Muhammad Irfan Yousuf Yousuf Dedicated to: Prof. Dr. Sohail Aftab Qureshi Conventions for Describing Networks
2-1. For the controlled (monitored) source shown in the figure, re!re ! lot simil!r to th!t given in Fig. 2-"(b).
v2 v1 # $b $b v1 # $! $!
i2 Fig. 2-" (b) %olution& 'en our book see the figure (*+) t is volt!ge controlled current source.
i2 /$e !0is
v2 -$e !0is gv1
i2
gv1
/ v2 current source -
Muhammad Irfan Yousuf Yousuf Dedicated to: Prof. Dr. Sohail Aftab Qureshi 2-2. ee!t *rob. 2-1 for the controlled source given in the !ccom!ning figure. %olution& 'en our book see the figure (*+) t is current controlled volt!ge source. v2 ri1
i2
2-. 3he network of the !ccom!ning figure is ! model for ! b!tter of oen-circuit termin!l volt!ge $ !nd intern!l resist!nce b. For this network, lot i !s ! function v. dentif fe!tures of the lot such !s sloes, intercets, !nd so on. %olution& 'en our book see the figure (*+) 3ermin!l 3e rmin!l volt!ge v # $ - i b i b # $ - v i # ($ - v )+ b 4hen v # 5 i # ($ - v )+ b i # ($ - 5 )+ b i # $+ b !m 4hen v # $ i # ($ - $ )+ b i # (5 )+ b i # 5 !m v#5 i # $+ v#$ i#5 i $+ b
$ %loe&
v
Muhammad Irfan Yousuf Yousuf Dedicated to: Prof. Dr. Sohail Aftab Qureshi 2-2. ee!t *rob. 2-1 for the controlled source given in the !ccom!ning figure. %olution& 'en our book see the figure (*+) t is current controlled volt!ge source. v2 ri1
i2
2-. 3he network of the !ccom!ning figure is ! model for ! b!tter of oen-circuit termin!l volt!ge $ !nd intern!l resist!nce b. For this network, lot i !s ! function v. dentif fe!tures of the lot such !s sloes, intercets, !nd so on. %olution& 'en our book see the figure (*+) 3ermin!l 3e rmin!l volt!ge v # $ - i b i b # $ - v i # ($ - v )+ b 4hen v # 5 i # ($ - v )+ b i # ($ - 5 )+ b i # $+ b !m 4hen v # $ i # ($ - $ )+ b i # (5 )+ b i # 5 !m v#5 i # $+ v#$ i#5 i $+ b
$ %loe&
v
Muhammad Irfan Yousuf Yousuf Dedicated to: Prof. Dr. Sohail Aftab Qureshi # m0 / c
(01, 1) # (5, $+ b)
(02, 2) # ($, 5) m # (2 6 1)+(02 6 01) # (5 6 $+ b)+($ - 5) # (-$+ b)+$ # (-$+b)(1+$) # -1+ b -intercet # $+ b 0-intercet # $ %loe -intercet 0-intercet -1+ b $+ b $ 2-. 3he m!gnetic sstem shown in the figure h!s three windings m!rked 1-17, 2-27, !nd -7. 8sing three different forms of dots, est!blish ol!rit m!rkings for these windings. %olution& 'en our book see the figure (*+) 9ets !ssume current in coil 1-17 h!s direction u !t 1 (incre!sing). t roduces flu0 (incre!sing) in th!t core in clockwise direction.
1
17 2
27
7
:ccording to the 9en;7s l!w current roduced in coil 2-27 is in such ! direction th!t it ooses the incre!sing flu0 . %o direction of current in 2-27 is down !t 27. )
Muhammad Irfan Yousuf Dedicated to: Prof. Dr. Sohail Aftab Qureshi
1
17
2
27
7
27
7
(!)
1
17
2
(b) 2-. 3he figure shows four windings on ! m!gnetic flu0-conducting core. 8sing different sh!ed dots, est!blish ol!rit m!rkings for the windings. %olution& 'en our book see the figure (*+>) i1
i 2
i2 Coil 1
Coil
i
Coil 2 Coil
1
(Follow Fleming7s right h!nd rule) 2->. 3he !ccom!ning schem!tic shows the e?uiv!lent circuit of ! sstem with ol!rit m!rks on the three-couled coils. Dr!w ! tr!nsformer with ! core simil!r to th!t shown for *rob. 2- !nd l!ce windings on the legs of the core in such ! w! !s
Muhammad Irfan Yousuf Dedicated to: Prof. Dr. Sohail Aftab Qureshi to be e?uiv!lent to the schem!tic. %how connections between the elements in the s!me dr!wing. %olution& 'en our book see the figure (*+>) 2
i2 9
92
91
φ
1
2
2-". 3he !ccom!ning schem!tics e!ch show two inductors with couling but with different dot m!rkings. For e!ch of the two sstems, determine the e?uiv!lent induct!nce of the sstem !t termin!ls 1-17 b combining induct!nces. %olution& 'en our book see the figure (*+>) 9et ! b!tter be connected !cross it to c!use ! current i to flow. 3his is the c!se of !dditive flu0. M 91
92
$ i (!)
$ # self induced e.m.f. (1) / self induced e.m.f. (2) / mutu!ll induced e.m.f. (1) / mutu!ll induced e.m.f. (2) $ # 91di+dt / 92di+dt / @ di+dt / @ di+dt 9et 9e? be the e?uiv!lent induct!nce then $ # 9 e? di+dt 9e? di+dt # (91 / 92 / @ / @) di+dt
Muhammad Irfan Yousuf Dedicated to: Prof. Dr. Sohail Aftab Qureshi 9e? # 91 / 92 / @ / @ 9e? # 91 / 92 / 2@ @ 91
92 i
$ (b)
3his is the c!se of subtr!ctive flu0. $ # 91di+dt / 92di+dt - @ di+dt - @ di+dt 9et 9e? be the e?uiv!lent induct!nce then $ # 9 e? di+dt 9e? di+dt # (91 / 92 - @ - @) di+dt 9e? # 91 / 92 - @ - @ 9e? # 91 / 92 - 2@ 2-A. : tr!nsformer h!s 155 turns on the rim!r (termin!ls 1-17) !nd 255 turns on the second!r (termin!ls 2-27). : current in the rim!r c!uses ! m!gnetic flu0, which links !ll turns of both the rim!r !nd the second!r. 3he flu0 decre!ses !ccording to the l!w # e-t 4eber, when t 5. Find& (!) the flu0 link!ges of the rim!r !nd second!r, (b) the volt!ge induced in the second!r. %olution& N1 # 155 N2 # 255 # e-t (t 5) *rim!r flu0 link!ge 1 # N1 # 155 e-t %econd!r flu0 link!ge 2 # N2 # 255 e-t @!gnitude of volt!ge induced in second!r v 2 # d 2+dt # d+dt(255 e -t) v2 # -255 e-t
Muhammad Irfan Yousuf Dedicated to: Prof. Dr. Sohail Aftab Qureshi
b
2
1
!
c
=
d
d
c
=
R 1
b
2
!
2-11. 3hree gr!hs !re shown in figure. Cl!ssif e!ch of the gr!hs !s l!n!r or nonl!n!r. %olution& 'en our book see the figure (*+") :ll !re l!n!r. n th!t the m! be dr!wn on ! sheet of !er without crossing lines.
Muhammad Irfan Yousuf Dedicated to: Prof. Dr. Sohail Aftab Qureshi 2-12. For the gr!h of figure, cl!ssif !s l!n!r or nonl!n!r, !nd determine the ?u!ntities secified in e?u!tions 2-1 2-1. %olution& 'en our book see the figure (*+") Cl!ssific!tion& Nonl!n!r Number of br!nches in tree # number of nodes 6 1 # = 6 1 # Number of chords # br!nches 6 nodes / 1 # 15 6 = / 1 # 15 6 # Chord me!ns B: str!ight line connecting two oints on ! curve7. 2-1. n (!) !nd (b) of the figure for *rob. 2-11 !re shown two gr!hs, which m! be e?uiv!lent. f the !re e?uiv!lent, wh!t must be the identific!tion of nodes !, b, c, d in terms of nodes 1, 2, , if ! is identic!l with 1 %olution& 'en our book see the figure (*+") (b) ! is identic!l with 1 b is identic!l with c is identic!l with 2 d is identic!l with 2-1. 3he figure shows ! network with elements !rr!nged !long the edges of ! cube. (!) Determine the number of nodes !nd br!nches in the network. (b) C!n the gr!h of this network be dr!wn !s ! l!n!r gr!h %olution& 'en our book see the figure (*+") Number of nodes # " Number of br!nches # 11 (b) es it c!n be dr!wn. 2-1=. 3he figure shows ! gr!h of si0 nodes !nd connecting br!nches. ou !re to !dd non!r!llel br!nches to this b!sic structure in order to !ccomlish the following different obEectives& (!) wh!t is the minimum number of br!nches th!t m! be !dded to m!ke the resulting structure nonl!n!r (b) 4h!t is the m!0imum number of br!nches ou m! !dd before the resulting structure becomes nonl!n!r %olution& 'en our book see the figure (*+A) @!ke the structure nonl!n!r @inimum number of br!nches # @!0imum number of br!nches # > 2-1. Disl! five different trees for the gr!h shown in the figure. %how br!nches with solid lines !nd chords with dotted lines. (b) ee!t (!) for the gr!h of (c) in *rob. 2-11. %olution& 'en our book see the figure (*+A)
Muhammad Irfan Yousuf Dedicated to: Prof. Dr. Sohail Aftab Qureshi
1)
2)
)
)
=)
b)& 1)
2)
Muhammad Irfan Yousuf Dedicated to: Prof. Dr. Sohail Aftab Qureshi
)
)
=)
2-1>. Determine !ll trees of the gr!hs shown in (!) of *rob. 2-11 !nd (b) of *rob. 215. 8se solid lines for tree br!nches !nd dotted lines for chords. %olution& 'en our book see the figure (*+A) :ll trees& 1) 2) ) )
=)
)
>)
")
A)
15)
11)
12)
