7
t4 F.5sl Uru ul Ioote,^-o, d,, ffipo"r c\ .\o!tn u,,ri\,to r c/v\ n\.rvc,.¡{to ürlo Frg ,-\ ( \ov \GV + : XN { Co\..r\o ü', \o vcsrs\t'^c\o\ de \hEv¡¿4ivr ?VIL bR4 6l^-^- Ap\i.o^ü, \V X cLA \ o ¡"a\\p' Jo Vob +6v +6v,(r, - 6*A) + :xI¡= o V*rb=36-A-?KIr Vab-- 3 o ^ 9( ¿4*A) = -G v=V+* Vo = -G (4) tr \ \q.vz - V" Ps.s5 -GV + Vo 4+4.b Vo= a-?e V -Tl - ' Yv^/v\\Ao\ \o ?n t\ j5- 3lf Dcrtz 'ffit. do \a t\3wra P3-s l ura^ ilo ¿\ I vo( eY\.t6 dc 1Vr¿wntt "1 '^ l- r / \ f<\rneü : (1V1)l:Y)= 4-SV __*- 9+9vtL b) (, o\.*\ o J"\ v e\l'a.',t c\a \\'ra'z't,n 2 "*l\ il C..\.*\o üq, \ ^ C¿ Th ev ¿'ni t'l vZs\s\anci'a R\nov -= 2 IAJL b) C.^\.', \o üo\ vo\\oiv Jo thaus"li' 2 -,4 { c\ bIr P + 6r^N Aplt ca^ü.o LV ( oun n,,cr\\. ! 3x 1r +6x(r, - ü*A) + 6v(r,-6, A) +3K Jl = o lB|'(\r =?2- f ,-- ;?,,.rA -- A"*A t8 + Au t¿ Vo 6r<4 6r1-'L \ vtu Jo ¿,(n 6v OK, 6v'. + tr¡-d

Ejercicios Resueltos de Thevenin y Norton

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Circuitos Electricos II

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    F.5sl Uru ul Ioote,^-o, d,,ffipo"r c\ .\o!tn u,,ri\,to rc / v \ n \ . r v c , . { t o r l o F r g

    ,-\( \ o v

    \ G V+

    : X N

    { Co \ . . r \ o ' , \ o vcs r s \ t ' ^ c \ o \de \hEv4ivr

    ? V I L

    b R 4 6l^-^-

    Ap\i.o^, \V X cLA \ o "a\\p' Jo

    V o b + 6 v + 6 v , ( r , - 6 * A ) + : x I = oV * r b = 3 6 - A - ? K I rV a b - - 3 o ^ 9 ( 4 * A ) = - G v = V + * ,

    V o = - G ( 4 )

    t r\ \q.vz -

    V"P s . s 5

    - G V+Vo 4 + 4 . b

    Vo= a -?e V

    -Tl - ' Yv^/v\\Ao\ \o ?n t\j 5 - 3 l f D c r t z

    ' f f i t . do \a t\3wra P3-s lura^ i lo \ I vo( eY\.t6 dc 1Vrwntt "1

    ' ^ l - r / \f < \ r n e : ( 1 V 1 ) l : Y ) = 4 - S V__*-

    9 + 9 v t L

    b) (, o\.*\ o J"\ v e\l 'a. ',t c\a \\ 'ra'z't,n

    2 "*l\

    il C..\.*\o q, \ ^C Th ev 'ni t'l

    v Z s \ s \ a n c i ' a

    R\nov -= 2 IAJL

    b) C.^\.', \o o\ vo\\oiv Jo thaus"li''l

    2 -,4

    {

    c\b I r

    P

    +

    6 r ^ NAplt ca^.o LV ( oun n,,cr\\. !3 x 1 r + 6 x ( r , - * A ) + 6 v ( r , - 6 , A )

    + 3 K J l = ol B | ' ( \ r = ? 2 -

    f , - - ; ? , , . r A - - A " * At 8

    +

    Au t Vo

    6r

  • A p \i cd,n"o l.,C X c^u. oI woo I- 4 * " A + 2 - , 4 + I R , n * = o

    ' IRrx ' . = ) " ' rAAp\iuo^tl., LV!( a,n lo *".r\\o IoV , ^ b - t u . ( e * A ) * ! t ( t " * A ) = o

    Vnb = O = V+Vtev= ) 5 . 2 = O A

    b) C["u lo " \ vo[ to;a [ ,Tlr r,r enr\A

    t 2 v

    Ag\i.-.,^t kvV.' o,^ l6t "o\\'. !/ 2 V + e ( [ r , ) + t l ( ( r , - 4 - h ) = o

    3 t ( \ r = 4 - t er\ __ _ 9 *o

    Apll..r^,\o L.V V.- -v"r To , porrorotut*\ no r .r.\ u o\\ 4.. c,I h O v v ' \ t v 'V . r b - V n r x - V n e x - O

    --) v.ru= A v - J 4 v = - { 3 V

    /

    3 3

    4 - A

    ") Cr\.o\o il., \o, rus\s\ernciod,.ct thcrvcrr\v1

    R+Vt vl( Ka+ \(rt-

    l("r : E Krr-b

    - t t lerT V. { vrz\ r 4,rd V o

    r \-.?,n \o\ ) t c1u.r o

    \ r \ - )v I, TV orv!4tl

    ?^ " \P s . 4 \

    Ao 1\navenlvr

    -Av3

    Cu^l*\, .\" \)o

    N o =-1n G3 s

    V e = B V

    - L3

    4 l ' )--

    t lq

    b

    + -.{* +

    +v,.1

    t + 2

  • @D*\o.,r^inq t au\ al cir-- c,,.i\o , \ a Ft q., P5.4 ? r,rs o^&p-\ t,r.o. kw.p\ Ao" T\nouar-iv"tg

    .

    Apli *n"o tV( aA 'oo\[tri K l a t P W I - \ V = Q

    g K l z = I Z V:) Ie = 4t^ A

    V * b = V t ^ r r u : e J r * l X l - K ( - 4 * A ) * i x ( 4 " ^ A )

    V+Vnv = -4 V

    G Vt o

    b

    = -4 - G6)j ( a )

    " ^ A tI

    )vlr

    ?(

    8*r.ruu :

    4 x I t3

    \ -) o

    { o V

    I o

    l) sa. "tr\r^i'to. ,\

    o\o*-.r^\"e rnt v ds'

    a) 5o- c* \ . .^ ' t " \o ,s\s \vrc \o'

    o th., En rv1= 7 t , "A

    2

    b{ ( t -3

    @l ! s q,\ fro,e*'a &n

    2 ( - r t

    z v 4

    No v\ovr p arc^ )'\rn*i vrafVo v\ a\ l-,,cc"t-itP d)\ [otFig- Ps.5+

    TK

    3) C\cJo }.'\ vo\\5s &s1V,susa',1

    2/t

    Ag)t\ co^dp t-V t( Q)/\ "nP'\\o

    I

    2 K I \ + 1 2 V + t t / ' ' - - o

    3 k a , = - l YI r = - 4 * A

    24v\

    ,r -:-:::^,r \ \ .c-vtto B1 ) 5 c" o. o oV to. c )' ?'l\?Yv/ \ r I I - -

    i^\uns l, "

    *[t"\* | a v-czsls -t ' , 'c io N/or\o 'n

    ?.

    1 ( "3

    4 (f,t

    Vo? "*A

    1-tluJW\T It K + q f e K 4

  • ffit a\, Ic,ub\,\a trTo
  • ffijD\urvr"rnr^ vo oA r\'ffi,\o

    a'^ \ cr Fig' P 5'5qaro^Jro o\ ToYr'*.t). ilrThcv '+,,7

    J l ; - . * , i . , . " ' i

    = * I " ( b : I ' : . . i , f ' \ * I eApIi ,o^A. Ia LvVe^nno\\a I

    lKfr, + t"^A -I*I-t V + J x I r : o2 K f r - l l , ( 1 2 : 0

    Agl\6wd.o L.VV- ovt ,^u\lu, l K I * 4 * t t ( ( r ,+? "^A - u ) =o- t t ( 5 l + 2 L ( I z : - 2 V

    E \ a\stca"^.o. \it,ea'\ os

    Iz - t l [ ] ; ' l - [o IK l \ l F I Il - r a 'L : r r J L - rJf r , l , [ r ] [ o rl _ l = r \ l \ l * F .L . 1 - 4 - L t L J L - ) J: ) r = I f r t o ) + e ( , - ) ) l . _ 4 . , ^ \

    3 L - 3J v : . e * ^ , A - t - { \ , ^ Av g JT v : 4 . * N

    Co\"w\, 'o 5o

    +Vo

    t b

    1

    Ao \V 3;Fri

    *.* /.

    / 2 v: r l

    l s".gqo s}' n\o*^un* o z iqt vvzs

    a sn .."\ "..^\ t

    \a R zs\s*anc\'cr'

    J o \\^ru" u^i ^ t\i v'"' c-vr\ o^-No

    o\ t rcw\to coln t^.^* Vt^t^!g

    l v

    Ap\\.o*'o tv \l' dr\ no\\^ \

    xr ' + Y.8r* \ ) = o6 V < I r + 2 ( I t ' = d

    A g\\.o*-"o Lv X v\/\ "^'or\\a 2

    K L r r ' J - ) - I V - 2 ( 4 K 1 ' ) = O- G K f r + ? ( 5 t = - L

    I :\s\ax.",a \,, ^ tJ a-s'

    . [c , 2 l [ r , ] - I o IK Lt ,JL'-'l=L'1\ - - - l I - r - > l [\ t ' \ r \ r : ' l \ o 1 * AL t , I = , ' l e G IL t \r : IL rLo)+af , ) ] = t *0 ,

    I I o4 K r

    _97r o = + - 7 _ = 9 * A

    ) { e/ ' 3 .+ j ! l l? ' ,

    + v {

    + .----.--

    { 3 ' b

  • C b r + ( r ^ ( \ * 4 -t* *o 3* 'i r.1g i*ri.?r\t{ J a ee> urla { '1"-s\s, \eqL\ , ' } r , ' \vr ,^ , , . i \

    z= \lV P+hov

    oi

    R\\6,

    : ) R+xev

    0 0 ,,\ c\a4 K

    -L: \ = 4\(I J-nl4

    xr\ votfo;< &n1ev

    b v

    J) 5a, d.porta z\ z\u"neut\o ln\ovry;j ."rt" v Rvv,rr. o\'u*\'-J'.;;

    ,^^.* {**U ' \ V, 6Ka1 l . . . -

    \V

    A p\i ca',\o LV l^ e\^ n6\\a- \ A v \ 4 \ ^ 1 r + 2 ( l = O

    G ( 1 , = \ 2I r = l : 2 r " 4

    6 'A p,\i cavtl ., tV ( ov\ IoVob O e'r.(r,*A) - L fon lYg

    \ \

    Ag\**il" L v ' c' =."":tt ;

    L" \ r +?K t I r - l t ) =^!8 t l l r - 2 X I = O

    ne.^..." L'r1 .: $]).t.1,t , i - ax [1*-I ' )+AY'\! :-Avr ts.-\J + 44 u < r 2 : - \

    \

    t

    t * A

    t O + n S ; v

    \r \ .'1... : ,'t (l i C l-- \t\ i ':l . 1\ I T '

    . r t- . - r - . " L A ( ' n u \ c \ r \ r -

    Vr^b = 4'=)

    [\ru4) C"\ c*\ ,,

    V = - l e VV

    : ) V s = - 6 V

    V ' r - J 6= : -12"n V0

    T ' = !R'trnc

    - -r-L \t - *

    *AJ

    R+vW

    - - \ / RlrcuL2

    V

    = 4\l-\ V

    nCI

    * yo-., t' r r F

    .

    lv '' ,

    . \ +i I , v :

    K

    -l ev

  • ' t * \ g* t \

    \

    )

    ba

    , l,l Ag\ica^s Lul ^ uto"o l

    r [u, + GY) +:,v, - 3"^A = P6K (l.

    I -I- *!) V, ( + \ )/{ -.,"vt = oL G 2 I , /- L V , = 2 - n - V , : a v3

    Do\ c,..,i\ur "p[i*^do

    LV t/\

    er\ , WrO.Vr, \O

    /qU =Vlv,o, -'Vn - t( ! *Vo,oiO K

    V+hor= V1 +. V, - 0 = O: G V

    Col*\o c' Voo= 3 V

    j

    ?