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