad/s. Express the result in both polar and rectangular forms. 10 220 mH 20 100 F FIGURE P8-15
Find the equivalent impedance Z in Figure P8–16. If v¼10 krad/s what two elements (R, L, and/or C) could be used to replace the phasor circuit? Z www 25 -j250 150 20 FIGURE P8-16 -j100 =
Find the equivalent impedance Z in Figure P8–17 when v¼50 krad/s. What two elements (R, L, and/or C) could be used to replace the phasor circuit? Z 33 w 2 mH m 0.47 F= 100 FIGURE P8-17
Find the equivalent impedance Z in Figure P8–18. If v¼100 krad/s what two elements (R, L, and/or C) could be used to replace the phasor circuit? Z j600 2 1900 600 -j300 FIGURE P8-18
The circuit in Figure P8–18 is operating in the sinusoidal steady-state with v¼5 krad/s.(a) How would the element impedances change if the steady-state frequency were reduced to 500 rad/s?(b) What is theequivalentimpedanceZat thisnewfrequency?(c) What two elements (R, L, and/or C) could be used
The circuit in Figure P8–20 is operating in the sinusoidal steady state with v¼100 krad/s.(a) Find the equivalent impedance Z.(b) What circuit element can be added in series with the equivalent impedance to place the circuit in resonance? Z 5 F 5 F 2.5 mH 20 FIGURE P8-20
The circuit of Figure P8–21 is operating at 60 Hz. Find the equivalent impedance Z. Z 15 W 8.2 mH -m vix(t) 220 F 3ix(t) FIGURE P8-21
The equivalent impedance in Figure P8–22 is known to be Z¼60þj180V. Find the impedance of the inductor. Z -j200 2 600 FIGURE P8-22 ZL
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 300j400V at v¼2 Mrad/s.
The circuit in Figure P8–24 is excited by a 1 krad/s sinusoidal source. As the circuit’s designer, select a capacitor C such that the impedance Z looking into the circuit is all real. 50 10 mH Z FIGURE P8-24 C
An 800-V resistor is connected in parallel with a 1000-pF capacitor. The impedance of the parallel combination is 400j400V. Find the frequency.
Avoltage vS(t)¼30 cos (2000t) V is applied to the circuit in Figure P8–26.(a) Convert the circuit into the phasor domain.(b) Find the phasor current flowing through the circuit and the phasor voltages across the inductor and the resistor.(c) Plot all three phasors from (b) on a phasor
Avoltage v(t)¼100 cos (3000t) Vis applied across a series connection of a 330-V resistor and 110-mH inductor. Find the steady-state current i(t) through the series connection.
The circuit in Figure P8–29 is operating in the sinusoidal steady state with vS(t)¼VA cos (vt). Derive a general expression for the phasor response IL and the voltage VO. + R ww + iL(t) L vs(t) Rvo(t) FIGURE P8-29
A current source delivering i(t)¼120 cos (500t) mA is connected across a parallel combination of a 10-kV resistor and a 0.2-mF capacitor. Find the steady-state current iR(t) through the resistor and the steady-state current iC(t)through the capacitor. Draw a phasor diagram showing I, IC, and IR.
The circuit in Figure P8–31 is operating in the sinusoidal steady state with iS(t)¼IA cos(vt). Derive general expressions for the steady-state responses VR and IC. Fic(t) R ww + RVR(t) is(t) C FIGURE P8-31
A practical voltage source of vS(t)¼120 cos 2p60t V is in series with a 50-Vresistor. Convert the source into the phasor domain and then do a source transformation into a current source in parallel with an impedance. Finally, convert the source back into the time domain.
A current source of IN¼20 ff33.8 mA is in parallel with an impedance of Z¼100j50V. Convert the practical current source into a practical voltage source in series with an impedance.
Avoltage v(t)¼12 cos (3030t45) V is applied across a parallel connection of a 1.5-kV resistor and a 0.22mF capacitor.Find the steady-state current iC(t) through the capacitor and the steady-state current iR(t) through the resistor. Draw a phasor diagram showing V, IC, and IR.
The circuit in Figure P8–35 is operating in the sinusoidal steady state. Find the steady-state response vX(t). 500 ww 0.25 H m + + 1 F 500 2vx(t) 20 cos 2000t V
The circuit in Figure P8–36 is operating in the sinusoidal steady state. Find the steady-state response vX(t). 0.2 + 1 2 ks vx(t) 2 cos 2500t A
Use the unit-output method to find VX and IX in the circuit of Figure P8–37. -j200 2 + 200 Vx 200-45 mA Ix FIGURE P8-37 400
The circuit in Figure P8–38 is driven by a 10-krad/s source and is operating in the sinusoidal steady state. Use OrCAD to find the steady-state phasor response Vx. 100/0 V +1 -j20 100 50 w FIGURE P8-38 +o Vx -j50 0

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