chap4 - 133 Techniques of Circuit Analysis Problems Section...

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Unformatted text preview: 133 Techniques of Circuit Analysis Problems Section 4.1 4.1 4.2 Assume the current ig in the circuit in Fig. P41 is known. The resistors R1 — R5 are also known. a) How many unknown currents are there? b) How many independent equations can be writ- ten using Kirchhoff’s current law (KCL)? c) Write an independent set of KCL equations. (1) How many independent equations can be derived from Kirchhoff’s voltage law (KVL)? e) Write a set of independent KVL equations. Figure P4.1 For the circuit shown in Fig. P42, state the numerical value of the number of (a) branches, (b) branches where the current is unknown, (c) essential branches, (d) essential branches where the current is unknown, (e) nodes, (f) essential nodes, and (g) meshes. Figure P4.2 4.3 a) How many separate parts does the circuit in Fig. P43 have? b) How many nodes? 4.4 a) If only the essential nodes and branches in 4.5 A current leaving a node is defined as positive. SmA c) How many branches are there? d) Assume that the lower node in each part ofth circuit is joined by a single conductor. Repea the calculations in (a)—(c). Figure P4.3 identified in the circuit in Fig. P42, how man simultaneous equations are needed to describ the circuit? b) How many of these equations can be derive using Kirchhoff’s current law? c) How many must be derived using Kirchhott’ voltage law? (1) What two meshes should be avoided in apply the voltage law? a) Sum the currents at each node in the circui shown in Fig. P45. b) Show that any one of the equations in (a) can derived from the remaining two equations Figure P45 : ection 4.2 4.6 PSP'IIIE 4.7 PSFICE 4.8 PSPIEE 4.9 PSPIEE 4.10 PSPILE Use the node-voltage method to find no in the cir- cuit in Fig. 134.6. Figure P4.6 a) Find the power developed by the 3A current source in the circuit in Fig. P46. b) Find the power developed by the 60 V voltage source in the circuit in Fig. P4.6. c) Verify that the total power developed equals the total power dissipated. A 10 Q resistor is connected in series with the 3A current source in the circuit in Fig. P46. a) Find ’00. b) Find the power developed by the 3A current source. c) Find the power developed by the 60 V voltage source. d) Verify that the total power developed equals the total power dissipated. ' e) What effect will any finite resistance connected in series with the 3A current source have on the value of on? Use the node-voltage method to find 2:1 and oz in the circuit shown in Fig. P49. 3) Use the node-voltage method to find the branch currents ta — i'e in the circuit shown in Fig. 134.10. b) Find the total power developed in the circuit. 4.11 P5 PICE 4.12 PSPICE 4.13 P5 P] U: 139 Problems Figure P4.10 The circuit shown in Fig. P4.11 is a dc model of a residential power distribution circuit. a) Use the node-voltage method to find the branch currents i1 — £6. b) Test your solution for the branch currents by showing that the total power dissipated equals the total power developed. ' Figure P4.11 24D Use the node-voltage method to find '01 and oz in the circuit in Fig. P412. Figure P442 4.0 800 Luvs“ Use the node-voltage method to find how much power the 2 A source extracts from the circuit in Fig. P413. Figure P4.13 140 Techniques of Circuit Analysis 4.14 a) Use the node—voltage method to find 191, v2, and Figure PM? PSP'EE 1);, in the circuit in Fig. P414. b) How much power does the 640 V voltage source deliver to the circuit? Figure 94.14 4.18 a) Find the node voltages 1;], ’02, and ’03 in the Cl] 2 0 2-5 0 PM cuit in Fig. P418. 4.15 Use the node-voltage method to find the total power ' '3) Find the mtal Power diSSiPated in the Chen“- P‘SFIEE dissipated in the circuit in Fig. P415. Figure P418 Figure P4.15 4.19 Use the node~voltage method to calculate ti P591“ power delivered by the dependent voltage source i the circuit in Fig. P419. 4.16 a) Use the node—voltage method to show that the P591“ output voltage ’00 in the circuit in Fig. P4.16 is figure [34.19 equal to the average value of the source voltages. b) Find a, if v1 = 150 V, ’02 = 200 V, and 50 109 v3 = ~50 V. Figure P4.16 R 4.20 3) Use the node-voltage method to find the tol O o o ’03 “SPIKE power developed in the circuit in Fig. P420. b) Check your answer by finding the total pow.I absorbed in the circuit. 59°50“ 4-3 Figure P420 4.17 a) Use the node-voltage method to find no in the 511 300 PSPICE circuit in Fig. P417. b) Find the power absorbed by the dependent source. c) Find the total power developed by the independ- ent sources. .421 Use the node-voltage method to find the value of “up HIE in the circuit in Fig. P4.21. Figure P4.21 80 Q 40 Q e: 750 mA 200 n 4.22 Use the node-voltage method to find r}, in the cir- Pfi’ItE cuit in Fig. P422. 5 fl _ @ 5 Q 700 120 50V Figure P422 80V© 4.23 3) Use the node—voltage method to find the power dissipated in the 5 (I resistor in the circuit in Fig. P423. b) Find the power supplied by the 500 V source. Figure P423 50 4Q 611 500V 30 4Q 60 30 4.24 3) Use the node—voltage method to find the branch PM currents i1, i2, and i3 in the circuit in Pig. P424. b) Check your solution for 1'], £2, and i; by showing that the power dissipated in the circuit equals the power developed. Problems 141 Figure P4.24 4.25 Use the node-voltage method to find the value of 2,10 “SPICE in the circuit in Fig. P425. Figure P435 4.26 Use the node-voltage method to find or, and the P5?“ power delivered by the 40 V voltage source in the circuit in Fig. P426. Figure P426 40V 50mA 4.2? Usc the node-voltage method to find co in the cir— PSP'EE cuit in Fig. P427. 6k!) 20 RD 4 [(0 Figure P42? 50V 142 Techniques of Circuit Analysis 4.28 Assume you are a project engineer and one of your Figure Flt-31 PM! staff is assigned to analyze the circuit shown in Fig. P428. The reference node and node numbers given on the figure were assigned by the analyst. Her solution gives the values of “U3, and 1:4 as 235 V 40 V and 222 V, respectively. Test these values by checking the total power developed in the circuit against the total power dis- sipated D0 3’3“ agree with the solution submitted 4.32 3) Use the mesh-current method to find the total by the analyst power developed in the circuit in Fig. P432. b) Check your answer by showing that the total Figure P428 power developed equals the total power dissipated. Figure No.32 6 .0 W ll] .0 12 Q T w» W 3 Q 110 V © 70' V 12 V 4.29 Use the node—voltage method to find the power devel— m % PW! oped by the 20 V source in the circuit in Fig. P429. 4.33 Solve Problem 4.10 using the mesh-current method. Figure P429 4.34 Solve Problem 4.11 using the mesh-current method. 2 Q 1 0 4 n 4.35 Solve Problem 4.22 using the mesh-current method. an 40 Q 4.37 Use the mesh-current method to find the power dis 430 Show that when Eqs_ 4_16 417 and 4_19 are solved WI“ sipated in the 8 I) resistor in the circuit in Fig. P43? for £3, the result is identical to Eq. 2.25. 4.36 Solve Problem 4.23 using the mesh-current method Section 4.6 Figure 94.37 Section 4.5 4.31 a) Use the mesh-current method to find the branch 95"“ currents in, fig, and it in the circuit in Fig. P431. b) Repeat (3) if the polarity of the 64 V source is reversed. 4.38 Use the mesh-current method to find the power WE delivered by the dependent voltage source in the circuit seen in Fig. 134.38. Figure P4.38 259 4.39 Use the mesh—current method to find the power 95”“ developed in the dependent voltage source in the circuit in Fig. P439. Figure P439 4.40 a) Use the mesh-current method to find no in the Pm circuit in Fig. P440. b) Find the power delivered by the dependent source. Figure P4.40 2 Q 12 Q 5 0 4V r'g‘ 3Q Section 4.7 4.41 3) Use the mesh-current method to find how much PM power the 12 A current source delivers to the circuit in Fig. P441. b) Find the total power delivered to the circuit. c) Check your calculations by showing that the total power developed in the circuit equals the total power dissipated. Problems 143 Figure P4.41 100 8 9 «M, «M 600 V© 400 @400 V 140 2 I) o w W a 12 A 4.42 3) Use the mesh-current method to solve for in in PSPICE the circuit in Fig. P442. b) Find the power delivered by the independent current source. 0) Find the power delivered by the dependent volt- age source. Figure P4.42 980 (l 1.8 k!) SmA 4.43 Use the mesh-current method to find the total power P5P“ developed in the circuit in Fig. P443. Figure P4.43 o Zia 4.44 Use the mesh-current method to find the total power P5P!“ developed in the circuit in Fig. P444. Figure P4.44 5 n U, «N» 25 (1 20 Q a w» 1w» —30 iii 144 4.45 3) Use the mesh-current method to find the power PSPICE 4.46 a) Use the mesh-current method to determine PSPIEE 4.4? Use the mesh-current method to find the total P5 PI£E 4.48 Assume the 18 V source in the circuit in Fig. P447 is PSPIE E 4.49 Techniques of Circuit Analysis b) Repeat (a) if the 3 A current source is replace by a short circuit. c) Explain why the answers to (a) and (b) at the same. delivered to the 2 I) resistor in the circuit in Fig. P445. b) What percentage of the total power developed in the circuit is delivered to the 2 fl resistor? 4.50 PSPICE a) Use the mesh-current method to find the branc figure “'45 currents in Ea — ie in the circuit in Fig. P450. Us. b) Check your solution by showing that the tot power developed in the circuit equals the tot power dissipated. Figure P4.50 100 (I which sources in the circuit in Fig. P446 are gen— erating power. b) Find the total power dissipated in the circuit. F' P4146 . . . . . mm 4.51 a) Find the branch currents Ia — to for the c1rcu1 PSPICE shown in Fig. P451. b) Check your answers by showing that the tot power generated equals the total pow dissipated. Figure 94.51 15 rd .. 3L. power dissipated in the circuit in Fig. P447. Figure P4.” 30 A Section 4.8 4.52 The circuit in Fig. P452 is a direct-current version PSPKE of a typical three-wire distribution system. The resistors Ra, Rb, and RC represent the resistances of the three conductors that connect the three loads R1, R2, and R3 to the 110/220 V voltage supply. The resistors R1 and R2 represent loads connected to increased to 100 V. Find the total power dissipated in the circuit. 3) Assume the 18 V source in the circuit in Fig. P447 is changed to —10 V. Find the total power dissi- pated in the circuit. the 110 V circuits, and R3 represents a load con- nected to the 220 V circuit. a) What circuit analysis method will you use and why? b) Calculate a], 1:2, and 93. c) Calculate the power delivered to R1, R2, and R3. (1) What percentage of the total power developed by the sources is delivered to the loads? e) The Rb branch represents the neutral conductor in the distribution circuit. What adverse effect occurs if the neutral conductor is opened? (Hint: Calculate 1:1 and v2 and note that appliances or loads designed for use in this circuit would have a nominal voltage rating of 110 V.) R3 = 54.625 0 "4.53 Show that whenever R1 = R2 in the circuit in Fig. P452, the current in the neutral conductor is zero. (Hint: Solve for the neutral conductor current as a function of R1 and R2). Assume you have been asked to find the power dissi- pated in the 1 k0 resistor in the circuit in Fig. P454. a) Which method of circuit analysis would you rec- ommend? Explain why. b) Use your recommended method of analysis to find the power dissipated in the 1 k0 resistor. c) Would you change your reconnnendation if the problem had been to find the power developed by the 10 mA current source? Explain. (1) Find the power delivered by the 10 mA cur- rent source. 4.55 l’SPlCE 4.56 PSPItE 4.51r PSPIEE Problems 145 a v Figure P454 10mA lkfl A 4k 0 resistor is placed in parallel with the 10 mA current source in the circuit in Fig. P454. Assume you have been asked to calculate the power devel- oped by the current source. a) Which method of circuit analysis would you rec- ommend? Explain why. b) Find the power developed by the current source. a) Would you use the node-voltage or mesh-current method to find the power absorbed by the 10 V source in the circuit in Fig. P456? Explain your choice. b) Use the method you selected in (a) to find the power. Figure P4.56 The variable dc current source in the circuit in Fig. P457 is adjusted so that the power developed by the 15 A current source is 3750W. Find the value 0f Ede. Figure P457 146 Techniques of Circuit Analysis 4.58 The variable dc voltage source in the circuit in 4.61 a) Use source transformations to find no in the ci P5P“ Fig. P458 is adjusted so that i0 is zero. PSP'EE cuit in Fig. P461. a) Find the value of 1’33. b) Find the power developed by the 340 V source b) Check your solution by showing the power c) Find the power developed by the 5 A curre developed equals the power dissipated. source. . d) Verify that the total power developed equals I] “9"”! “~53 total power dissipated. 30 o _. gr, Figure P4.61 5.0 150 230V 0 V“ 20.0 250 4.62 a) Use a series of source transformations to find Section 4.9 Pm“ in the circuit in Fig. 134.62. b) Verify your solution by using the mesh-curre 4.59 a) Use a series of source transformations to find _ ’ method to flnd to. PSPIEE the current i0 in the circuit in Fig. P459. 1)) Verify your solution by using the node-voltage figure MM method to find i0. Figure P459 4.60 a) Find the current in the 10 k0 resistor in the cir- PSPIG cuit in Fig. P460 by making a succession of appropriate source transformations. b) Using the result obtained in (a), work back seam“ 4'10 through the circuit to find the power developed 4.63 Find the Thévenin equivalent with respect to I by the 100 V source. P5P“ terminals a,b for the circuit in Fig. P463. Figure P4.60 Figure P4.63 20 k0. 3 k0. 5 k0 ©100V 12mA 60kfl is. 100 8.0 a 10kg Govfi b Problems 14? 4.64 Find the Thevenin equivalent with respect to the Figure P4-57 PM! terminals a,b for the circuit in Fig. P464. 4 kit 3 k0 Figure 94.64 I s A 12 o 2 o . b a 4.68 a) Find the Thévenin equivalent with respect to the 12 V o 6 Q 75”“ terminals a,b for the circuit in Fig. P4.68 by find— ing the open-circuit voltage and the short-circuit b current. b) Solve for the Thévenin resistance by removing the independent sources. Compare your result to the Thévenin resistance found in (a). 4.65 Find the Thevenin equivalent with respect to the ’9‘!“ terminals a,b for the circuit in Fig. P4135. Figure P455 figure No.68 4.69 An automobile battery, when connected to a car radio, provides 12.5 V to the radio. When connected to a set of headlights, it provides 11.? V to the head— lights. Assume the radio can be modeled as a 6.25 0 resistor and the headlights can be modeled as a 0.65 0 resistor. What are the Thevcnin and Norton equivalents for the battery? 4.66 Find the Norton equivalent with reSpe'ct to the ter- ' WE minals a,b in the circuit in Fig. P4.66. 4.70 Determine i0 and an in the circuit shown in Fig. P430 PSPICE when R, is 0, 2, 4, 10, 15, 20, 30, 50, 60, and 70 D. Figure 94.10 6 o ". 4.67 A voltmeter with a resistance of 100 k9 is used to 5"“ measure the voltage vab in the circuit in Fig. P4137. a) What is the voltmeter reading?l b) What is the percentage of error in the voltmeter reading if the percentage of error is defined as {(measured — actual)/actual] X 100? 148 Techniques of Circuit Analysis 4.71 Determine the Thévenin equivalent with respect to PSPIEE the terminals a,b for the circuit shown in Fig. P471. Figure P431 4.72 Find the Thévenin equivalent with respect to the PS?!“ terminals a,b for the circuit seen in Fig. P472. Figure P432 30 ta 2 k0 5 kn 10 k0 MN MN W ---O a 40 V I ' 20 k0 50 k0 40 k0 is o b 4.73 When a voltmeter is used to measure the voltage we PSPIEE in Fig. P433, it reads 7.5 V. a) What is the resistance of the voltmeter? b) What is the percentage of error in the voltage measurement? Figure P433 0.4 V 0.2 g} 4 k0 100 .0 15 k0 ii) 16 V 6 kit 10 kn a. 2 V 4.74 When an ammeter is used to measure the current fig PSPICE in the circuit shown in Fig. P474, it reads 10 A. a) What is the resistance of the ammeter? b) What is the percentage of error in the current measurement? 4.75 4.76 PSPICE Figure P674 114! A Thévenin equivalent can also be determir from measurements made at the pair of termin of interest. Assume the following measureme were made at the terminals a,b in the circuit Fig. P475. When a 15 k0 resistor is connected to the t minals a,b, the voltage cab is measured and fou to be 45 V. When a 5 k!) resistor is connected to the t minals a,b, the voltage is measured and found be 25 V. Find the Thévenin equivalent of the netwr with respect to the terminals a,b. Figure P4.75 Linear resistive network with independent and dependent ‘ ' b Sources The Wheatstone bridge in the circuit shown Fig. P476 is balanced when R3 equals 1200 0.1f' galvanometer has a resistance of 30 (1 how m1 current will the galvanometer detect when ' bridge is unbalanced by setting R3 to 1204. (Him: Find the Thévenin equivalent with respect the galvanometer terminals when R3 = 1204 Note that once we have found this Thévenin eqt alent, it is easy to find the amount of unbalani current in the galvanometer branch for differ galvanometer movements.) Problems 149 sure P456 Figure P4519 50.0 600 4.80 The variable resistor (RL) in the circuit in Fig. P480 PSPICE is adjusted for maximum power transfer to RL. a) Find the numerical value of RL. flit?“ 4-11 b) Find the maximum power transferred to RL. 24.77 Find the Thévenin equivalent with respect to the :- ram: terminals a,b in the circuit in Fig. P4.77. “9"” "'30 4Q 6Q 80 4.81 The variable resistor in the circuit in Fig. P481 is “PM adjusted for maximum power transfer to R0. a) Find the value of R0. b) Find the maximum power that can be delivered to R0. Figure PM’?r 4.78 Find the Thévenin equivalent with respect to the figure “'31 WE terminals a,b for the circuit seen in Fig. P438. 4 k0 1.25 k0 Figure P4.?8 10 Q 12 Q 4.82 What percentage of the total power developed in “ME the circuit in Fig. P481 is delivered to R0 when R0 is set for maximum power transfer? 500 4.83 A variable resistor RE, is connected across the ter- PSPIEE minals a,b in the circuit in Fig. P472. The variable resistor is adjusted until maximum power is trans- ferred to R0. 5.: ction 4.12 a) Find the value of R0. 4.79 The variable resistor (R0) in the circuit in Fig. P439 b) Find the maximum Power delivered to Ro- .-PSPI¢E is adjusted until the power dissipated in the resistor c) Find the percentage of the total power devel— is 1.5 W. Find the values of R, that satisfy this condi— oped in the circuit that is delivered to R0. tion. 150 4.84 4.85 PSFICE 4.86 PSPIEE 4.87 FSP'ICE 4.88 PSPICE Techniques of Circuit Analysis a) Calculate the power delivered for each value of b) Find the maximum power. R0 used in Pmb‘em 4-70- c) Find the percentage of the total power dev b) Plot the power delivered to R0 versus the resist— oped in the circuit that is delivered to R0. ance R0. Figure P438 c) At what value of R0 is the power delivered to R0 a maximum? The variable resistor (R0) in the circuit in Fig. P485 is adjusted for maximum power transfer to R0. What percentage of the total power developed in the circuit is delivered to R0? Figure P4.85 R0 4.89 The variable resistor in the circuit in Fig. P48! PM! adjusted for maximum power transfer to R0. a) Find the numerical value of R0. b) Find the maximum power delivered to R0. 0) How much power does the 280 V source deli to the circuit when R, is adjusted to the va found in (a)? Figure P439 50 a. The variable resistor (R0) in the circuit in Fig. P486 is adjusted for maximum power transfer to R0. a) Find the value of R0. b) Find the maximum power that can be delivered to R0. Figure P436 4.90 a) Find the value of the variable resistor R0 in P5?!“ circuit in Fig. P490 that will result in maxim power dissipation in the 6 Q resistor. (H Hasty conclusions could be hazardous to 31 career.) b) What is the maximum power that can be de ered to the 6 fl resistor? What percentage of the total power developed in Figure P430 the circuit in Fig. P486 is delivered to R0? Ra The variable resistor (R0) in the circuit in Fig. P488 is adjusted until it absorbs maximum power from the circuit. a) Find the value of R0. 30V 6.0 Problems 151 f-Section 4.13 Figure P494 4.91 a) Use the principle of superposition to find the voltage 1) in the circuit of Fig. P491. 1)) Find the power dissipated in the 20 5'1 rcsistor. Figure P491 7 mA 20 km :2. 6A 4.95 Use superposition to solve for it, and on in the cir— PWE cuit in Fig. P495. 75 V o 1211 Figure P495 4.92 Use the principle of superposition to find the volt— r” age 1) in the circuit of Fig. P492. I 40 (I 250 Figure P492 4.96 Use the principle of superposition to find the cur- ' rsPltE rent in in the circuit shown in Fig. P496. Figure P496 4-93 Use the Ptincipte 0t superposition to find the cut- 4.97 a) In the circuit in Fig. P497, before the 10 mA cur- mfi rem iv in the drum in Fig- P493 PSPItt rent source is attached to the terminals a,b, the current to is calculated and found to be 1.5 mA. Use superposition to find the value of it, after figure P433 the current source is attached. 5 Q 10 n b) Verify your solution by finding in when all three sources are acting simultaneously. Figure P43? 8A 0 4.94 Use the principle of superposition to find no in the “PM circuit in Fig. P494. 10 mA SmA 152 Techniques of Circuit Analysis Sections 4.1—4.13 4.98 4.99 Laboratory measurements on a dc voltage source yield a terminal voltage of 75 V with no load con- nected to the source and 60 V when loaded with a 20 Q resistor. a) What is the Thévenin equivalent with respect to the terminals of the dc voltage source? b) Show that the Thévenin resistance of the source is given by the expression I1 = [I — R RT}: (1)0 1) Ls where "an. = the Thévenin voltage, v0 = the terminal voltage corresponding to the load resistance RL. Two ideal dc voltage sources are connected by elec— trical conductors that have a resistance of r Q/m, as shown in Fig. P499. A load having a resistance of R 0 moves between the two voltage sources. Let x equal the distance between the load and the source a], and let L equal the distance between the sources. a) Show that ’leL + RUIZ — vflx RL + 2er — 2er ‘ b) Show that the voltage u will be minimum when L — ——./ —i( —v)2 '02—'01 ’01" 0102 2rL vi 2 ' c) Find x when L = 16km, v1 = “IOOOV, v2 = 1200 V, R = 3.9 o, and r = 5 x 10-5 mm. d) What is the minimum value of u for the circuit of part (c)? I: :: Figure No.99 x —-4 rflfim fix rflfm _\ ‘J | 4/ R (movable 4.100 Assume your supervisor has asked you to determi the power developed by the 16 V source in the circ in Fig. P4100. Before calculating the power develop by the 16V source, the supervisor asks you to submj proposal describing how you plan to attack the prt lem. Furthermore, he asks you to explain why y have chosen your proposed method of solution. a) Describe your plan of attack, explaining yr reasoning. b) Use the method you have outlined in (a) to fi the power developed by the 16 V source. Figure H.100 4.101 Find the power absorbed by the 2 A current sou PM“ in the circuit in Fig.P4.101. Figure H.101 60 3 0 4.102. Find 1:1, ’02, and '03 in the circuit in Fig. P4102. PSPICE Figure P4402 0.2 o _' 103 Find i in the circuit in Fig. P4103. Problems 153 4.105 Assume the nominal values for the components in HIKE P REL-{ICE l PERSPEUIVE PS P] C E Figure H.103 4.106 P R AU'IUI L PERSPECTIVE PSPICE 4.107 PRACTICAL PERSPECIIVE PSPIEE 4.108 PRAC‘I'ILAL PERSPECI'E VE . 104 For the circuit in Fig. 4.69 derive the expressions for the sensitivity of '01 and oz to changes in the source currents I g1 and Igg. DESIGN the circuit in Fig. 4.69 are: R1 = 25 0; R3 = 5 0; R3 = = [his] : A;and [5,2 = A. Predict the values of 1:1 and a; if Igl decreases to 11 A and all other components stay at their nominal values. Check your predictions using a tool like PSpice or MATLAB. Repeat Problem 4.105 if I32 increases to 17 A, and all other components stay at their nominal values. Check your predictions using a tool like PSpicc or MATLAB. Repeat Problem 4.105 if 15.1 decreases to '11 A and 182 increases to 17 A. Check your predictions using a tool like PSpice or MATLAB. Use the results given in Table 4.2 to predict the val- ues of v1 and “v: if R1 and R3 increase to 10% above their nominal values and R2 and R4 decrease to 10% below their nominal values. I31 and 15,: remain at their nominal values. Compare your predicted values of v] and 1:2 with their actual values. ...
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chap4 - 133 Techniques of Circuit Analysis Problems Section...

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