CHAPTE R 5 A DDI TION AL A NALYSIS TEC H N I O UE...
Transcript of CHAPTE R 5 A DDI TION AL A NALYSIS TEC H N I O UE...
232 CHAPTE R 5 A DD I TION AL A NA LYSIS TEC H N I O UE S
0 5.7 In the network in Fig. PS.7 find I(J using superposition.
6 kf!
12 V 6 mA
Figure PS.7
5.8 Find 10 in the circuit in Fig. P5.S using superposit ion.
30V 12 kf!
Figure PS.8
o 5·9 Find Vo in the network in Fig. PS.9 using superpos ition.
+
3 kf! 8 kf!
2kD
12V 6 kf! 2 mA
Figure PS.9
2 kf!
0 5.10 Find Vo in the network in Fig. P5.IO using superpos iton.
1 kf! 2 kf!
2 kf! 6mA 12 V
Figure PS.l0
S·l1 Find Vo in the network in Fig. PS. II using superposition.
3 kf! 3 kf! 3 kf!
+ 9V VO 3 kf! 3 kf! 6V
Figure PS.l1
5.12 Find I" in the network in Fig. PS. 12 lIsing superposition.
12 kf!
4 mA
12 kf! 6V
Figure PS.12
5.13 Find 10 in the network in Fig. PS.13 using superposition.
6 kfl
6 V + SmA 6 kf!
Figure PS.13
5.14 Find J" in the network in Fig . P5.14 using superposition.
4A Sf!
Sf! 10 f!
20 f! 40V
Figure PS.14
5.15 Us ing superposition, find I" in the circuit in Fig. PS . IS. ~
2 kf! + 6V
4 kf! 8 kf!
12 V + fA 12 kf!
Figure PS.1S
5.16 Find I,.. in thl! network in Fig. PS. 16 using superposit ion.
6V + 2 kfl t 2 mA
6 kfl 12 kfl
3 kfl 6 kfl
Figure PS.16
o 5·17 Find Vo in the circuit in Fig. PS. 17 using superposition.
~ 2 kfl t 4mA 1 kfl
6V
12V +
2 kfl 1 kfl 1 kfl
Figure PS.17
0 5.18 Use superposition to tind 10 in the network in Fig. PS. l S.
2mA r---------~--------~__{--
4 mA t 4 kfl
2 kfl 4 kfl
12 kfl
Figure PS.18
fil 5·19 Find 10 in the ci rcuit in Fig. PS. 19 using WWW' superposition.
1 kfl 1 kfl 1 kfl
2V
2mA t + -.}-<p-------'
4kfl 4V
PROBLEMS 233
5.20 Use superposition to find II, in the circuit in Fig. P5.20. 0
2 kfl
12 V
Figure PS.20
12V
4 kfl
I 2 mA
5.21 Use superposition to find 10 in the circui t in Fig. PS.21.
6 kfl
6 kfl
4 mA
12V
Figure PS.21
3kfl
10
4 kfl
2mA
2 kfl
5.22 Use Thevenin 's theorem to tind Vo in the network in Fig. P5.22.
6V 12V
+
2 kfl 4 kfl 2 kfl
Figure PS.22
5.23 Use TIlt'!venin's theorem to find Vo in the network in Fig. P5.23
r 3 kfl 4 kfl
12 V 6 kfl 2 kfl 2mA
10 Figure PS·23 L-______ ~------~
Figure PS.19
234 C H AP T E R 5 AD DIT IO NAL A N A LYSIS T ECHNIQ U ES
5.24 Find I" in the network in Fig. PS.24 lIsing Thcvenin 's theorem.
4 kl1
3kl1 2mA
12 V 6kl1 2 kfl
Figure PS.24
iii 5.25 Find v" in the circui t in Fig. PS.25 ll sing Thevcnin's -- theorem.
1 kfl
2 mA
12 V 1 kl1
Figure PS.2S
5.26 Use Thevenin's theorem (Q ti nd 10 in the network in Fig. PS.26.
5.28 Find 10 in the circuit in Fig. PS.28 using Theveni n's theorem.
12V + 4kl1
4 kl1 6 kfl
6 kfl I 6 mA
Figure PS.28
5.29 Find I" in the network in Fig. PS.29 using Thcven in's theorem.
+ 6V 2kl1
1 kfl 2 kl1
t 2 mA 2kl1
Figure PS.29
5.30 Find 10 in the network ill Fig. P5.30 using Thcvcnin 's 2 rnA theorem.
,-- ---{- 1 kl1
6 kfl 2 kfl
12V + 2 kfl 1 kl1
Figure PS.26
5.27 Find v" in the network in Fig. PS.27 using Thevenin's theorem.
6 kl1
3V
r-----~-+~----~
1 mA 3 kfl
-r--~-~V---+·---~O +
6 kl1 2 kl1
L--------+--------.-----~O
Figure PS.27
1 mA 1 k!l
6 V 1 kl1
Figure PS.30
5.31 Fi nd If, in the network in Fig. P5.3 1 using Thevenin 's theorem.
2 mA
.-----{- r--- ---, 1 kfl
6V
+---,MI~_.--_{+ -
1 mA I 1 kfl
Figure PS.31
1 kfl
o
5.32 Find v" in the Fig. P5 .32 using Theveni n's theorem.
+
3mA 2 kO 4 kO
4 kO 12 kO
6V 2 kO
Figure P5.32
5.33 Use Thevenin's theorem to find v" in the circuit in Fig. PS.33
1 kO
4mA
2mA
2mA
1 kO
2 kO
1 kO
L--------+--------.-----~O
Figure P5.33
5.34 Find 1(, in the circuit in Fig. PS.34 using lllt':venin's theorem.
2mA 2 kO 1 kO --'}---~--~Ar---+
12V + 2 kO 4 mA
Figure P!;.34
o 5·35 Find V,I in the network in Fig. P5.34 using Thevenin 's theorem.
I 1 rnA 1 kO
O.S kO O.S kO
+ Vo
-
1 kl! 6V
Figure P5.35
PROBLEM S 235
5.36 Us ing Thevenin 's theorem. find I" in the circuit in Fig. PS.36.
4A so
so 100
200 2A 40V
Figure P5.36
5.37 Find Va in the network in Fig. P5.37 using Thevenin's theorem.
8 kO 40V
,---'V'o/Ir----{- +
4 kO 6 kO
+
2 mA t 20V +
4kO
Figure P5.37
2 kO
5.38 Use T hevenin's Iheorcm lO find I" in the network in Fig. PS.38.
24 V + 6 kO
2 mA
2 mA
3 kO 4 kO
10
Figure P5.38
2 kO
o
236 CHAPTER 5 ADD IT IONAL ANALYS I S TECHNIQUES
(} S·39 Use Thevenin 's theorem to find to in the circuit in PS.39.
C} - +~-.--------~--~~-,
18 V 4kO
6 kO 6 kO 4 kO
6kO
1 mA 3 kO
Figure PS.39
(} S·40 Given the linear circuit in Fig. P5.40, it is known that when a 2-kQ load is connected to the terminals A - B, the load current is 10 rnA. If a IO-k.Q load is connected to the terminals, the load current is 6 rnA. Find the cucrent in a 20-kn load.
L---~--oB
Figure PS.40
o 5·41 If an 8-kn load is connected to the terminals of the network in Fig. P5.41 , VA H = 16 Q. If a 2-kQ load is connected to the tcnninais, VAB = 8 V. Find VAB if a 20-kQ load is connected to the tenninals.
"<-----QA
Linear circuit
Figure PS.41
'r---oB
e 5·42 Find /0 in the network in Fig. P5.42 using Norton's theorem.
6 kO 3 kO
12 V 3kO 3 kO
Figure PS .42
5.43 Use Norton 's theorem to find '0 in the circuit in Fig. PS.43.
12 V
-+.~~--~~--~--~~-, 3 kO 2 kO
3 kO 2 kO 1 kO
Figure PS.43
5.44 Use Norton's theorem to find to in the circuit in Fig. P5.44.
12 V
+-~~--~~~--~~-. 4kO 2 kO
2kO 2 kO 4 kO
Figure PS.44
5.45 Find '0 in the network in Fig. P5.45 using Nonon's theorem.
6 kO 3 kO
Figure PS.4S
5.46 Use Nonon 's theorem (Q find Vo in [he network in Fig. PSA6.
2 kO
4 kO 2 mA +
24 V 2 kO
Figure PS.46
240 CHAPTER 5 A DDITIONAL A NALYS IS T ECH N I Q UES
o 5.67 Find Vo in the network of Fig. P5.67 using 4J Thevenin 's theorem.
1 kll 1 kll
- V + x
2 kll 1 rnA j 1 kll
1 kll 1 kll
2 kll
Figure P5.67
+
0 5.68
~ Use Thevenin 's theorem to find I" in the network in Fig. PS.68.
1 kll
+
Vx 1 kll 1 kll
+ 6V 2 kll
2 Vx 1 kll + 2 V 10
Figure P5.68
Use Thevenin 's theorem to find VQ in the network in Fig. PS .69.
2 I , j 1 kll 1 kll
2 rnA
1 kll
5.70 Find the Thevenin equiva lent of the circuit in Fig. PS.70 at the terminals A-B.
2 kll
1 kll
3kll
4 Vx 1000
L-------~------~B
Figure P5.70
5.71 Find the Thevenin equiva lent of the network in Fig. PS.7 1 al the terminals A-B using a l-mA current source.
2 kll
4 kll A B
+
2 kll 1 kll Vx
Figure P5.71
5.72 Find the Thevenin equivalent of the network in Fig. PS.72 at the terminals A-B.
1 kll 2 kll A
+
V, 1 kll ~ 1 kll 1000
B
Figure P5.72
5.73 Find the Thevenin equivalent of the network in Fig. PS.73 al the termi nals A-B.
1 kll 1000 I ,
r----vW'---~----(:+ - r ---1r--0 A
2 kll
L-----~------~--o B
C} 5.61 Find Y" in the circuit in Fig. P5.61 lIsing Thevcnin's theorcm.
4 kO 2kO 4 kO
6 V ~ 1000
+ V, 2kO j
Figure PS .61
A~ 5.62 Find Vo in the network in Fig. PS.62 using Norton's '0// theorem.
1 mA
r-------~---------..----< +
t V. 1 kll 4000
2 kO 3 kO Vo
+
Vx 3kO
L-------~~------~____c
Figure PS.62
12 V
5·63 Find I" in the network in Fig. P5.63 using Thevenin's theorcm.
2 kO
1 kO 2 Vr
4V +
Figure PS.63
PROBLEMS 239
5.64 Usc Thcvcnin 's theorcm lo find the power suppl ied by the 2-V source in the circuit in Fig. PS.64.
2 kO
1 kO 2 Vx + 1 kO 1 kO
+ 4V + V. 1 kO
Figure PS.64
5.65 Find \~, in the circuit in Fig. 1'5.65 using Thevenin's theorem.
j 2 l r 1 kO I 2mA
l r ~
1 kO 1 kO +
1 kO 12 V 1 kO Vo
Figure PS.6S
2V
5.66 Find v" in the network in Fig. P5.66 using Thevenin's theorem.
+ 1 kll 1 kO V,.
2mA
1 kO
~
+
L---____ -+ ______ --4~
figure PS.66
5.74 Find the Thevenin equivalent of the network below at the terminals A-8 in Fig. PS.74.
1 kl1 A
2 i ,. 1 kl1 an 1 kl1
i , B
Figure PS.74
5.75 Find thc Thcvcnin equ ivalent ci rcuit of the network in Fig. PS.7S at terminals A-B.
2000 i , 4 kl1
t----1"- <- +>-----'WV- ...,-----o A
6 kl1 2 kl1 4 kl1
~----+-------------~------_oB
Figure PS.7S
5.76 Find 10 in the network in Fig. PS.76 using source lfansform'ltion.
6 kl1 6 kl1
6V 6kl1 6 kl1 1 mA
Figure PS.76
C 5·77 ~se .source transfonnal ion to lind Vo in the network 111 Fig. PS.77.
r-------~~-+r-~--~~--,
6V 12 kl1
6 kl1 4 kl1
Figure PS.77
24 V
PROBLEMS 241
5.78 Find 10 in the network in Fig. PS .78 using source transformation.
Figure PS.78
5.79 Find Vo in the network in Fig. PS.79 usi ng source transformation.
6kf.! 2 kl1 +
3 kl1
6V + 4 kl1
12 V
~------~--------~·------~O
Figure PS.79
5.80 Use source transformation to find 10 in the network in Fig. P5.80.
4 kl1 6 kl1
2 kl1 2mA 2 kl1 3V
Figure PS.80
5.81 Find Vo in the network in Fig. PS.8 1 using source transformation.
+
3 kl1 4 kl1
3 kn 2 mA 12 kl1 12 kl1
Figure PS.81
6V
o
o
o
242 CHAPTER 5 ADDI T IONAL ANALYSIS TECHNIOU E S
5.82 Find v,J in the network in Fig. P5 .82 using source transformation.
4kfl 3 kfl 4kfl
2kfl 2 rnA 12 kfl 12 kfl
Figure PS.82
o 5.83 Find 11' in the network in Fig. PS.83 using source transformation.
4 rnA
r---{-~--'
3kfl
3kfl 12 kfl
Figure PS.83
5.84 Find 10 in the circuit in Fig. P5.84 using source transfonnation.
r-~¥-~--~~~~+-r-~~~--' B kfl 3kfl
9V
4 kfl
4 kfl I 2 rnA 3kfl
12 V I"
Figure PS.84
C 5·85 Find /0 in the ci rcuit in Fig. PS. 85 using source tr:.lIlsformation.
+ 6 k!l 3kfl 3kfl
12V
4 kfl
6k!l I 2 rnA 3 kfl
r6V 10
Figure PS.8S
12 V
3k!l
3kfl
5.86 Find I" in the network in Fig. PS.86 using source transform.Hian.
6V
4 kfl
3 kfl 4 kfl
Figure PS.86
5.87 Find 10 in the nCI\\'ork in Fig. P5.87 using source transform ation.
6mA
3kO
6kO 18 kO
Figure PS.87
5.88 Use source I rans forl11~ltion to fi nd I" in the network in Fig. PS .88.
6 k!l 3k!l
12 V 6k!l 6kfl
10 -2 rnA
3 kfl
Figure PS.88
5.89 Using source transformation. find Vo in the circuit in Fig. PS .89.
r-~~--~~~--~--o 6 kfl 8 kfl +
12V + 3 kfl 4 kfl
2 kfl ~------+-~~--~.--o
'-------{- }-----'
2 rnA
Figure PS.89
()
()
e 5.90 Using source transfonnation, find 10 in the circu it in
Fig. PS.90.
8 kfl
2 kfl
1 mA t 3 kfl
6 kfl
Figure PS.90
e 5·91 Use source transformation to find 10 in the circuit in Fig. PS.91.
4 kfl
6 kfl
6 kfl - )---"-1'--{-
4 rnA 2 rnA
12V +
Figure PS.91
e 5.92 Using source transformation, lind lu in the
network in Fig. PS .92 .
2 kfl
2mA ,---------~--------~~-
4 kfl
2 kfl 4 kfl
12 kfl
Figure PS.92
P R O 8 L EMS 243
5.93 U se source transform,Hion to find 10 in the circuit in
Fig. PS.93.
2 kfl 6 V 6 kfl
+- ~ 2 mA 3kfl
12V
12V + 4 kfl
10
Figure PS.93
5.94 U se source transformalion to find I" in the circuit in Fig. PS .94.
-+r-~--------~--~~-. 4 kfl
18 V
6 kfl 6 kfl 4 kfl
6 kfl
2mA 1 mA t 3 kfl
Figure PS.94
5.95 Using source transformation. find 1(, in the circu it in
Fig. PS.9S.
24 V + 6 kfl 2 kfl
2mA
2 mA
3 kfl 4 kfl
Figure PS.9S
o
244 CHAPTER 5 ADDITIONA L ANALYS I S TECHNIQUES
o 5·96 Find RL in the nelwork in Fig. PS.96 in order 10 achieve maximum power transfer.
0 5.97
2 kG 2 kG
12 V 2 kG 2 kG
Figure P5.96
In the network in Fig. P5.97 find RL for maximum power transfer and the maximum power transferred to this load.
1 kG 2 kG
2 kG 4mA 4 kn
Figure P5.97
Find RL for maximum power transfer and the maximum power that can be transferred to the load in Fig. PS.98.
2 mA
3 kG 2 kG
6V 6 kG
Figure P5.98
5.99 Find RL for maximum power transfer and the maximum power that can be transferred to the load in the circuit in Fig. P5.99.
1 kG 2mA
0.5 k!1
1 kG 2mA 6V
Figure P5.99
5.100 Find Rl. for maximu m power transfer and the maximum power that can be transferred to the load in the network in Fig. P5.IOO.
2 kG 4mA t 4 kG
4 kG 2 mA
8mA 2 kG
Figure P5 .100
5.101 Find RL for maximum power transfer and the maximum ~ power that can be transferred to the load in the circuit in Fig. P5.IOI.
3V + 2 kG
1 kG 1 mA
3 kG t 0.5 mA 1 kG
Figure P5.101
5.102 Choose RL in (he network of Fig. PS.102 for maximum 0 power transfer.
5 kG 5 kG
I
12 V 1001 t
Figure P5.102
5.103 Find RI. for maximum power transfer and the maximum power thaI can be transferred 10 the load in Fig. PS.103.
2 k[l +
1 mA Vx 1 kG
Figure P5.103
j
3 kG
4 V, 1000
Find the value of RI• in the network in Fig. PS. I04 for maximum power transfer.
4 V, + 2A
Figure PS.104
5.105 Find the value of RL for maximum power transfer and the maximum power that can be transferred to RL in the circuit of Fig. PS.IOS.
12 fl 4fl
+
30V + V, 4 fl
4 V,
Figure PS.10S
5.106 Find the maximum power that can be transferred to RL in the network of Fig. PS.106.
+ Va
500 fl 1000 fl
0.5 Va + + 12V
500 fl
Figure PS.106
5.107 Find the value of RL for maximum power transfer in the circuit in Fig. PS.l 07.
2fl 4fl
4 V, + t 2A
4fl
Figure PS.107
S·108
PROBLEMS 245
In the network of Fig. PS. I08, find the va lue of RI. for maximum power transfer. In addition, calculate the power diss ipated in RI. under these conditions.
LOOO ' I 1 0 kfl
- +)----"Nv---,
10 kfl
Figure PS.108
5.109 Calculate the maximum power that can be transferred to RL in the circuit in Fig. PS. l 09.
4 V.r 4fl
- +>----I\No---,
4 fl + 4fl
V, 4 fl
100V +
+ 20V
Figure PS.109
5.110 Find RL for max imum power transfer and the maximum power that can be transferred in the network in Fig. PS.I I O.
2 kfl
4 kfl
2 kfl 1 rnA t + ~
2000 t 2kfl V,
Figure PS.110