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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 nodevoltage 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 nodevoltage method to find 2:1 and oz in
the circuit shown in Fig. P49. 3) Use the nodevoltage 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 nodevoltage 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 nodevoltage method to find '01 and oz in
the circuit in Fig. P412. Figure P442 4.0 800
Luvs“ Use the nodevoltage 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 25 0 PM cuit in Fig. P418. 4.15 Use the nodevoltage 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 nodevoltage 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“ 43 Figure P420
4.17 a) Use the nodevoltage 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 nodevoltage 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 nodevoltage 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 nodevoltage method to ﬁnd the value of 2,10
“SPICE in the circuit in Fig. P425. Figure P435 4.26 Use the nodevoltage 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 nodevoltage 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 Flt31
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 meshcurrent 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 meshcurrent method.
Figure P429 4.34 Solve Problem 4.11 using the meshcurrent method. 2 Q 1 0 4 n 4.35 Solve Problem 4.22 using the meshcurrent method. an 40 Q
4.37 Use the meshcurrent 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 meshcurrent method Section 4.6 Figure 94.37 Section 4.5 4.31 a) Use the meshcurrent 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 meshcurrent 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 meshcurrent 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 meshcurrent 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 meshcurrent 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 meshcurrent method to find the total power
P5P“ developed in the circuit in Fig. P443. Figure P4.43 o Zia 4.44 Use the meshcurrent 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 meshcurrent method to find the power PSPICE 4.46 a) Use the meshcurrent method to determine PSPIEE 4.4? Use the meshcurrent 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 meshcurrent 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 directcurrent version
PSPKE of a typical threewire 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 nodevoltage or meshcurrent
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 meshcurre 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 nodevoltage 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 P457
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 opencircuit voltage and the shortcircuit
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?“ 411 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 470 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 Fig...
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 Spring '08
 MOHAMED
 Fig, Thévenin's theorem, Voltage source, Norton's theorem

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