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232 CHAPTE R 5 A DD I TION AL A NA L YSIS TEC H N I O UE S
0 5.7 In th e ne tw o rk in Fig. PS. 7 find I(J us in g
superpos iti o n.
6 kf!
12 V (^) 6 mA
Figure PS.
5.8 Find 10 in th e circ uit in Fi g. P5.S us in g superpos it io n.
30V 12 kf!
Figure PS.
o 5·9 Find Vo in th e net wo rk in Fi g. PS.9 us in g s upe rpos ition.
3 kf! 8 kf!
2k D
12V 6 kf! (^2) mA
Figure PS.
2 kf!
0 5.10 Find Vo in th e net wo rk in Fi g. P5.IO us in g supe rp os it o n.
1 kf! 2 kf!
2 kf! (^) 6mA 12 V
Figure PS .l
S·l1 Fin^ d^ Vo^ in^ th^ e net^ wo^ rk^ in^ Fi^ g.^ PS.^ II^ us^ in^ g supe^ rp^ os^ iti^ o^ n.
3 kf! (^3) kf! 3 kf!
9V (^) VO 3 k f! 3 kf! 6V
Figure PS .l
5.12 Find I" in th e network in Fi g. PS. 12 lI s in g
superpos iti o n.
12 kf!
4 mA
12 kf! 6V
Figure PS.
5.13 Find 10 in th e network in Fi g. PS .13 us in g superpos iti on.
6 kfl
6 V + Sm^ A^6 kf!
Figure PS. 13
- 14 Find J" in the network in Fi g. P5.14 using superpositi on.
4A (^) Sf!
Sf! 10 f!
20 f! 40V
Figure PS.
5.15 Us in g supe rp os ition, find I" in th e circ uit in Fig. PS. IS. ~
2 kf! +^ 6V
4 kf! 8 kf!
12 V + fA (^) 12 kf!
Figure PS.1S
5.16 Fi nd I,.. in thl! network in Fig. PS. 16 us ing superpo s it ion.
6V + (^) 2 kfl (^) t 2 mA
6 kfl 12 kfl
3 kfl (^6) kfl
Figure PS. 16
o 5·17 Fi nd Vo in the c ircuit in Fig. PS. 17 using s uperpo sition.
~ 2 kfl (^) t 4mA 1 kfl 6V
12V + 2 kfl (^) 1 kfl 1 kfl
Figure PS. 17
0 5.18 Use superpo siti on to tin d 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 rc uit in Fig. PS. 19 using WWW' superpos iti on.
1 kfl (^) 1 kfl 1 kfl 2V 2mA t +^ -.^ }-<p-------'
4kfl 4V
PROBLEMS 233
5.20 Use s uperpo s it ion to find II, in the circuit in Fi g. P5.20. 0
2 kfl
12 V
Figure PS.
12V 4 kfl
I 2 mA
5.21 Use superposit ion to find 10 in the circ ui t in Fig. PS.21.
6 kfl
6 kfl 4 mA 1 2V
Figure PS.
3kfl
4 kfl
2mA 2 kfl
5.22 Use Theve nin 's theore m to tind Vo in the network in Fig. P5.22.
6V 1 2V
2 kfl 4 kfl 2 kfl
Figure PS.
5.23 Use TIlt'!ve nin 's th eore m to find Vo in the netw ork in Fig. P5.
r 3 kfl 4 kfl
12 V 6 kfl 2 kfl 2mA
10 Figure PS·
L-__ ____~------ ~
Figure PS.
5.32 F in d v" in the Fi g. P5 .32 using Th eve ni n's theo rem.
3mA 2 kO^4 kO
4 kO 12 kO
6V 2 kO
Figure P5.
5.33 Use Th eve ni n' s th eore m to find v" in th e circuit in Fi g. PS.
1 kO
4mA
2mA 2mA
1 kO
2 kO
1 kO
L--------+--------. -----~O
Figure P5.
5. 34 Fi nd 1 (, in th e circ uit in Fi g. PS. 34 us in g lllt': ve nin 's theore m.
2mA (^2) kO 1 kO --'}---~--~Ar ---+
1 2V + (^2) kO 4 mA
Figure P!;.
o 5· 35 Find V, I in the network in Fi g. P5.34 us in g Thev enin 's theo rem.
I^1 rnA^^1 kO O. S kO O.S kO
+ Vo -
1 kl! 6V
Figure P5.
PROBLEM S 235
5.36 Us in g Th evenin 's th eorem. find I" in the c irc uit in Fi g. PS .36.
4A (^) so
so 100
200 2A 40V
Figure P5. 36
5.37 Find Va in the netwo rk in Fig. P5.37 using Theve nin' s th eo rem.
8 kO
40V ,---'V'o/Ir----{ - +
4 kO 6 kO
2 mA t 20V^ +
4kO
Figure P5.
2 kO
5.38 Use T heve nin 's Ih eorc m lO find I" in th e netwo rk in Fig. PS. 38.
24 V +^6 kO 2 mA
2 mA 3 kO 4 kO
10
Figure P5.
2 kO
o
236 CHAPTER 5 ADD IT IONAL ANALYS I S TECHNIQUES
(} S·39 Use^ Th^ evenin 's theorem to find^ to^ in^ th^ e^ circuit^ in^ PS.^ 39. C}
- ~ -.--------~--~~-, 18 V 4kO
6 kO 6 kO 4 kO
6kO
1 mA 3 kO
Figure PS.
(} S·40 Gi^ ven^ the^ lin^ ear circu^ it^ in^ Fig.^ P5.40,^ it^ is^ kn^ o^ wn^ that
when a 2-kQ load is co nn ected to th e terminal s A - B, th e load current is 10 rnA. If a IO-k.Q load is co nn ected
to the terminal s, the load current is 6 rnA. Find the cuc -
rent in a 20-kn load.
L---~--oB
Figure PS.
o 5·41 If an 8-kn load is connected to th e terminal s of the network in Fig. P5.41 , VA H = 16 Q. If a 2-kQ load is connected to the tcnninai s, VAB = 8 V. Find VA B if a 20-kQ load is connected to the tenninals.
"<-----QA
Linear circuit
Figure PS.
'r- --oB
e 5· 42 Find /0 in th e network in Fi g. P5.42 us in g No rt on's th eore m.
6 kO 3 kO
12 V 3kO 3 kO
Figure PS. 42
- 43 Use Norton 's theorem to find '0 in the circu it in
Fig. PS.4 3.
12 V -+.~ ~-- ~~ --~-- ~~ -,
3 kO 2 kO
3 kO 2 kO 1 kO
Figure PS.
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.
5.45 Find '0 in the network in Fig. P5.45 using Nonon' s theore m.
6 kO 3 kO
Figure PS.4S
5.46 Use Nonon 's th eorem (Q find Vo in [he network
in Fig. PSA6.
2 kO
4 kO (^) 2 mA
24 V 2 kO
Figure PS.
C} 5. 61 Find Y" in the circui t in Fig. P5. 61 lI sin g Th evc nin's theorc m.
4 kO 2kO^4 kO
6 V ~ 1000
V, 2kO j
Figure PS. 61
A~ 5.62 Fin d Vo in th e netw ork in Fig. PS.6 2 usin g N or ton's
'0// theo rem.
1 mA
r-------~-------- -. .----<
t
V. (^) 1 kll 4000 2 kO
3 kO Vo
Vx 3kO
L-------~~------~ ____c
Figure PS.
12 V
5·63 Fi nd I" in the netw ork in Fi g. P5. 63 usin g Th eve nin's
th eo rcm.
2 kO
1 kO 2 Vr
4V +
Figure PS.
PROBLEMS 239
5.64 Usc Thcvcnin 's theor cm lo find the power suppl ied by the 2-V so urce in th e ci rcui t in Fi g. PS. 64.
2 kO
1 kO (^) 2 Vx + 1 kO^1 kO
4V +^ V.^1 kO
Figure PS.
5.65 Find \ ~, in the circuit in Fi g. 1'5 .6 5 using Theveni n's theor em.
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 F in d v" in the net wo rk in Fi g. P5. 66 usin g Th ev enin's
th eo rem.
1 kll (^1) kO V,.
2mA 1 kO
~
L---____-+______--4 ~
figure PS.
5.74 Find th e Th eve nin equi va lent of th e network below at th e
termina ls A-8 in Fig. PS.74.
1 kl1 A
2 i ,. (^) 1 kl1 an 1 kl
i , (^) B
Figure PS.
5.75 Find thc Th cvc nin equ iva len t ci rcuit of the network in
Fig. PS.7S at terminal s A-B.
2000 i ,
4 kl t----1"- <- +>-----'WV- ...,-----o A
6 kl1 2 kl1 4 kl
~----+-------------~------_oB Figure PS.7S
5.76 Find 10 in th e network in Fig. PS.76 using source
lfansform ' lt ion.
6 kl1 6 kl
6V 6kl1 6 kl1 1 mA
Figure PS.
C 5·77 ~se .source tran sfonnal ion to lind Vo in the network 111 Fig. PS.77.
r-------~ ~ -+r-~--~~--, 6V 12 kl
6 kl1 4 kl
Figure PS. 77
24 V
PROBLEMS 241
5.78 Find 10 in the net work in Fi g. PS .78 usin g so ur ce
tran sfor mati on.
Figure PS.
5.79 F ind Vo in th e network in Fig. PS .79 usi ng sour ce
tr ansform ation.
6kf.! 2 kl1 (^) +
3 kl
6V + (^4) kl
12 V
~------ ~--------~ ·------~O Figure PS.
5.80 Use sou rce tran sfor mati on to find 10 in th e net wo rk in
Fig. P5.80.
4 kl1 (^6) kl
2 kl1 2mA (^2) kl1 3V
Figure PS. 80
5.81 Find Vo in th e network in Fig. PS.8 1 usin g source
tra nsfor mation.
3 kl1 4 kl
3 kn 2 mA 12 kl1 12 kl
Figure PS.
6V
o
o
o
e 5.9 0 U sing so ur ce transfonnati on, find 10 in th e circu it in Fig. PS.90.
8 kfl
2 kfl
1 mA t 3 kfl
6 kfl
Figure PS.
e 5·91 Use so ur ce transfor mation to find 10 in th e circuit in Fig. PS .91.
4 kfl
6 kfl
6 kfl - )---"-1'--{ -
4 rnA 2 rnA 1 2V +
Figure PS.
e 5.9 2 U sing so ur ce transfo rm ati on, lind lu in th e
network in Fig. PS..
2 kfl
2mA ,---------~-------- ~~-
4 kfl
2 kfl 4 kfl
12 kfl
Figure PS.
P R O 8 L EMS 243
5.93 U se so urce tran sform, Hi on to find 10 in th e circ u it in
Fig. PS.93.
2 kfl 6 V^6 kfl
- (^) ~ 2 mA 3kfl 12V 1 2V + 4 kfl
10
Figure PS.
5.94 U se so ur ce transformali on to find I" in th e circuit in
Fi g. PS .94.
-+r- ~--------~--~~-. 4 kfl 18 V 6 kfl 6 kfl 4 kfl
6 kfl
2mA (^1) mA t 3 kfl
Figure PS.
5.95 Us in g so ur ce tran sforma ti on. find 1 (, in th e cir cu it in
Fi g. 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 ac hieve maximum power tran sfer.
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 tran s fer and the maximum power tran s ferred to this load.
1 kG 2 kG
2 kG 4mA 4 kn
Figure P5.
Find RL for maximum power tran sfe r 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.
5.99 Find RL for maximum power tran sfe r and the maximum power that ca n be tr ansferred to the load in th e circuit in Fig. P5.99.
1 kG 2mA
0.5 k!
1 kG 2mA 6V
Figure P5.
5.100 Find Rl. for maximu m power transfer and the maximum power that can be transferred to th e load in the network in Fig. P5.IOO.
2 kG (^) 4mA t 4 kG
4 kG (^) 2 mA
8mA 2 kG
Figure P5.
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 (h e network of Fig. PS.102 for maximum 0 power tr ansfe r.
5 kG 5 kG
I
12 V 1001 t
Figure P5.
5.103 Fi nd RI. for maximum power tran s fer and the maximum power thaI can be tran s ferred 10 the load in Fig. PS.103.
2 k[l
1 mA Vx 1 kG
Figure P5.
j
3 kG
4 V,
1000
