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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

3–21 The circuit in Figure P3−21 seems to require two supermeshes since both current sources appear in two meshes. However, sometimes rearranging the circuit diagram will eliminate the need for a supermesh.(a) Show that supermeshes can be avoided in Figure P3−21 by rearranging the connection
3–22 (a) Formulate mesh-current equations for the circuit in Figure P3−22.(b) Formulate node-voltage equations for the circuit in Figure P3−22.(c) Which set of equations would be easier to solve? Why?(d) Find vx and ix using whichever method you prefer 2.5 mA ic VB ww 18 Vx iB VA 10V(+ 1 w 2
3–23 Use simple engineering intuition to find the input resistance of the circuit in Figure P3−23. Use either node-voltage or mesh-current analysis to prove your intuition. (Hint: It is a balanced bridge.) VS 1+ RIN R ww www www FIGURE P3-23 R w R R
3–24 In Figure P3−24 all of the resistors are 1 kΩ and vS =12V.The voltage at node C is found to be vC = −2:4 V when node B is connected to ground.(a) Find the node voltages vA and vD, and the mesh currents iA and iB.(b) Use Multisim to validate your answers VS A R B R3 ww +1 iA R R iB R D
3–25 Use Figure P3−24 and MATLAB to solve the following problems:(a) Using mesh-current analysis, find a symbolic expression for iA in terms of the circuit parameters.(b) Compute the ratio vS=iA.(c) Find a symbolic expression for the equivalent resistance of the circuit by combining resistors
3–26 (a) Formulate mesh-current equations for the circuit in Figure P3−26.(b) Formulate node-voltage equations for the circuit in Figure P3−26.(c) Which set of equations would be easier to solve?Why?(d) Use Multisim to find the node voltages vA and vB and the mesh currents iA, iB, and iC in
3–27 (a) Formulate mesh-current equations for the circuit in Figure P3−27. Arrange the results in matrix form Ax= b.(b) Use MATLAB and mesh-current analysis to solve for the mesh currents iA, iB, iC, and iD.(c) Formulate node-voltage equations for the circuit in Figure P3−27. Arrange the
3–28 (a) Find vO for the block diagram shown in Figure P3−28(a).(b) Find the proportionality constant K for the circuit in Figure P3−28(b).(c) Find the proportionality constant K for the circuit in Figure P3−28(c). 5.6 mV 40 0.2 Vo (a) 6.0 mA 150 K (b) 12 V 150 K (c) FIGURE P3-28
3–29 Design a voltage-divider circuit that will realize the block diagram in Figure P3−28(a).
3–30 Design a current-divider circuit that will realize the block diagram in Figure P3−28(b).
3–31 Using a single resistor, design a circuit that will realize the block diagram in Figure P3−28(c).
3–32 Find the proportionality constant K = vO=vS for the circuit in Figure P3−32. +1 2 ww 1 www 2 FIGURE P3-32 vo
3–33 Find the proportionality constant K = iO=vS for the circuit in Figure P3−33 500 ww www 1 kQ www 1 FIGURE P3-33
3–34 Find the proportionality constant K = vO=iS for the circuit in Figure P3−34. is 33 www 56 22 Vo FIGURE P3-34
3–35 Find the proportionality constant K = iO=iS for the circuit in Figure P3−35. is R3 www RR R4 www FIGURE P3-35 io
3–36 Find the proportionality constant K = vO=vS for the circuit in Figure P3−36. Then select values for the resistors so that vO is −0:1 vS. +1 www R R K vs R3 R4 www FIGURE P3-36 www Vo
3–37 Use the unit output method to find K and vO in Figure P3−37 20 mA 22 K www 47 22 ks21 Vo FIGURE P3-37
3–38 Use the unit output method to find K and vO in Figure P3−38. 24 V ( 1 + 1.25 w 1 - 1 K w 32.5 3 2 FIGURE P3-38
3–39 Use the unit output method to find K in Figure P3−39. Then select a value for vS that will produce an output current of iO = 250 mA VS + 30 ww 47 K w 60 40 220 2 FIGURE P3-39
3–40 Use the superposition principle to find vO in Figure P3−40. 15 V 1 + 200 + Vo w 200 w 200 FIGURE P3-40 + 1 5V
3–41 Use the superposition principle to find iO and vO in Figure P3−41. Verify your answer using Multisim + io vo 6 mA( 2 ks 12 V w 2
3–42 Use the superposition principle to find vO in Figure P3−42. 5.6 ww 3.3 w +10- +24 V 6.8 5 mA 5 mA 10 k
3–43 Use the superposition principle to find vO in Figure P3−43. ww 2 ww 5 + 10 mA 2.5 vo 20 mA - 3 ww FIGURE P3-43
3–44 Use the superposition principle to find iO in Figure P3−44.Verify your answer using Multisim. 1 mA 5 k 10 www 5kQ 15 10 V 20 V +1 FIGURE P3-44 www 10
3–45 (a) Use the superposition principle to find vO in terms of v1, v2, and R in Figure P3−45. (This circuit is a 3-bit R– 2R network.)(b) Use MATLAB and node-voltage analysis to verify your answer symbolically. R ( 2R V2 +1 R 2R R V3 + R vo B.
3–46 (a) Use the superposition principle to find vO in terms of vS, iS, and R in Figure P3−46.(b) Use MATLAB and node-voltage analysis to verify your answer symbolically. VS 1 + 2R R A ww is RVO FIGURE P3-46 B
3–47 Alinear circuit containing two sources drives a 100-Ω load resistor. Source number 1 delivers 1W to the load when source number 2 is off. Source number 2 delivers 9W to the load when source number 1 is off. Find the power delivered to the load when both sources are on. (Hint: The answer is
3–48 Ablock diagram of a linear circuit is shown in Figure P3–48.When vS = 10 V and iS = 10mA the output voltage vO =1V.The output voltage is 2 V when the voltage source is vS = 10 V and the current source is off or iS = 0 mA. Find the output voltage when vS = 20 V and iS = −20 mA. VS K + is
3–49 A certain linear circuit has four input voltages and one output voltage vO. The following table lists the output for different values of the four inputs. Find the input-output relationship for the circuit. Specifically, find an expression for vO in terms of the four input voltages DSI (V) 2
3–50 When the current source is turned off in the circuit of Figure P3−50 the voltage source delivers 25W to the load.How much power does it deliver to the load when both sources are on? Explain your answer PSI 100 www 100 V PL 1A 100 FIGURE P3-50
3–51 For the circuit in Figure P3−51, find the Thévenin and Norton equivalent circuits 10 www 10 www + 25 V 15 FIGURE P3-51 VT. RT. IN
3–52 For the circuit in Figure P3−52, find the Thévenin and Norton equivalent circuits 1 www 1 mA 1 FIGURE P3-52 VT. RT. IN
3–53 For the circuit of Figure P3−53, find the Thévenin equivalent circuit. 25 www 20 ww 150 50 30 - 1.5 mA VT. RT FIGURE P3-53
3–54 (a) Find the Thévenin or Norton equivalent circuit seen by RL in Figure P3−54.(b) Use the equivalent circuit found in part (a) to find iL if RL =15 kΩ. 5 www 5 www 15 15 V 10 RL FIGURE P3-54
3–55 (a) Find the Thévenin or Norton equivalent circuit seen by RL in Figure P3−55.(b) Use the equivalent circuit found in part (a) to find iL in terms of iS, R1, R2, and RL.(c) Check your answer to part (b) using current division. is R ww R (A) www B iL RL
3–56 Find the Thévenin equivalent circuit seen by RL in Figure P3−56. Find the voltage across the load when RL =5 Ω, 10 Ω, and 20 Ω. 10 www 10 www 10 www 10 V www 10.02 FIGURE P3-56 1002 RL
3–57 Find the Norton equivalent seen by RL in Figure P3−57.Find the current through the load when RL =4:7 kΩ, 15kΩ, and 68 kΩ. 15 20 FIGURE P3-57 www 1.5 www 15 RL
3–58 You need to determine the Thévenin equivalent circuit of a more complex linear circuit. A technician tells you she made two measurements using her DMM. The first was with a 10-kΩ load and the load current was 91 μA. The second was with a 1-kΩ load and the load voltage was 124 mV.
3–59 Find the Thévenin equivalent seen by RL in Figure P3−59.Find the power delivered to the load when RL =50 kΩ.Repeat for RL = 100 kΩ 68 ww 91 ww PL 12 V + 22 RL FIGURE P3-59
3–60 (a) Use Multisim to find the Norton equivalent at terminals A and B in Figure P3−60. (Hint: Use the multimeter to find the open-circuit voltage and short-circuit current at the requisite terminals.)(b) Use the Norton equivalent circuit found in part (a) to determine the power dissipated in
3–61 The purpose of this problem is to use Thévenin equivalent circuits to find the current iL in Figure P3−61. Find the Thévenin equivalent circuit seen looking to the left of terminalsAand B. Find the Thévenin equivalent circuit seen looking to the right of terminals C and D. Connect these
3–62 The circuit in Figure P3−62 was solved earlier using supermeshes (Problem 3–43). In this problem solve for the voltage across the load resistor vL by first finding the Thévenin equivalent circuit seen by the load resistor. Find vL when RL =2:5 kΩ. w 2 ww 5 10 mA 3 - 3 RL 20 mA
3–63 Assume that Figure P3−63 represents a model of the auxiliary output port of a car. The output current is i = 1 A when measured by a very low-resistance ammeter. The voltage is v = 12 V when measured by a very high-input resistance voltmeter.Suppose you wanted to charge a 9-V battery by
3–64 The i – v characteristic of the active circuit represented by Figure P3−63 is 5v + 500i = 100. Find the output voltage when a 100-Ω resistive load is connected.
3–65 You have successfully completed the first course in Circuits I, and as part of an undergraduate work–study program your former professor has asked you to help her grade a Circuits I quiz. On the quiz, students were asked to find the power supplied by the source both to the 10-kΩ load
3–66 The Thévenin equivalent parameters of a practical voltage source are vT = 30 V and RT = 300 Ω. You want the maximum current to the load without exceeding 10 mA.Find the smallest 5% load resistance (see inside back cover)for which the load current does not exceed 10:0 mA.
3–67 Use a sequence of source transformations to find the Thévenin equivalent at terminals A and B in Figure P3−67.Then select a resistor to connect across A and B so that 2 V appears across it. +1 50 w A 15 ww 20 V 1A 50 3 A ww 15 B 5 V FIGURE P3-67
3–68 The circuit in Figure P3−68 provides power to a number of loads connected in parallel. The circuit is protected by a 1-mA fuse with a nominal 100-Ω resistance. Each load is 10 kΩ. What is the maximum number of loads the circuit can drive without blowing the fuse? 20 V+ 10 ww 2.5 k 1 mA
3–69 Find the Thévenin equivalent at terminals A and B in Figure P3−69. Use Multisim to verify your result 15 V A 1+ 10 mA 500 1 www 2 ww B
3–70 A nonlinear resistor is connected across a two-terminal source whose Thévenin equivalent is vT = 5 V and RT = 500 Ω. The i – v characteristic of the resistor is i=10‒ 4 v + 2v3:3 . Use the MATLAB function solve to find the operating point for this circuit and determine the voltage
3–71 A blue LED is connected across a two-terminal source whose Thévenin equivalent is vT = 3 V and RT =10 Ω. The i – v characteristic of the LED is i=10‒12 (e10v ‒ 1).Figure P3−71 shows the LED’s i – v characteristic. Using either MATLAB or a graphical approach, determine the
3–72 Find the Norton equivalent seen by RL in Figure P3−72.Select the value of RL so that(a) 3 V is delivered to the load.(b) 300mA is delivered to the load.(c) 100mW is delivered to the load. A 20 ww 500 mA 2012 402 RL FIGURE P3-72 B
3–73 Find the Thévenin equivalent seen by RL in Figure P3−73 15 V 1+ 10 ww w 10 50 mA www FIGURE P3-73 A 10 RL B
3–74 Find the Thévenin equivalent seen by RL in Figure P3−74.Select a value of RL so that 5 V appears across it. 30 RL 20 60 V 60 A B FIGURE P3-74 www 20
3–75 For the circuit of Figure P3−75, find the value of RL that will result in(a) Maximum voltage. What is that voltage?(b) Maximum current. What is that current?(c) Maximum power. What is that power 10 mA 7 ww 3 FIGURE P3-75 RL
3–76 For the circuit of Figure P3−76, find the value of RL that will result in:(a) Maximum voltage. What is that voltage?(b) Maximum current. What is that current?(c) Maximum power. What is that power? 4.7 www 1 www 100 V 3.3 RL FIGURE P3-76
3–77 The resistance R in Figure P3−77 is adjusted until maximum power is delivered to the load consisting of R and the 12-kΩ resistor in parallel.(a) Find the required value of R.(b) How much power is delivered to the load? 50 2 www - 3 R 12 1 ww Load FIGURE P3-77
3–78 When a 5-kΩ resistor is connected across a two-terminal source, a current of 15mA is delivered to the load. When a second 5-kΩ resistor is connected in parallel with the first, a total current of 20mA is delivered. Find the maximum power available from the source.
3–79 Find the value of R in the circuit of Figure P3−79 so that maximum power is delivered to the load. What is the value of the maximum power? 10 V 50 R www-ww FIGURE P3-79 5 - 2 Load
3–80 For the circuit of Figure P3−80, find the value of RL that will result in:(a) Maximum voltage. What is that voltage?(b) Maximum current. What is that current?(c) Maximum power. What is that power? 1.25 24 3 + FIGURE P3-80 VL RL
3–81 A 1-kΩ load needs 10mA to operate correctly.Design a practical power source to provide the needed current.The smallest source resistance you can practically design for is 50 Ω, but you can add any other series resistance if you need to.
3–82 A practical source delivers 25mA to a 300-Ω load. The source delivers 5 V to a 100-Ω load. Find the maximum power available from the source.
3–84 (a) Select RL and design an interface circuit for the circuit shown in Figure P3−84 so that the load voltage is 2 V.(b) Suppose that the load was set at 15 kΩ. Now design an appropriate interface so that the load voltage is 2 V. 10 ww 10 V (+10 k www 5 Interface circuit RL FIGURE P3-84
3–85 The source in Figure P3−85 has a 100-mA output current limit. Design an interface circuit so that the load voltage is v2 = 20 V and the source current is i1 100 VI +1 50 w i2 Interface VI V2 circuit FIGURE P3-85 www 500
3–86 Figure P3−86 shows an interface circuit connecting a 15-V source to a diode load. The i – v characteristic of the diode is i=10−14 (e40 v − 1)(a) Design an interface circuit so that v=0:7V.(b) Validate your answer using MATLAB. 15 V+ +1 Interface circuit FIGURE P3-86 V
3–87 Designthe interface circuit inFigureP3−87so that the voltage delivered to the load is v = 10V ± 10%. Use one or more of only the following standard resistors: 1:3 kΩ, 2kΩ, 3 kΩ, 4:3 kΩ, 6:2 kΩ, and 9:1 kΩ. These resistors all have a tolerance of ± 5%, which you must account for in
3–88 In this problem, you will design two interface circuits that deliver 150 V to the 5-kΩ load shown in Figure P3−88.(a) Design a parallel resistor interface to meet the requirements.(b) Convert the source circuit to its Thévenin equivalent and then design a series interface to meet the
3–89 Two teams are competing to design the interface circuit in Figure P3−89 so that the 25mW± 10% is delivered to the 1-kΩ load resistor. Their designs are shown in Figure P3−89. Which solution is better considering the use of standard values, number of parts, and power required by the
3–90 The bridge-T attenuation pad shown in Figure P3−90 was found in a drawer. You need an attenuation pad that would match to a 75-Ω source and a 75-Ω load and provide for a– 12-dB drop of signal (reduction of four times). Use Multisim to determine if the device will work. VIN=VS RIN = 75
3–91 Design two interface circuits in Figure P3−91 so that the power delivered to the load is 100 mW. In one case use a series interface resistor, and in the second case use a parallel resistor to attain the same result. Evaluate your interface circuits and determine which one results in the
3–92 Design the interface circuit in Figure P3−91 so that the voltage delivered to the load is 1:0 V. Repeat for a voltage of 3:0V.
3–93 Design the interface circuit in Figure P3−93 so that RIN = 100 Ω and the current delivered to the 50-Ω load is i = 50 mA. (Hint: Use an L-pad.) 15 V +1 100 w RIN Interface circuit 50 ROUT
3–94 Design the interface circuit in Figure P3−93 so that ROUT =50 Ω and the voltage delivered to the 50-Ω load is v=2:5V. (Hint: Use an L-pad.)
3–95 The circuit in Figure P3−95 has a source resistance of 50 Ω and a load resistance of 300 Ω. Design the interface circuit so that the input resistance is RIN =50 Ω ±10% and the output resistance is ROUT = 300 Ω ±10%. Validate your design using Multisim. +1 50 ww RIN Interface 300
3–96 It is claimed that both interface circuits in Figure P3−96 will deliver v = 4 V to the 75-Ω load. Verify this claim. Which interface circuit consumes the least power? Which has an output resistance that best matches the 75-Ω load? 20 V 1+ 150 ww w 150 Circuit 1 FIGURE P3-96 Interface
3–97 Audio Speaker Resistance-Matching Network A company is producing an interface network that they claim would result in an RIN of 600 Ω ± 2% and ROUT of 16, 8, or 4 Ω ±2%—depending on whether the connected speakers are 16, 8, or 4 Ω—selectable via a built-in switch. The design is
3–98 Attenuator Analysis In Figure P3−98, a two-port attenuator connects a 600-Ω source to a 600-Ω load. Find the power delivered to the load in terms of vS. Remove the attenuator and find the power delivered to the load when the source is directly connected to the load. By what fraction does
3–99 Attenuator Design Use the general procedure shown in Application Example 3–31 to design a 75 Ωto 75 Ω, Use Multisim to verify that your design meets these characteristics. PORT CHARACTERISTICS CONDITION VALUE UNITS Output Thvenin 75-02 source VT < Vs/10 V voltage connected at the input
3–100 Interface Circuit Design Using no more than three 50-Ω resistors, design the interface circuit in Figure P3−100 so that v = 4 V and i = 50mA regardless of the value of RL. 12 V(+ 50 Interface circuit FIGURE P3-100 + RL
3–101 Battery Design A satellite requires a battery with an open-circuit voltage vOC = 36 V and a Thévenin resistance RT =10 Ω. The battery is to be constructed using series and parallel combinations of one of two types of cells. The first type has vOC =9V, RT =4 Ω, and a weight of 30 g. The
3–102 Design Evaluation Arequirement exists for acircuit todeliver 0to6 Vto a 100-Ω load from a 24-V source rated at 3:0W. Two proposed circuits are shown in Figure P3−102. Which one would you choose and why? 24 V 24 V 1+ 1+ 150 W 100 150 w Circuit 1 100 23 Vo Circuit 2 ww + vo ww 100 100
3–103 Design Interface Competition The output of a transistorized power supply is modeled by the Norton equivalent circuit shown in Figure P3−103. Two teams are competing to design the interface circuit so that 25mW± 10% is delivered to the 1-kΩ load resistor. Their designs are shown in
3–104 Analysis of Competing Interface Circuits Using MATLAB Figure P3−104 displays two generalized interface circuit designs.In both circuits, resistors R1 and R2 connect a Thévenin equivalent circuit to a load resistor. Using MATLAB, develop symbolic expressions for the load current, iL, and
3–105 Maximum Power Transfer Using Multisim Figure P3−105 shows a circuit with two sources, a fixed load and a resistor R. Select R for maximum power transfer to the load.The result is not an obvious one. (Hint: Simulate in Multisim using the “Parameter sweep” under “Analyses” and do a
3–106 Noninverting Summer Anoninvertingsummerinterface device is shown in Figure P3−106.Of importance is that the input to the device has infinite resistance—that is, no current flows into the device. The output voltage for this configuration is two times the input voltage.Develop a
A 2:2-kΩ resistor has 12 V impressed across its terminals. Find the current through the resistor and the power it dissipates.
A resistor operates as a linear element as long as the voltage and current are within the limits defined by its power rating. Suppose we have a 47-kΩ resistor with a power rating of 0.25 W. Determine the maximum current and voltage that can be applied to the resistor and have it remain within its
What is the maximum current that can flow through a 18-W, 6:8-kΩ resistor? What is the maximum voltage that can be across it?
The analog switch is an important device found in analog-to-digital interfaces.Figure 2–5(a) and (b) shows the two basic versions of the device. In either type, the switch is actuated by applying a voltage to the terminal labeled gate. The switch in Figure 2–5(a) is said to be normally open
Given an ideal voltage source with the time-varying voltage shown in Figure 2–8(a), sketch its i−υ characteristic at the times t = 0, 1, and 2 ms. Vs(f) (V) @t=0ms, v=5V @t = 1 ms, v=0V 5 5. e 1 (ms) @t 2 ms, v=-5 V (b) -5 0 +5 V
Adigital clock is a voltage that switches between two values at a constant rate that is used to time digital circuits.Aparticular clock switches between 0 V and 5 V every 10 μs. Sketch the clock’s i – v characteristics for the times when the clock is at 0 V and at 5 V.
Given i1 = +4A, i3 = +1A, i4 = +2Ain the circuit shown in Figure 2–11, find i2 and i5.
Refer to Figure 2–12.(a) Write KCL equations at nodes A, B, C, and D.(b) Given i1 = −1 mA, i3 =0:5 mA, i6 =0:2 mA, find i2, i4, and i5. A B C D
Given υ1 =5V, υ2 = −3 V, and υ4 = 10 V in the circuit shown in Figure 2–13, find υ3 and υ5.
Find the voltages υx and υy in Figure 2–14. + +2V + FIGURE 2-14 + 6 V + IV
Find the voltages υx, υy, and υz in Figure 2–15. +5V +20 V + + 40 V Vx 10 V + FIGURE 2-15 5V + + Vz
Identify the elements connected in parallel and in series in each of the circuits in Figure 2–18. B 3 (a) B 3 5 (b) 6 B + D
Identify the elements connected in series or parallel when a short circuit is connected between nodes A and B in each of the circuits of Figure 2–18. B 3 (a) B D 3 5 (b) 6 B + D
Identify the elements in Figure 2–19 that are connected in (a) parallel, (b) series, or (c)neither. 2 11 8 m 10. 5 6 Multiple grounds form a single node
(a) Find the responses ix, υx, iO, and υO in the circuit in Figure 2–20(a) when iS = +2mA and R=2 kΩ.(b) Repeat for iS = −2 mA.

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