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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

A 1-kΩ resistor RR is inserted between nodes A and B in Figure 2–20(a) as shown in Figure 2–20(b).The voltage across it is labeled vR and the current through it is labeled iR. Write a set of element and connection constraints defining the circuit. Then find ix, vx, iO, iR, vR, and vO if iS =
Find all of the element currents and voltages in Figure 2–21 for VO =10V, R1 =2000 Ω, and R2 = 3000 Ω.
Use element and connection equations to find the voltages across the resistors in Figure 2–22. 30 V A 100 w B 1 + + 300 w Loop 1 FIGURE 2-22 Loop 2 + 2 200
Repeat the problem of Example 2–10 if the 30-V voltage source is replaced with a 2-mA current source with the arrow pointing up toward node A.
Use element and connection equations to find the voltages across and the currents through each of the elements in Figure 2–23. 100 V + A + = 22 B + V2 VA Loop 1 33 FIGURE 2-23 Loop 2 iB VB 1 mA
In Figure 2–24, write a loop equation around Loop 1 and a node equation at Node A. Then if i1 = 200mA and i3 = −100 mA, use the appropriate element equations to find the voltage υx.
Find the voltages across the resistors and current sources in Figure 2–25(a). 2 A 3 A 100 ww 1002 www w 50 5 A 2 A (a) 3 A 100 w +4- +VB- 100 w +13- V250 (b) +01 5 A
In Figure 2–25(a), the 2-A source is replaced by a 100-V source with the + terminal at the top, and the 3-A source is removed. Find the current and its direction through the voltage source 2 A 3 A 3 A +VB- -1 A 100 +100 V- 2 A 100 100 Bi3 100 2 w ww ww +-100 V- ww +200 V- -3 A +1- +13- + 2 A +
Find the equivalent resistance for the circuits in Figure 2–28 (a) and (b). REQ w 100 100 100 w REQ 2.2 3.3 5.6 w 10 (b) (a) REQ W 100 502: REQ ww 1.32 10 ko 15.6/kQ REQ 150 (e) (d) REQ REQ 1.32 w 7.41 16.09 (f) (8)
Find the equivalent resistance for the circuit in Figure 2–29. REQ 500 2 ww 500 2 11.5 1.5 FIGURE 2-29
Given the circuit in Figure 2–30(a),(a) Find the equivalent resistance REQ1 connected between terminals A and B.(b) Find the equivalent resistance REQ2 connected between terminals C and D. (A) REQ1 B R R ww (a) A R REQ1 B ww RR3 R+ R3 FIGURE 2-30 (b) www R3 D REQ2 D REQ2
Find the equivalent resistance between terminalsA–C, B–D,A–D, and B–C in the circuit in Figure 2–30. (A) R ww R REQ1 B A REQ1 B) ww (a) R www RR3 R+ R3 FIGURE 2-30 (b) www R3 D REQ2 D REQ2
Find the equivalent resistance between terminals A–B, A–C, A–D, B–C, B–D, and C–D in the circuit of Figure 2–31. For example: RA−B = ð80k80Þ + 60 = 100 Ω. A 80 BW 602 80 30 wwC w 25 FIGURE 2-31 D
(a) Convert the practical voltage source into the left of nodes A and B in Figure 2–34(a) to an equivalent current source.(b) Suppose the practical voltage source is connected to a 5-Ω load across nodes A and B. How much power is provided by the voltage source? +- is 10 w A) 50 V (a) B A 5A 10
A practical current source consists of a 2-mA ideal current source in parallel with a 500-Ωresistance. (a) Find the equivalent practical voltage source. Then (b), connect a 1-kΩ resistor in parallel with the first and find the power delivered by the current source. Finally(c), find the power
Find the equivalent circuit for each of the following(a) Three ideal 1.5-V batteries connected in series.(b) A 5-mA current source in series with a 100-kΩ resistor.(c) A 40-A ideal current source in parallel with an ideal 10-A current source.(d) A 100-V source in parallel with two 10-kΩ
Find the voltage across the 330-Ω resistor in the circuit of Figure 2–39. 100 w 560 ww + Vx +Vy- 24 V 330 vo Vz + + I FIGURE 2-39 ww 220
Usingonly the available20%tolerance3 standard-value resistors in the insideback cover, design a voltage divider to obtain 2:9 V20% from a 5-V source using only two resistors
Using only the available 10% tolerance resistors in the inside back cover, design a voltage divider to obtain 6:5V 10% from a 20-V source using only two resistors.
Select a value for the resistor Rx in Figure 2–40 so υO =8V. +1 2 www 10V R Rx FIGURE 2-40 + 10 kVo
In Figure 2–40 Rx =10 kΩ. The output voltage υO = 20 V. Find the voltage source that would produce that output. (Hint: It is not 10 V.) +1 2 www + R 10 kVo 10V FIGURE 2-40
Use the voltage division rule to find the output voltage υO of the circuit in Figure 2–41. +1 R A) R3 i=0 ww www VS R FIGURE 2-41 + Vo
In Figure 2–41, suppose that a resistor R4 is connected across the output. What value should R4 be if we want 12υS to appear between node A and ground?
The operation of a potentiometer is based on the voltage division rule. The device is a three-terminal element that uses voltage (potential) division to meter out a fraction of the applied voltage. Simply stated, a potentiometer is an adjustable voltage divider. Figure 2–42 shows the circuit
Ten volts ðυSÞ are connected across the 10-kΩ potentiometer ðRTOTALÞ shown in Figure 2–42(c). A load resistor of 10 kΩ is connected across its output. At what resistance should the wiper ðRTOTAL −R1Þ be set so that 2 V appears at the output, υO?
For the circuit shown in Figure 2–43, find the values of the output vO as the potentiometer is moved across its range. Then determine the value of vO if the potentiometer is set to exactly halfway of its range.
Design a voltage divider that will provide 5:5V5% from a 9-V battery using only the 10% standard-value resistors (see inside back cover). The current from the source should be at or below 0.5 mA to avoid draining the source too quickly.
Find the current ix in Figure 2–47(a). 5A 5A Desired path www ix Ly 50 ww - 20 : 20 (a) Equivalent path 20 6.6721 Equivalent resistance (b)
Batteries chemically produce electricity that is used to power many portable devices including cell phones, tablet computers, flashlights, hearing aids, back-up power, and automobiles to mention just a few. Batteries are rated in both voltage and amperehours.A typical car battery delivers a nominal
The R−2R ladder circuit in Figure 2–50 is a binary current divider that finds applications in digital-to-analog signal conversion. The operation of this circuit can be explained using current division together with series and parallel equivalent resistance.The equivalent resistance connected to
Use series and parallel equivalence to find the output voltage υO and the input current iS in the ladder circuit shown in Figure 2–52(a). R ww VS 2RR Vo (a) R www B REQI VS 2R/3 VS 5R/3 w REQ2
Use source transformations to find the output voltage υO and the input current iS in the ladder circuit shown in Figure 2–53(a). + R 2R w R (a) ww Vo R is X R w R 2R (b) R ww 2R/5 w Vo (c)
In Figure 2–52, R=15 kΩ. The voltage source υS = 5 V. Find the power delivered to the circuit by the source R 2RR (a) Vo R www B REQI VS 2R13 VS 5R/3 w REQ2
Find υx in the circuit shown in Figure 2–54(a). 15 V ww 20 www www 10 10 20 102 20 0.75 A (a) 20 22002 + Vx w 10 2002 2002 REQ3 Y (b) REQI www REQ2 10 0.75 A 10 10 @ ww w W +x- www 102 10 7.5 V 102 H Z FIGURE 2-54 (d)
In Figure 2–53(a), find the current through the 2R resistor. VS R www X 2R w e R www vo R SR ww 2R ww (b) 2R/5 R Vo w Vo
Find υx and ix using circuit reduction on the circuit in Figure 2–55. ww ix w 15 2002 2A 1002 30 FIGURE 2-55 150
Find υx and υy using circuit reduction on the circuit in Figure 2–56. 2.2 +Vx- ww 1.5 3.3 1 ww 6 V + 1 kQ ww 3.3 6 V
Using circuit reduction, find υO in Figure 2–57(a). R R w w- R 2R 2R vo Vs (a) 2R 2R VS R w 2R Vo R + 2R 2R 2R VO w R R ww 2R (d)
Find the voltage across the current source in Figure 2–58. 1.5 www 1 w + 2.2 VS 3.3 0.1 mA T FIGURE 2-58
Use Multisim to find the voltages and currents for the circuit in Figure 2–22(Example 2–10).
Use Multisim to find all the voltages and currents in the circuit of Figure 2–47(a) (Example 2–22).
2–1 The current through a 33-kΩ resistor is 2:2 mA. Find the voltage across the resistor.
2–2 The voltage across a particular resistor is 8.60 V and the current is 366 μA. What is the actual resistance of the resistor?Using the inside back cover, what is the likely standard value of the resistor?
2–3 You can choose to connect either a 4:7-kΩ resistor or a 47-kΩ resistor across a 5-V source. Which will draw the least current from the source? What is that current?
2–4 A model railroader wants to be able to electrically throw a rail switch RSwitch from two different locations. He designs the circuit in Figure P2−4 using two single-pole double-throw switches. Will it work? Explain. Location A 102 Location B VS FIGURE P2-4 Rswitch
2–5 A 100-kΩ resistor dissipates 50 mW. Find the current through the resistor.
2–6 The conductance of a particular semiconductor resistor is 0.05 mS. Find the current through the resistor when connected across a 1:5-V source.
2–7 In Figure P2−7 the resistor dissipates 25 mW. Find Rx 15 V FIGURE P2-7 Px = 25 mW Rx
2–8 In Figure P2−8 find Rx and the power supplied by the source. 10 mA + 100 VR FIGURE 2-8
2–9 A resistor found in the lab has three orange stripes followed by a gold stripe. An ohmmeter measures its resistance as 34:9 kΩ. Is the resistor properly color coded? (See inside back cover for color code.)
2–10 The i – v characteristic of a nonlinear resistor is v = 82i +0:17i3.(a) Calculate v and p for i = 0:5, 1, 2, 5, and 10 A.(b) Find the maximum error in v when the device is treated as an 82-Ω linear resistance on the range jij < 0:5A.
2–11 A 100-kΩ resistor has a power rating of 0:25 W. Find the maximum current that can flow through the resistor.
2–12 A certain type of film resistor is available with resistance values between 10 Ω and 100MΩ. The maximum ratings for all resistors of this type are 500 V and 0:25 W.Show that the voltage rating is the controlling limit for R > 1MΩ and that the power rating is the controlling limit when R <
2–13 Figure P2−13 shows the circuit symbol for a class of twoterminal devices called diodes. The i–v relationship for a specific pn junction diode is i = 5×10−17 e40 v − 1 A.(a) Use this equation to find i and p for v = 0, 0:1, 0:2,0:4, 0:8, and 1:0 V. Use these data to plot the i – v
2–14 A thermistor is a temperature-sensing element composed of a semiconductor material, which exhibits a large change in resistance proportional to a small change in temperature. A particular thermistor has a resistance of 5 kΩ at 25C. Its resistance is 340 Ω at 100C. Assuming a
2–15 In Figure P2−15 i2 = −6A and i3 = 2 A. Find i1 and i4. B A FIGURE P2-15
2–16 In Figure P2−16 determine which elements are in series, parallel, or neither. How many different nodes and loops are there in the circuit? Then if v2 = 3 V and v3 = 5 V, find v1, v4, and v5. + V + V2 VA + + V3 + V5 FIGURE P2-16
2–17 For the circuit in Figure P2−17:(a) Identify the nodes and at least two loops.(b) Identify any elements connected in series or parallel.(c) Write KCL and KVL connection equations for the circuit A 3 B 2 + FIGURE P2-17
2–18 In Figure P2−17 i2 = – 30mA and i4 = 20 mA. Find i1 and i3.
2–19 For the circuit in Figure P2–19:(a) Identify the nodes and at least five loops in the circuit.(b) Identify any elements connected in series or in parallel.(c) Write KCL and KVL connection equations for the circuit + A + V3 - 3 +1 22 4 B 6 + 6 V6 5 (D C vs+ FIGURE P2-19
2–20 In Figure P2−19 v2 = 20V, v3 = −20 V, and v4 = 6V.Find v1, v5, and v6.
2–21 In many circuits the ground is often the metal case that houses the circuit. Occasionally a failure occurs whereby a wire connected to a particular node touches the case causing that node to become connected to ground. Suppose that in Figure P2−19 node C accidently touches ground.How would
2–22 The circuit in Figure P2−22 is organized around the three signal lines A, B, and C.(a) Identify the nodes and at least five loops in the circuit.(b) Write KCL connection equations for the circuit.(c) If i1 = −30 mA, i2 = −18 mA, and i3 = 75 mA, find i4, i5, and i6.(d) Show that the
2–23 Are any of the elements in Figure P2−23 in series or parallel?If so, identify the ones that are. Then if v2 = 10V, v4 = 10 V, and v5 = 5 V, find v1, v3, and v6. + + 12 2 + V6 6 + + V4 4 + 3 3 5 V5 FIGURE P2-23 T
2–24 Are any of the elements in Figure P2−24 in series or parallel?If so, identify the ones that are. Then if i1 = −5 mA, i2 = 10 mA, and i3 = −15 mA, find i4 and i5. A FIGURE P2-24 E B C 5
2–25 (a) Use the passive sign convention to assign voltage variables consistent with the currents in Figure P2−24. Write three KVL connection equations using these voltage variables.(b) If v4 = 0 V, what can be said about the voltages across all the other elements?
2–26 If a wire is connected between nodes B and C in Figure P2−24, what can be said about the voltages across each of the elements?
2–27 TheKCL equations for a three-node circuit are as follows:Draw the circuit diagram and indicate the reference directions for the element currents. Node A +12-14=0 Node B-12-13+ is=0 Node C i+is+i4-is=0
2–28 For the circuit in Figure P2−28, write a complete set of connection and element constraints and then find vx and ix. 33 500 A 56 FIGURE P2-28 +
2–29 For the circuit in Figure P2−29, write a complete set of connection and element constraints, then find vx and ix. + 24 V 22 www 47 FIGURE P2-29 +
2–30 Find vx and ix in Figure P2−30. Compare the results of your answers with those in problem 2–29. What effect did adding the 33-kΩ resistor have on the overall circuit? Did the power supplied by the source change? 24 V +1 22 w 33 47 ix + Vx FIGURE P2-30
2–31 A modeler wants to light his model building using miniature grain-of-wheat light bulbs connected in parallel as shown in Figure P2−31. He uses two 1:5-V “C-cells” to power his lights. He wants to use as many lights as possible but wants to limit his current drain to 500 μA to preserve
2–32 Find vx and ix in Figure P2−32. 50 ix ww Rest of the +0.5 A Vx 100 10 50 circuit FIGURE P2-32
2–33 In Figure P2−33:(a) Assign a voltage and current variable to every element.(b) Use KVL to find the voltage across each resistor.(c) Use Ohm’s law to find the current through each resistor.(d) Use KCL to find the current through each voltage source. 200 w +10 V 5V 200 W 200 ww 15 V
2–34 Find vO in the circuit of Figure P2−34. 200 www 100 100 w w 0+ 10 V +1 5V vo +1 FIGURE P2-34
2–35 Find the power provided by the source in Figure P2−35. Ps 500 ww 10 mA ( 1 1.5 FIGURE P2-35
2–36 Figure P2−36 shows a subcircuit connected to the rest of the circuit at four points.(a) Use element and connection constraints to find vx and ix.(b) Show that the sum of the currents into the rest of the circuit is zero.(c) Findthe voltage vA with respect to the ground in the circuit Rest
2–37 In Figure P2−37 ix = 0:33 mA. Find the value of R. ww 10 ww 10 4 V R 15 V Rest of the circuit FIGURE P2-37
2–38 Figure P2−38 shows a resistor with one terminal connected to ground and the other connected to an arrow.The arrow symbol is used to indicate a connection to one terminal of a voltage source whose other terminal is connected to ground. The label next to the arrow indicates the source
2–39 Find the equivalent resistance REQ in Figure P2−39. REQ w 25 300 w w 100 FIGURE P2-39
2–40 Find the equivalent resistance REQ in Figure P2−40. REQ ww 68 82 FIGURE P2-40 w 33 47
2–41 Find the equivalent resistance REQ in Figure P2−41. REQ ww 47 ww 56 15 FIGURE P2-41 www ww 15
2–42 Equivalent resistance is defined at a particular pair of terminals. In Figure P2−42, the same circuit is looked at from two different terminal pairs. Find the equivalent resistances REQ1 and REQ2 in Figure P2−42. Note that in calculating REQ2 the 33-kΩ resistor is connected to an open
2–43 Find REQ in Figure P2−43 when the switch is open.Repeat when the switch is closed. REQ 100 w w 50 ww 100 100 FIGURE P2-43
2–44 Find REQ between nodes A and B for each of the circuits in Figure P2−44. What conclusion can you draw about resistors of the same value connected in parallel? w R A ww B ww R www R w R R A w B (a) R ww R ww R A w B R w R w R (b) FIGURE P2-44 n Rs R (c)
2–45 Showhowthe circuit in Figure P2−45 could be connected to achieve a resistance of 100, 200, 150, 50, 25, 33:3, and 133:3 Ω. B (A) ww 100 w 100 2 C w 50 D FIGURE P2-45
2–46 In Figure P2−46 find the equivalent resistance between terminals A–B, A–C, A–D, B–C, B–D, and C–D. A 22 k2 ww www 100 FIGURE P2-46 B 100 D
2–47 In Figure P2−47 find the equivalent resistance between terminals A–B, A–C, A–D, B–C, B–D, and C–D. A 60 100 w ww (B) 100 BW w 50 40 15 D FIGURE P2-47
2–48 Select a value of RL in Figure P2−48 so that REQ = 15kΩ.Repeat for REQ = 11kΩ. REQ -22 22 W FIGURE P2-48 RL
2–49 Using no more than four 1-kΩ resistors, show how the following equivalent resistors can be constructed: 2 kΩ, 500 Ω, 1:5 kΩ, 333 Ω, 200 Ω, and 400 Ω.
2–50 Do a source transformation at terminalsA and B for each practical source in Figure P2−50. A Bo A 47 (a) w 100 Bo (b) FIGURE P2-50 10 mA 5 V +
2–51 For each of the circuits in Figure P2−51, find the equivalent practical voltage source at terminals A and B. A w 10 5 A B (a) R A) W ww Bo FIGURE P2-51 R +1 www (b)
2–52 In Figure P2−52, the i – v characteristic of network N is v + 50i = 5 V. Find the equivalent practical current source for the network. N V A FIGURE P2-52 B
2–53 Select the value of Rx in Figure P2−53 so that REQ =100 kΩ. ww 40 47 w Rx 22 10 REQ FIGURE P2-53
2–54 Two 10-kΩ potentiometers (a variable resistor whose value between the two ends is 10 kΩ and between one end and the wiper—the third terminal—can range from 0 Ω to 10 kΩ) are connected as shown in Figure P2−54. What is the range of REQ? 10 w ww 10 REQ FIGURE P2-54
2–55 Select the value of R in Figure P2−55 so that RAB = RL. R ww w R www AR www B FIGURE P2-55 RL
2–56 What is the range of REQ in Figure P2−56? 10 ww 15 15 REQ FIGURE P2-56
2–57 Find the equivalent resistance between terminals A and B in Figure P2−57. A) a R w R R ww w B FIGURE P2-57
2–58 Use voltage division in Figure P2−58 to find vx, vy, and vz Then show that the sum of these voltages equals the source voltage. +Vx- ww +Vy- ww 2 8 24 V 4 FIGURE P2-58
2–59 Use voltage division in Figure P2−59 to obtain an expression for vL in terms of R, RL, and vS. R w R w RLVL FIGURE P2-59

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