UNIVERSIDAD TECNOLÓGICA METROPOLITANA FACULTAD DE INGENIERÍA DEPARTAMENTO DE ELECTRICIDAD
APUNTES INTRODUCCIÓN ANÁLISIS DE CIRCUITOS UNIDAD Nº 1: CIRCUITOS DE CORRIENTE CONTINUA ANÁLISIS FUNDAMENTAL FUNDAMENTAL
PROFESOR
: HÉCTOR PINO CORTÉZ CORTÉZ
2015
CONCEPTOS INTRODUCTORIOS FORMA DE EMPLEO DEL TEXTO O!ETIVOS GENERALES DE CADA UNIDAD UNIDAD N"# $CIRCUITOS DE CORRIENTE CONTINUA$
%I&'()*+,,-.& %O/'-)3 G&(4#3 %D34(()##) * #4 U&-*4* %R3+3'4 4 P()/#643 P()+3')3 %T3' %T3' * A+')4#+4,-.& %S)#+,-.& 4 T3' T3' * A+')4#+4,-.& %-/#-)7(4894
CONCEPTOS INTRODUCTORIOS E# 44&, ('-7-&)3) *# + ;4,( ',&)#.7-,) ;4, + <-3'4 +&4 (#4,-.& 6+= 3'(,;4 &'( #43 *-(343 *-3,-#-&4& '>,&-,43? = 6@3 4+&? & 6+,;)3 ,43)3 +&4 *&*&,-4 *-(,'4 &'( ##43 E3 439 + #)3 ,)&,')3 '>,&-,)3 3 '(43#44& & # *&-( 4,'+4# = # 3'+*-4&' * ,+4#+-( *-3,-#-&4 '>,&-,4 &) */ 3'4( 4&) 4 3'4 (4#-*4* L4 #,'(-,-*4* B& ,)((-&'3 #>,'(-,43 8+&'3 = #4 #,'(.&-,4 B& ,)((-&'3 #>,'(-,43 *>/-#3? ,)& 3+ -&6&34 -6#-,4&,-4 = 4#-,4,-.& ;4,& + >3')3 34& #6&')3 * , & 3+ (#4,-.& ,)& )'(43 *-3,-#-&43 *-3,-#-&43 = P)( &* 3+ 3'+*-) 3'+*-) = 3+ 4&@#-3-3 &) */& 3'4( 4+3&'3 * ,+4#+-( 3'+*-) 3-3'6@'-,) E# (46) A&@#-3-3 * R*3 1 & #4 ,4(((4 * E#,'(.&-,4 ? '-& )( )/'-) &'(74( #)3 ,)&),-6-&')3 4*,+4*)3 4(4 #)7(4( +&4 8)(64,-.& -&'7(4# *# 4#+6&) F)(64 * E6#4( *# T<') E3' '<') 3'@ )(-&'4*) ;4,-4 # 4#+6&)? + 3'+*-4 6'.*-,46&'? /+3,4&*) (-6() 4*+-(-( #)3 ,)&,')3 = *3+>3 #4 ;4/-#-*4* 4(4 4#-,4(#)3 C)((3)&* 4 +& ,+(3) & # ,+4# 3 *34(()##4 #4 ')(94 * A&@#-3-3 A&@#-3-3 * C-(,+-')3 E#>,'(-,)3 & 3+ *8-&-,-.& * 3-3'643 ,)&'-&+)3 = 4#'(&)3
CONCEPTOS INTRODUCTORIOS FORMA DE EMPLEO DEL TEXTO O!ETIVOS GENERALES DE CADA UNIDAD UNIDAD N"# $CIRCUITOS DE CORRIENTE CONTINUA$
%I&'()*+,,-.& %O/'-)3 G&(4#3 %D34(()##) * #4 U&-*4* %R3+3'4 4 P()/#643 P()+3')3 %T3' %T3' * A+')4#+4,-.& %S)#+,-.& 4 T3' T3' * A+')4#+4,-.& %-/#-)7(4894
CONCEPTOS INTRODUCTORIOS E# 44&, ('-7-&)3) *# + ;4,( ',&)#.7-,) ;4, + <-3'4 +&4 (#4,-.& 6+= 3'(,;4 &'( #43 *-(343 *-3,-#-&4& '>,&-,43? = 6@3 4+&? & 6+,;)3 ,43)3 +&4 *&*&,-4 *-(,'4 &'( ##43 E3 439 + #)3 ,)&,')3 '>,&-,)3 3 '(43#44& & # *&-( 4,'+4# = # 3'+*-4&' * ,+4#+-( *-3,-#-&4 '>,&-,4 &) */ 3'4( 4&) 4 3'4 (4#-*4* L4 #,'(-,-*4* B& ,)((-&'3 #>,'(-,43 8+&'3 = #4 #,'(.&-,4 B& ,)((-&'3 #>,'(-,43 *>/-#3? ,)& 3+ -&6&34 -6#-,4&,-4 = 4#-,4,-.& ;4,& + >3')3 34& #6&')3 * , & 3+ (#4,-.& ,)& )'(43 *-3,-#-&43 *-3,-#-&43 = P)( &* 3+ 3'+*-) 3'+*-) = 3+ 4&@#-3-3 &) */& 3'4( 4+3&'3 * ,+4#+-( 3'+*-) 3-3'6@'-,) E# (46) A&@#-3-3 * R*3 1 & #4 ,4(((4 * E#,'(.&-,4 ? '-& )( )/'-) &'(74( #)3 ,)&),-6-&')3 4*,+4*)3 4(4 #)7(4( +&4 8)(64,-.& -&'7(4# *# 4#+6&) F)(64 * E6#4( *# T<') E3' '<') 3'@ )(-&'4*) ;4,-4 # 4#+6&)? + 3'+*-4 6'.*-,46&'? /+3,4&*) (-6() 4*+-(-( #)3 ,)&,')3 = *3+>3 #4 ;4/-#-*4* 4(4 4#-,4(#)3 C)((3)&* 4 +& ,+(3) & # ,+4# 3 *34(()##4 #4 ')(94 * A&@#-3-3 A&@#-3-3 * C-(,+-')3 E#>,'(-,)3 & 3+ *8-&-,-.& * 3-3'643 ,)&'-&+)3 = 4#'(&)3
P4(4 #4 ,)6(&3-.& 3-3'6@'-,4 * 3' '<')? 3 (+-( * (((+-3-')3 /@3-,)3 '4#3 ,)6): Á#7/(4 * M4'(-,3 = D'(6-&4&'3? Á#7/(4 V,')(-4# ? T)(94 * C46) E#,'()647&>'-,) ? Á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
% R,)&),( R,)&),( 6>')*)3 = ')(643 ')(643 + (6-'4& (6-'4& +&4 4*,+4*4 (3)#+,-.& (3)#+,-.& & ,-(,+-')3 ,-(,+-')3 #>,'(-,)3 * ,)((-&' 4#'(&4 UNIDAD I CIRCUITOS DE CORRIENTE CONTINUA INTRODUCCIÓ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
FIGURA 1
E#,'()&3 = &,#) * +& @')6) É# &,#) 3'> 8)(64*4 4( *-(343 4('9,+#43? * #43 ,+4#3 #43 6@3 -6)('4&'3 4(4 #4% #,'(-,-*4* 3)& #)3 #,'()&3 L)3 #,'()&3 4# 7-(4( 4#(**)( *# &,#) ,(4& *-(343 .(/-'43 ) &-#3 * &(794? #)3 C+4#3 3 *3-7&4& ,)& #43 #'(43 J? L? M? N? O? ,4*4 +&4 * #43 ,+4#3 +*& 4,'4( +&4 ,4&'-*4* 6@<-64 * #,'()&3 L4 ,44 J? L4 ,44 L? L4 ,44 M? L4 ,44 N?
3 3 3 3
,)6#'4 ,)& *)3 #,'()&3 ,)6#'4 ,)& ),;) #,'()&3 ,)6#'4 ,)& *-,-3>-3 #,'()&3 ,)6#'4 ,)& '(-&'4 = *)3 #,'()&3
L)3 #,'()&3 *# #'-6) &-# ) ,44 <'(&4 3 *&)6-&4& #,'()&3 * 4#&,-4 E# 3'4*) &)(64# * +& @')6) 3 * #>,'(-,46&' &+'()? 3 *,-(? + #4 ,4&'-*4* * ,4&'-*4* * ,4(743 &74'-43 3 ,4(743 )3-'-43 3 -7+4# 4 #4 ,4&'-*4* * ,4(743 &74'-43 A#7+&)3 @')6)3 +*& ,*( ) 4,'4( +&) ) 643 #,'()&3 * 4#&,-4 U& @')6) + ;4 ,*-*) #,'()&3 * 4#&,-4 3 *&)6-&4 I)& )3-'-)? +& @')6) + ;4 4,'4*) #,'()&3 * 4#&,-4 3 *&)6-&4 I)& &74'-) L)3 #,'()&3 3-'+4*)3 & #43 .(/-'43 <'(643 * #)3 @')6)3 +*& 3( *3(&*-*)3 * ##43 ,)& (#4'-4 84,-#-*4* = 3 ,)&-('& & #,'()&3 #-/(3 E& ,46/-)? #)3 #,'()&3 3-'+4*)3 & #43 .(/-'43 -&'(&43 3)& 4'(49*)3 )( # &,#) ,)& 8+(4 6+,;) 64=)( + #)3 #,'()&3 * #43 .(/-'43 <'(&43K )( 3'4 (4.&? 3 6+= *-89,-# + #)3 @')6)3 3 *3(&*4& * #)3 #,'()&3 * #43 ,443 + .(/-'43 -&'(&43? ##46@&*)3 )( 3' 6)'-) #,'()&3 $8-)3$ L)3 @')6)3 + '-&& 3+3 ,443 #,'(.&-,43 ,)6#'43 )( 6#): H#-)? N.&? A(7.&? ',? 3)& +96-,46&' -&4,'-)3? E& ,46/-)? #)3 @')6)3 + '-&& 3+3 ,443 #,'()&-,43 -&,)6#'43 +*& ,)6/-&4(3 = +&-(3 4(4 8)(64( 6)#>,+#43? ,)6#'@&*)3 #43 ,443 #,'(.&-,43 E& 7&(4#? #43 ()-*4*3 +96-,43 * +& #6&') *&*& * #4 3'(+,'+(4 * #4 ,44 #,'(.&-,4 <'(&4 L)3 8&.6&)3 #>,'(-,)3 3 <#-,4& )( # 6)-6-&') * #43 #,'()&3 #-/(3 &'( #)3 @')6)3 E#,'(-,-*4* 3 +* ##464( 4 #4 ,4+34 * ,-(')3 8&.6&)3? 4 #)3 ,+4#3 3 #3 *4 # &)6/( * 8&.6&)3 #>,'(-,)3? ) 6)( *-,;)? 3 4 3')3 8&.6&)3 6-36)3 ,)&3-*(4*)3 & 3+ ')'4#-*4* 4 #)3 + 3 4#-,4 # &)6/( * #,'(-,-*4* L)3 #,'()&3 1-/(3 <+#34*)3 )( +& Á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
FIGURA 2 FIGURA E& # ,-(,+-') #>,'(-,) * #4 8-7+(4 #4 ,4&'-*4* * 47+4 ,)((3)&* 4 #)3 #,'()&3 + 3 +-( *3#44( 4(4 + ;4=4 #,'(-,-*4* P4(4 + 3' *3#446-&') ),+((4 3 &,34(-) + <-3'4 +& *3&-# ) (3-.& #>,'(-,4? + ##464(6)3 )#'4 C+4&*) ;4= +& *3&-# &'( *)3 3'4&+3 & # ,-(,+-') ;-*(@+#-,)? # 47+4 * +& 3'4&+ 3,+(( 4 '(4>3 * #4 ,4(94 ;43'4 # )'() 3'4&+ S- <-3' +& *3&-# ) )#'4 & +& ,-(,+-') #>,'(-,)? ;4/(@ '46/->& +& 6)-6-&') ) *3#446-&') * #,'()&3 4# + ##464(6)3 3 ,)((-&' #>,'(-,4 BI E# 47+4 + 4 )( # -&'(-)( * +&4 ,4(94 ()4 #43 4(*3 * >3'4 = ,)6) #43 4(*3 & #4 (@,'-,4? (3&'4& 43(43? 3') ;4, + #4 ,)((-&' * 47+4 B# &6() * #-'()3 )( 37+&*) &,+&'( +&4 (3-3'&,-4 )( 4(' *# 64'(-4# + 3 '(4*+, & ,4#)(? D# 6-36) 6)*)? # ,43) #>,'(-,)? #4 *-8-,+#'4* + (3&'4 # 64'(-4# 4# 43) * #4 ,)((-&' #>,'(-,4 3 *&)6-&43 R3-3'&,-4 E#>,'(-,4 BR S +* 8@,-#6&' -3+4#-4(? + &'( #)3 ,)&,')3 * )#'4? ,)((-&' = (3-3'&,-4 <-3' +&4 3'(,;4 (#4,-.& + 3-( * /43 4# 3'+*-) * #4 #,'(-,-*4*% 122 L= D O;6 E# 893-,) A#6@& S-6.& O;6? *3,+/(-. + #4 -&'&3-*4* * #4 ,)((-&' *&*94 3)#46&' * #4 *-8(&,-4 * )'&,-4# = * #4 (3-3'&,-4? *# ,)&*+,')( R#4,-)&4&*) 3'43 '(3 ,4&'-*4*3 ##7. 4# 3-7+-&' &+&,-4*): L4 -&'&3-*4* * ,)((-&'? & +& ,-(,+-') #>,'(-,) 3 *-(,'46&' ())(,-)&4# 4 #4 *-8(&,-4 * )'&,-4# -&(346&' ())(,-)&4# 4 #4 (3-3'&,-4 B1 I =
V R
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
FIGURA E# A&@#-3-3 * C-(,+-') '-& )( )/') ,)&),( #43 (#4,-)&3 &'( <,-'4,-.& = (3+3'4 4(4 +&4 (* ,)&),-*4 3 *-, + 3'43 (#4,-)&3 &'( <,-'4,-.& = (3+3'4 3)& 8+&,-)&3 ()-43 * #4 (* S- 3 ,)&),& #4 <,-'4,-.& (3+3'4 *34*4? 3 +* ,4#,+#4( #4 (* L4 <,-'4,-.& ##464*4 '46/->& 8+&'? 3 +& *-3)3-'-) + -&'()*+, &(794 *3* # <'(-)( 4# ,-(,+-') E3'4 &(794 3(@ '(4&38)(64*4 =Q) '(4&36-'-*4 )( #4 (* L43 <,-'4,-)&3 = #43 (3+3'43? & #) + 4 A&@#-3-3 * ,-(,+-') 3 (8-(? +*& 3( )#'43 ) ,)((-&'3 P)*6)3 '46/->& D8-&-( # )#'4 B) *-8(&,-4 * )'&,-4# &'( *)3 +&')3 4 = / * +& ,-(,+-')? ,)6) # '(4/4) ,+'4*) )( +&4 ,4(74 +&-'4(-4 )3-'-4 4# 434( * $4$ ;4,-4 $/$ b
V a
a
− V = V = − ∫ Edl = ∫ Edl b
ab
a
b
EL )#'4 V *8-&-*) & #4 ,+4,-.& 4&'(-)(? 3 ##464*) $C49*4 * )'&,-4#$ )(+ -6#-,4 + # )'&,-4# *# +&') $4$ 3 64=)( + # )'&,-4# *# +&') $/$ %C)((-&'A: S *8-& )( -&'&3-*4* * ,)((-&' #>,'(-,4? #4 ,4&'-*4* * ,4(74 #>,'(-,4 + 4'(4-34 )( +&4 3,,-.& '(4&3(34# * +& ,)&*+,')( & #4 +&-*4* * '-6) E3 *,-(? #4 -&'&3-*4* 3 #4 (4.& &'( #4 ,4(74 = # '-6) + *6)(4 & 434( )( +&4 3,,-.& '(4&3(34# * +& ,)&*+,')( S+ +&-*4* * 6*-*4 3 # 46( A D3-7&4&*) #4 -&'&3-*4* )( I? (3+#'4: B2 I =
q t
Bamperes C
U& 46( 3 #4 -&'&3-*4* * +&4 ,)((-&' #>,'(-,4 ,+4&*) 434 #4 ,4(74 * +& ,)+#)6/ & +& 37+&*)? )( +&4 3,,-.& '(4&3(34# * +& ,)&*+,')( S 4/(-4 )( A S- #4 ,4&'-*4* * ,4(74 4(94 ,)& (3,') 4# '-6)? 3 '-# *8-&-( #4 ,)((-&' #>,'(-,4 6*-4 & +& #43) * '-6) ,)6): O /-& i
=
Q t
i
=
dQ dt
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ÓN DE LA LE DE OHM E6#) N"1 S ,)&,'4 4 +& % ,-(,+-') #>,'(-,)? ,+=4 *-8(&,-4 *) )'&,-4# 3 * 1?5 )#'3? +& 4('84,') ,+=4 (3-3'&,-4 3 * 2 B S -*4 *'(6-&4( #4 -&'&3-*4* * ,)((-&' + ,-(,+#4 )( 3' ,-(,+9')
S)#+,-.&: V 15V R 2 I < A#-,4&*) ,+4,-.& B1
I =
V
=
15 V
R
2 R
= 0W5B amperes C
E6#) N"2 S- ,)&,'46)3 +&4 ,464&-##4 * 2B 4 +&4 8+&' * &(794? = )( # ,-(,+-') ,-(,+#4 +&4 ,)((-&' * 0?5 BA S -* *'(6-&4( # )#'4 + 7&(4 #4 8+&' * &(794
S)#+,-.& A&@#)746&' 4 6#) N" 1 I = 0?5 BAC V = < V = R • I V = 0?5 • 2 V = 1 )#' BVC
1 CALCULO DE RESISTENCIA E& #)3 #6&')3 ,44,3 * ,)&*+,-( #4 ,)((-&' #>,'(-,4? <-3' +&4 7(4& *-8(&,-4 &'( ##)3 & #) + 4 (3-3'&,-4 3 (8-(? 3 )( 3') + #4 #,'(-,-*4* +* 3( ,)&*+,-*4 4 )#+&'4* = )( #43 6*-43? + 6@3 ,)&&74& A'&*-&*) 4 3+ (3-3'&,-4? #)3 ,+()3 #)3 )*6)3 *--*-( & *)3 7(4&*3 7(+)3: C)&*+,')(3 = A-3#4*)(3 C)&*+,')(3 3)& 4+##)3 ,+()3 + 84,-#-'4& # 43) * #4 ,)((-&' #>,'(-,4K +*& 3( 6'@#-,)3? #,'()#9'-,)3 = 743)3)3 P4(4 8,')3 * 3' ,+(3)? 3)#) ,)&'6#4(6)3 4 #)3 ,)&*+,')(3 6'@#-,)3 E&'( #)3 ,)&*+,')(3 6'@#-,)3 #? 6)( 3 #4 #4'4 37+-*) *# ,)/( L)3 *6@3 6'4#3 = 4#4,-)&3 '-&& 7(4&*3 4(-4/#3 * ,)&*+,'--*4* A-3#4*)(3 S)& 4+##)3 + )8(,& 7(4& (3-3'&,-4 4# 43) * #4 ,)((-&' #>,'(-,4 E&'( #)3 4-3#4&'3 '&6)3: 4,-'3? -*(-)? )(,#4&4? 4#? /)&-'4? 8-/(4? ,4+,;)? ', E& (4#-*4*? &) ;4= +&4 *8-&-,-.& & 3&'-*) 3'(-,') P+3') + #)3 /+&)3 4-3#4&'3 * 4#7& 6)*) '46/->& 3)& ,)&*+,')(3
P4(4 4&4#-4( #)3 ,)&*+,')(3 ;4= + &'&*( + ,+4#+-(4 * ##)3 3-6( )8(, 4#7+&4 (3-3'&,-4 4# 43) * #4 ,)((-&' #>,'(-,4? 4(4 &'&*( 6)( #)3 84,')(3 * #)3 ,+4#3 *&* #4 (3-3'&,-4? )*6)3 (8(-(&)3 &+46&' 4 #4 8-7+(4 2% P)*6)3 )/3(4( + #4 ,4(94 3 # 6*-) ,)&*+,')( *# #9+-*)? 3 )( #) '4&') #4 + ))& (3-3'&,-4 4 3+ 43) L4 (3-3'&,-4 + ))&& #)3 ,)&*+,')(3 4# 43) * #4 ,)((-&'? 3 +* 43),-4( 4# 8,') * ()46-&') 6,@&-,) + -6-* 4# #-/( *3#446-&') * #)3 ,+()3 E& #4 8-7+(4 ? ,)&3-*(4(6)3 +&4 ,4(94 B) +& ,)&*+,')( ,)64(4&*) 3,,-.& #)&7-'+* = 43(4 * #43 4(*3
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
S- 3 ,)&), #4 (3-3'--*4* * +& 64'(-4#?% +* *'(6-&4(3 #4 (3-3'&,-4 * +& ,)&*+,')( * ,+4#+-( #)&7-'+* = 3,,-.& '(4&3(34#? 4#-,4&*) #4 3-7+-&'3 8.(6+#43 B R =
ρ ⋅ l
Ω
A
E& *)&* R (3-3'&,-4 *# ,)&*+,')( & O;63 1 #)&7-'+* *# ,)&*+,')( & 6'()3 A @(4 * #4 3,,-.& '(4&3(34# *# ,)&*+,')( & 66 ρ
2 Ω ⋅ mm =
m
C4/ ;4,( &)'4( + #4 #)&7-'+*? # @(4 * #4 3,,-.& '(4&3(34# = #4 (3-3'--*4* * #4 ,+4,-.& B? */& * 3'4( & +&-*4*3 ,);(&'3 4(4 <(34( # 4#)( * #4 (3-3'&,-4 & );63 E6#) C4#,+#4( #4 (3-3'&,-4 * +& ,)&*+,')( * ,)/( + '-& +&4 #)&7-'+* * 50 6'()3 = +&4 3,,-.& * 0?5 662 S)#+,-.& R = < L = 50 6'()3 S = 0?5 66 Ω ⋅ 662
: = 001Z
6
D 4,+(*) 4 ,+4,-.& B: R =
L
⋅
:
=
s
E# 4#)( * M4'(-4#
50
⋅
0?01Z
05
= 1ZΩ
4(4 # ,)/(
3 )/'-& * #4 '4/#4 &"1
( B(3-3'--*4* & 6
4 & J%1
4 0 º ,&'97(4*)3 B2W2 J
RBTRB0ºB1 Y 4 T
A#+6-&-) C4(/.& C)&3'4&'@&
2 < 10% 500 < 10% [0 < 10%
20 < 10%5 %50 < 10%5 D3(,-4/#
C)/(
1 < 10%
20 < 10%5
H-(() L4'.& M4&74&-&4 M(,+(-) N-,()6 P#4'4 P#)6) )#8(46-) '+&73'&) O()
120 < 10% W0 < 10% < 10% [ < 10% 111 < 10% 1 < 10% 22 < 10% ) 5 < 10% 2 < 10%
20 < 10%5 200 < 10%5 D3(,-4/# < 10%5 0 < 10%5 00 < 10%5 0 < 10%5 0 < 10%5 < 10%
C)&*+,'4&,-4 A39 ,)6) ,#43-8-,46)3 #)3 64'(-4#3 ,)&3-*(4&*) 3+ (3-3'&,-4 ) ,)64(4*)3 6-(4&*) #4 *-8-,+#'4* + ))&& 4# 43) * #4 ,)((-&' ? +*& ,#43-8-,4(3 '46/->& & ,+4&') 4 #4 84,-#-*4* * ,)&*+,,-.& S &'-&* &')&,3 )( ,)&*+,'4&,-4? #4 84,-#-*4* + '-&& 4#7+&)3 ,+()3 4(4 ,)&*+,-( #4 ,)((-&' L4 <(3-.& 4(4 #4 ,)&*+,'4&,-4 3: G=
1 R
B MC
S+ +&-*4* * 6*-*4 3 # S-6&3 ) 6;) 1 EFECTOS DE LA TEMPERATURA SORE LA RESISTENCIA L4 (3-3'&,-4 #>,'(-,4 * ')*)3 #)3 ,)&*+,')(3 6'@#-,)3 4+6&'4 4 6*-*4 + >3')3 4+6&'4& * '6(4'+(4 C+4&*) 3 +-( '&( +& 4#)( 6+= <4,') * #4 (3-3'&,-4 3 */ 4&)'4( #4 '6(4'+(4 4 + 3 ;-) #4 6*-,-.& \ C)8-,-&' * '6(4'+(4 B]: A# 4+6&') * (3-3'&,-4 & );63? )( ,4*4 );63 * (3-3'&,-4 = )( ,4*4 7(4*) * '6(4'+(4? 3 # ##464 ,)8-,-&' * '6(4'+(4 = 3 # *3-7&4 ,)& #4 #'(4 ] B'4/#4 &"1 T)*)3 #)3 ,+()3 &) 3)& 48,'4*)3 & #4 6-364 ())(,-.& O( L)3 ,46/-)3 * '6(4'+(4? * 6)*) &')&,3? + 4 ,4*4 64'(-4# ,)&*+,')(? 439 ,)6) # ,)((3)&* +& ,)8-,-&' ) # ,)((3)&*4 '46/->& +& ,)8-,-&'] L4 8.(6+#4? 6*-4&' #4 ,+4# 3 *'(6-&4 # 4+6&') * (3-3'&,-4 )( # 8,') * #4 '6(4'+(4 3: R 2
= R1B1 + α 1 Bt 2 − t 1 B5
R2 R3-3'&,-4 8-&4# 4(4 +&4 '6(4'+(4 '2 R1 R3-3'&,-4 -&-,-4# *'(6-&4*4 4 '1 ] C)8-,-&' 4(4 +&4 '6(4'+(4 ' '2 '6(4'+(4 8-&4# & 7(4*)3 1, '1 '6(4'+(4 -&-,-4# & 7(4*)3 , L4 '4/#4 &" 1 -&*-,4 #)3 4#)(3 *'(6-&4*)3 4 20", B] 20 A#7+&)3 4#)(3 3)& *'(6-&4*)3 4(4 ] 4 ,() 7(4*) B]) C+4&*) 3 *4 +& 4#)( * R1? 4(4 +&4 '6(4'+(4 '1 + &) 34 0" 0 20"? 3 */ ,4#,+#4( ]1 3)/( #4 /43 * ]) ? 6*-4&' #4 8.(6+#4 α 0 1 B = α 1 = 1 + α 0 t 1 1 + t 1 α 0
S- 3 ,)&), 4(4 ' = 3 &,3-'4 *'(6-&4( 4(4 +& *'(6-&4*) 64'(-4#? * #4 ,+4,-.& B '&6)3:
=
α 1
BW 1 − α 1t 1 E& #4 ,+4,-.& B5? 3- (6#44(&)3 B '2 % α 0
'1 )( T :
R2 = R1 B 1 + α 1 ) (8)
S-&*) T # 4+6&'4 * '6(4'+(4 * +& ,)&*+,')( E6#): U& ,)&*+,')( * ,)/(? 4 #4 '6(4'+(4 46/-&' B20",? '-& +&4 (3-3'&,-4 * 15 );63 ^C+@# 3(@ #4 (3-3'&,-4 * 3' 6-36) ,)&*+,')( 4 50",_ S)#+,-.& D 4,+(*) 4 #4 ,+4,-.& B5:
= R1B 1 + @1 (τ 2 − τ 1)) Ρ = 15 ( 1 + Ο,00393 (50 − 20)) Ρ = 16.768 R2
P)( #) '4&')? #4 (3-3'&,-4 4 50", 3 * 1?W );63 = # 4+6&') * #4 (3-3'&,-4 8+ * 1?W );63 4(4 +& 4+6&') * 0" 3)/( #4 '6(4'+(4 46/-&' E6#) S ;4 6*-*4 #4 (3-3'&,-4 * #)3 &()##4*)3 * +& 6)')( 4&'3 * &'(4( & 8+&,-)&46-&')? = >3'4 3 -7+4# 4 20 B);6 B4 20",` D3+>3 * +& ,-(') '-6) * 8+&,-)&46-&') 3 +# 4 6*-( #4 (3-3'&,-4 = >3'4 3 * 2 );63 S *34 34/( 4 + '6(4'+(4 3 &,+&'(4& #)3 &()##4*)3 S)#+,-.&
R = 20 Ω
Ρ = 24Ω Τ = t 2 − t 1 = x A#-,4&*) ,+4,-.& B: R2
= R1 B1 + α 1t C
R2
= R1 + R1α 1T
R2 − R1 T =
= R1α 1T
R2 − R1 R1α 1
P)( #) '4&'): T=
2M % 20 20 f 000Z
⇒ T = 50°c
P(): T = ' 2 % '1 ⇒ ' 2
= T + ' 1 = 50 + 20 =
W0°,
15%UNIDADES DE MEDIDA DE LOS CONDUCTORES ELÉCTRICOS P4(4 3,-8-,4( +& *'(6-&4*) '-) * ,)&*+,')(? 3 &,34(-) 34#4( 3+ *-@6'() =Q) 3,,-.& L43 3,,-)&3 ,)6(,-4#3 3 &,+&'(4& &)(64#-4*43? 439 '&6)3? + 4-(4 # S-3'64 SI BS-3'64 I&'(&4,-)&4# # *-@6'() 3 <(34 & 66 = #4 3,,-.& & 66 P4(4 ># 3-3'64 I&7#>3? # *-@6'() *# ,)&*+,')( 3 <(34 & +#74*43 ) & 6-#3 = #4 3,,-.& & +#74*43 = ,)6&6&' & ,-(,+#4( 6-#3 BCM D8-&-&*): 1 M-# 0?001 a+#74*4 1 C6 Á(4 * +& C)&*+,')( ,+=) *-@6'() 3 -7+4# 4 1 M-# D 4,+(*) 4 #) 4&'(-)(: 1 C6 bQ B10c%c2 bQ < 10c% B+#7 0?50W<10c% B66 1 66 1[W?55 C6 %d 2000 C6 B4(4 3'-64,-)&3 (@,'-,43 S- # *-@6'() B* * +& ,)&*+,')( 3 <(34 & M-#3? = 3+ @(4 BA & C6 ? (3+#'4 -7+4# 4: A bQ B* < 10c%c2 K & +#74*43 *c2 E& ,)&3,+&,-4? #4 3,,-.& * +& ,)&*+,')( <(34*) K& C6 , :e -7+4# 4# ,+4*(4*) * 3+ *-@6'() <(34*) & M-#3 E& #4 3,-8-,4,-.& * #)3 *-@6'()3 B,4#-/( * ,)&*+,')(3 & ':# 3-3'64 I&7#>3? (3 6+= +'-#-4*) # 3-3'64 AG BA6(-,^6 - ( G47 E3' 3-3'64 3 *8-& & /43 4 +&4 3(-1 * ,4#-/(43? & # ,+4# #4 (43 +& &'( *-@6'()3 ,)&3,+'-)3 3
64&'-& ,' E# (-6( ,4#-/( *g #4 3(- 3 -,#&'-%8-,4 ,)6) Q0%%0000 h = 3 # 43-7&4 4(/-'(4(-46&' +& *-@6'() -7+4# 4 0 M-#-3 A# ,4#-/( N2 * #4 3(- 3 # 43-7&4 4(/-'(4(-46&' +& *-@6'() -7+4# 4 5 M-#3 E&'( #)3 ,4#-/(3 34#4*)3? <-3'& #)3 3-7+-&'3 *-@6'()3: N" 0000Q0 000Q0 002Q0 01Q0 1 2
D-@6'() & M-#3 0Q1 0 0Qi 0Qi 0Qi 0Qi 0Qi
0Qi 5
L4 (4.& J &'( *-@6'()3 ,)&3,+'-)3? 3 )/'-& * #4 (#4,-.& &'( #)3 <'(6)3 34#4*)3: MS0 5
=
MS0 MS0 L[
k
L4 T4/#4 N"2 6+3'(4 #4 (#4,-.& &'( 4#7+&)3 4#)(3 * 3,,-)&3 = *-@6'()3 ,)6(,-4#3 TALA N" 2 CALIRE D-46
A(4
AG M>'(-,) (&6
CM2
M62
Qi -
Qi6
0000 000
11 100 100 [2 [0 252 0
211?00 1W 00 155?000 1?100 125500 105 00 [[?200
10W2 501 W5 W 2 5[ 502W
00[01 0011 00[1 00WW[ 002 00[21 01055
010 0202 021[5 0255W 02W11 0222 00
W000 5 0 52W 51[ 50 20 5 115
W5?[50 0 55 00 52 20 1 W0 W50 0[0 1?[0 2 20
[ 2 22W 2W 2115 1[ 1WW 15[0 10
0155 0152 015 01[W0[ 02W 02W 012 00[ 0[52
00 0512 00[ 0W 0152 0W1 102 10 12[W
00 0 1 2 5
100 [0 0 W0 0 50 5
R3-3'&,-4
0
W
5
[ 10 11 12 1 1 15 1 1W 1
0 25 20 1 1 12 10
0 5 5 2 0 2[0 25 25 20 205 20 1 1 1 1 15
2 20?20 1 [[0 1 510 1?[50 1 0[0 100 [ W 20 50 ?200 5 10 5 022 110 [ ?20
125W 1055 [22 W W0 1 521 [0 1W0 10 12 20 255 20 201 1 9 50
12[ 12 1150 102 100
250 2 22 2050 1?20 1?550
110 111 100 02 0?W5
011[ 0[1 051 021 0W 0W[22 0[[[1 10W0 1202 152 1W2W 20021 2051 252 21W 11 % 01[ 5 505[0 01[ [10
1W2 1 1W[2 201 2[ 25[[ 2W 51 15 5211 5 5[ WW 2W[ 5W 0 11[ 1525 15[[ 21005 2I[5
1% POTENCIA ELÉCTRICA P)*6)3 *,-( + 3 8,'4 '(4/4) ,+4&*) +&4 8+(4 6+ +& ,+() 4 +&4 ,-('4 *-3'4&,-4 L4 ,4&'-*4* * &(794 + 3 -&-(' & # 6)-6-&') *# ,+() 3 -7+4# 4# '(4/44 (4#-4*4 E& # 3-3'64 SI * +&-*4*3? +& )+# * &(794 ((3&'4 #4 ,4&'-*4* * '(4/4) (4#-4*) )( +&4 a8+(4 * +& &j')& + 4,'4 3)/( +&4 *-3'4&,-4 * +& 6'() P)( #) '4&')3 B[ W
= F ⋅ d
E& *)&*: E&(794 & )+#3 B! F F+(4 & &j')& BN * D-3'4&,-4 & 6'()3 B* E& 8)(64 4&@#)74? 3 ;4, '(4/4) ,+4&*) +&4 8+&' * )#'4 ;4, 6)( +&4 ,4(74 #>,'(-,4 4 '(4>3 * +&4 *-8(&,-4 * )'&,-4#k L4 ,4&'-*4* * &(794 ,)&3+6-*4 & # 6)-6-&') * ,4(743 #>,'(-,43 3 -7+4# 4# '(4/4) (4#-4*) D 4,+(*) 4 #)3 ,)&,')3 ('-*)3? #4 )'&,-4 & +& ,-(,+-') #>,'(-,) 3 *8-& ,)6 #4 #),-*4* * '(4&38(&,-4 * &(794 = 3 <(34 7&(4#6&' & j4''3 ) & )+#3 )( 37+&*) E& ,+4#+-( -&3'4&' * '-6)? #4 )'&,-4 #>,'(-,4 + 3 &'(74 4 +& ,-(,+-')? 3 -7+4# 4# ()*+,') * #4 ,)((-&' * &'(4*4 & 46(3 = #4 '&3-.& * <,-'4,-.& & )#'3: B1O P
= V ⋅ I
E& *)&*: P P)'&,-4 & j4''3 I C)((-&' & 46(3 V V)#'4 & /)#43
L4 +&-*4* * )'&,-4 #>,'(-,4 3 # j4''3 1 j4''3 1 )#' = 1 46( S *-, + +&4 64+-&4 4/3)(/ +&4 )'&,-4 * +& j4'' ,+4&*) 4# 4#-,4(# 1 )#' ,)&3+6 #4 ,)((-&' * 1 46( E6#) S- '&6)3 4#-,4*) 4 +& ,-(,+-') #>,'(-,)? +& )#'4 * 22BJV = )( # ,-(,+#4 +&4 ,)((-&' * 20BA ^C+4# 3(@ #4 )'&,-4 ,)&3+6-*4 )( 3' ,-(,+-')_
S)#+,-.& V = 220BV I = 20 BA = < D #4 ,+4,-.& B10 = VfI = 220 f 20 = 00 j4''3 = ? Jj 11 O'(43 F)(6+#43 * P)'&,-4 E& /43 4 #4 ,+4,-.& B#0 = ;4,-&*) -&'(&-( # F4,')( (3-3'&,-4? 3 +*& *4( )'(43 <(3-)&3 4(4 #4 )'&,-4 D #4 ,+4,-.& B10 '&946)3: P
= V ⋅ I
P)( )'(4 4('? * #4 ,+4,-.& B1 3 '-& +: V
= R ⋅ I
S+3'-'+=&*) ,+4,-.& B# & ,+4,-.& B10? '&6)3 +: P = R ⋅ I ⋅ I = R ⋅ I
2
B11
L4 ,+4,-.& B1 &)3 (6-' *'(6-&4( #4 >(*-*4 * )'&,-4 )( ,4#)( & #43 (3-3'&,-43
S +* )/3(4( +&4 '(,(4 8.(6+#4 4(4 ,4#,+#4( #4 >(*-*4 * )'&,-4 ,4#.(-,4 & +&4 (3-3'&,-4 D #4 ,+4,-.& B1? '&6)3: I=
V R
S+3'-'+=&*) ,+4,-.& B1 & ,+4,-.& B10? '&6)3 +: B12 P = V ⋅
V R
⇒ P =
V
2
R
L43 +&-*4*3 6@3 +34*43 & #4 (@,'-,4 3)& # HP = # 4'' ,)& 3+3 6#'-#)3 = 3+/6#'-#)3 1 HP W j4'' 0?W Jj 1 Jj 1? HP E6#) U&4 8+&' * 20 B 3 ,)&,'4 4 +&4 (3-3'&,-4 * D'(6-&4( #4 )'&,-4 *-3-4*4 & #4 (3-3'&,-4? +'-#-4&*) #43 '(3 8.(6+#43 * )'&,-4 S)#+,-.& V 2 B20 2 = = = W200 B = W?2 BJj R I=
V R
=
2M0 Z
= 0A
= I 2 ⋅ R = B0 2 ⋅ B = W200 = W?2 Jj = V ⋅ I = B20 B0 = W?2 Jj 1W TRAA!O ELÉCTRICO D #4 ,+4,-.& B11? 3 *3(&* +& -6)('4&' (-&,--) F93-,)? 64&-83'@&*)&)3 + 3- +&4 (3-3'&,-4 R 3 (,)((-*4 )( +&4 ,)((-&' I = # ,4#)( ()*+,-*) +-4# 4 +&4 &(794 -7+4# 4# ()*+,') * R- <(34*) & j4''3 ) & )+#Q37 D-, '46/->& + ,+4&*) +&4 (3-3'&,-4 R? 3 (,)((-*4 )( +&4 ,)((-&' I? 3 ()*+, +&4 >(*-*4 * &(794 #>,'(-,4 + 44(, /4) 8)(64 * ,4#)( = ,+=) 4#)( 3: R f I E3'4 3(94 #4 &(794 743'4*4 & #4 +&-*4* * '-6) B1 37 D+(4&' ' 37 #4 &(794 743'4*4 3(94
Rf92f'? + 3 '(4&38)(64 ')'4#6&' & ,4#)( E3') 3 <(34 7&(4#6&' *-,-&*) + 3 ()*+, & # ,)&*+,')( ) (3-3'&,-4 +&4 >(*-*4 * &(794 )( 8,') )+# L4 ##464*4 #= * )+#? )*(946)3 &+&,-4(14 * #4 3-7+-&' 64&(4: E& ')*) ,)&*+,')( (,)((-*) )( +&4 ,)((-&' #>,'(-,4 3 ()*+, ,4#)( L4 8.(6+#4 *# '(4/4) ) &(794 (*-*4 )( 8,') )+# 3: T = R ⋅ I 2 ⋅ ' B)+# ) j4'' % 37+&*) B1 O 34? # ,4#)( ()*+,-*) & +& ,)&*+,')( (,)((-*) )( +&4 ,)((-&' #>,'(-,4? 3 ())(,-)&4# 4 #4 (3-3'&,-4? 4# ,+4*(4*) * #4 ,)((-&' = 4# '-6) L4 &(794 *34(()##4*4 & +& ,)&*+,')( = + 3 '(4&38)(64 ')'4#6&' & ,4#)(? )*(94 <(34(3 #.7-,46&' & ,4#)(943 S4/6)3 + <-3'& *)3 '-)3 * ,4#)(943? + 3)& #4 ,4#)(94 7(4&* = #4 ,4#)(94 +4 J-#),4#)(94 BCAL E3 #4 ,4&'-*4* * ,4#)( &,34(-4 4(4 #4( & +& 7(4*) ,&'97(4*) #4 ,4&'-*4* * 1 #-'() * 47+4 C4#)(94 7(46) B,4# E3 #4 ,4&'-*4* * ,4#)( &,34(-4 4(4 #4( & - 7(4*) ,&'97(4*) #4 ,4&'-*4* * +& 7(46) * 47+4 L+7)? +&4 ,4#)(94 7(46) 3 -7+4# 4 0?001 * J-#),4#)(94 L)3 '(4/4)3 * 4#7+&)3 893-,)3 *6)3'(4()&? + 1 CAL +* '(4&38)(64(3 & '(4/44 6,@&-,) ()*+,-&*) 25 J76? ) /-& # '(4/4) 6,@&-,) +* '(4&38)(64(3 & ,4#)( 3-&*) (,-3) 4(4 ##) 743'4( 25 J76 4(4 ()*+,-( +&4 CAL R3+6-&*)? '&6)3 + 1 CAL 25 J76 R#4,-.& &'( # !)+# = #4 CAL S4/6)3 +: 1 J76 [?1 )+# = + B1 1 CAL 25 J76 B15 P)( #) '4&')? (#4,-)&4&*) ,+4,-.& B1 ,)& ,+4,-.& B15? '&6)3: 1CAL = 25 f [?1 )+#3 1CAL = 1W0 )+#3? = 1CAL = ?1W )+#3 P)( #) '4&'):
1 CAL 1W0 1 )+# = 0?0002 CAL 1 )+# = 0?2 ,4# 1 )+# =
B1
S- <(346)3 #4 ,4&'-*4* * ,4#)( *34(()##4*) )( +& ,)&*+,')( ,)& #4 #'(4 l? )*6)3 3,(-/-( &')&,3: l = 0?2 R f Ic2 f ' ,4#? ) l = 0?0002 R f Ic2 f ' CALB1W mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm mmmmmmmmmmmmmm R3+6-&*): A# *8-&-( #4 )'&,-4? ;4/946)3 *-,;) + >3'4 (4 -7+4# 4# '(4/4) *34(()##4*) (- #4 +&-*4* * '-6)? 4 34? TQ' D 3'4 8.(6+#4 &)3)'()3 )*6)3 *34( T : Tf' E3') &)3 *-, + # '(4/4) 3 -7+4# 4 #4 )'&,-4 6+9 '-#- ,4*4%)( # '-6) D 4,+(*) ,)& #43 *-8(&'3 8.(6+#43 '- )'&,-4 + ;4/946)3 **+,-*)? #4 8.(6+#4 *# '(4/44 +* <(34(3 439 : T = R ⋅ I 2 ⋅ '
)?
T = V ⋅ I ⋅ '
S-&*) # '(4/4) # ()*+,') * +&4 )'&,-4 )( # '-6)? #43 +&-*4*3 & + 3 <(34 # '(4/4) 3(@&: +&-*4*3 * )'&,-4 )( +&-*4*3 * '-6)? = 3'43 +*& 3(: 4''%37 1 j4'' )( +& 37+&*) 4''%;)(4 1 j4'' )( +&4 ;)(4 J-#)j4''%;)(4 1J9#)j4'' )( +&4 ;)(4 BJj; E# '(4/4) ) &(794 #>,'(-,4 3 (7-3'(4 ) 3 6-* )( 6*-) * 44(4')3 ##464*)3 6*-*)(3 ) ,)&'4*)(3 * &(794 E6#)
E& +&4 ,434 ;4/-'4,-.& ;4= 46)##'43 * O j4''3 ,4*4 +&4? ,)&,'4*43 *+(4&' ,+4'() ;)(43 *-4(-43K +& 4&48( #>,'(-,) * 500 j4''3 ,)&,'4*) *+(4&' 6*-4 ;)(4 *-4(-4: +&4 (4*-) * W5 j4''3 ,)&,'4*4 3-3 ;)(43 *-4(-43K +&4 #4&,;4 * 5OO j4''3 ,)&,'4*4 *+(4&' 3-3 ;)(43 364&4#3 C4#,+#4( # 743') 6&3+4#? 3- # Jj%; 4# n?0 S)#+,-.& 1 46)##'43 * O Bj ,4*4 +&4? *+(4&' ,+4'() ;)(43 *-4(-43 12O ;(3 2 1 4&48( * 5OO Bj *+(4&' 6*-4 ;)(4 *-4(-4 15 ;(3 1 (4*-) * W5 Bj *+(4&' 3-3 ;)(43 *-4(-43 1O ;(3 1 #4&,;4 * 500Bj *+(4&' 3-3 ;)(43 362 ;(3 T 1 = P 1 ⋅ T 1 P 1 = ⋅ 0 = 0BW T 1 = 120hrs T 1 = 0 ⋅120 = 200BW − H T 1 = 2B KW − H T 2 = P 2 ⋅ T 2 P 2 = 500BW T 2 = 15hrs T 2 = 500 ⋅ 15 = W500BW − H T 2 = W5B KW − H T = P ⋅ T P = W5BW T = 10hrs T = W5 ⋅10 = 1500BW − H T = 15B KW − H
T = ⋅ ' K = 500 T = 500 ⋅ 2 = 12000 B % H T = 12 BJ % H P)( T' T' T'
#) = = =
K ' = 2 ;)(43
'4&'): T1 + T2 + T + T ?2 + W?5 + 1?5 + 12 W?2 BJ % H
P)( #4 '4&'): G43') 6&3+4# W?2 f ? n2W?2 E6#) C4#,+#4( #4 ,4&'-*4* * ,4#)( *34(()##4*) )( +&4 #4&,;4 #>,'(-,4 * OO j4''3? ,)&,'4*4 *+(4&' *)3 ;)(43 S)#+,-.&
B%H ) B)+#3
T = X ⋅ ' T = L00 ⋅ 2
= S00
PROLEMAS PROPUESTOS 1 D'(6-&4( # #4(7) * +& ,)&*+,')( * ,)/( ,+=4 (3-3'&,-4 3 * = ,+=4 3,,-.& 3 * 1?5 66 2 A 0" * '6(4'+(4 +& ,)&*+,')( * 4#+6-&-) 6-* 10 );63 * (3-3'&,-4 ^,+@# 3(@ 3+ (3-3'&,-4 4 50", L4 (3-3'&,-4 * +& &()##4*) 4 #4 '6(4'+(4 46/-&' B20" 3 * 5? *3+>3 * +& 6)6&') * 3'4( ,)&,'4*) 3 ;4 +#') 4 6*-( = 3+ 4#)( 3 * ?5 B ^,+@# 3 # 4+6&') * '6(4'+(4 + ;4 <(-6&'4*)_ ^C+@# * #43 3-7+-&'3 ,)6/-&4,-)&3 * ,)((-&' = '-6) ()*+,-(@? +& 64=)( ,)&3+6) * &(794 & +&4 (3-3'&,-4 * 05 4 150 A 4(4 1 37+&*) / O A 4(4 37+&*)3 , 25 A 4(4 0 37+&*)3
1% CONEXIÓN DE RESISTENCIAS T)*)3 #)3 ,-(,+-')3 #>,'(-,)3 ,)&'-&& 3,,-)&3 ,)&,'4*43 & 3(-? & 4(4##) ) 46/43 L43 #=3 8+&*46&'4#3 + (-7& # ,)6)('46-&') * 3')3 3-3'643? ())(,-)&4& #43 ;((46-&'43 /@3-,43 4(4 # 4&@#-3-3 * ')*)3 #)3 ,-(,+-')3? -&,#+3) #)3 6@3 ,)6#)3 11o R3-3'&,-43 & S(-
FIGURA W P4(4 ,)&,'4( (3-3'&,-43 & 3(-? 3 ,)&,'4& +&43 4 ,)&'-&+4,-.& * #43 )'(43 * 6)*) + ')*43 34& (,)((-*43 )( #4 6-364 ,)((-&' L4 (3-3'&,-4 ')'4# * +& ,-(,+-') 8)(64*) )( $N$ (3-3'&,-43 & 3(-? 3 -7+4# 4 1 ^3+64 * #43 (3-3'&,-43 4(4##43 R' = R1 + R2 + R + + R&
B1ZC
L4 ,)((-&' + ,-(,+#4 )( # ,-(,+-') 3 ,)64& 4(4 ')*43 #43 (3-3'&,-43 = 3+ 4#)( 3 *'(6-&4 * 4,+(*) 4 #4 ,+4,-.& B1 S- #4 ,)((-&' 434 4 '(4>3 * '-&4 (3-3'&,-4? 3 ()*+, & >3'4 +&4 ,49*4 * '&3-.& ) )#'4 + 3 ())(,-)&4# 4 #4 (3-3'&,-4 = 4 #4 ,)((-&' + 434 4 '(4>3 * ##4? ,9 64&(4 + & #4 8-7+(4 W? 3 '&*(@& '(3 ,49*43 * )#'4 V 1
= I ⋅ R1
V 2
= I ⋅ R2
V
= I ⋅ R
L43 (#4,-)&3 &'( #4 ,)((-&'? = # )#'4? -&;(&'3 4 #43 (3-3'&,-43? ,)&,'4*43 & 3(-? 3 *34(()##4& ,)& 4=+*4 * #43 #=3 8+&*46&'4#3 * );63 = * J9(,;;)88 L= * )#'43 * J-(,;;)88 BLVJ E& ,+4#+-( ,-(,+-') #>,'(-,) 3 ,+6# + #4 3+64 4#7/(4-,4 * #43 '&3-)&3 * <,-'4,-.& 4#(**)( *# ,-(,+-') 3 -7+4# 4 #4 3+64 4#7/(4-,4 * #43 ,49*43 * )#'4 4 '(4>3 * #)3 #6&')3 *# ,-(,+-') P)( #) '4&')? #4 3+64 * #)3 )#'43 & ,4*4 (3-3'&,-4? &)3 */& *4( # )#'4 4#-,4*) 4# ,-(,+-')
= V 1 + V 2 + V E& 7&(4#? 4(4 +& ,-(,+-') 8)(64*) )( $N$ (3-3'&,-43 & 3(- 3 ,+6# + B1[ V = V 1 + V 2 + V + + V V T
T
N
E6#)3 P4(4 # ,-(,+-') * #4 8-7+(4 BW R W K R 10 K R 5 C4#,+#4( 4 R3-3'&,-4 ')'4# +-4#&' *# ,-(,+-') / L4 ,)((-&' + ,-(,+#4 )( # ,-(,+-') , L)3 )#'43 & #43 (3-3'&,-43
S)#+,-.& 4 RT
/
= R1 + R2 + R = W + 10 + 5 = 22Ω
I = VQR = 220 Q 22 = 10 BAC
, V1 = I = W ⋅10 = W0 BV V2 = I = 10 ⋅10 = 100 BV V = I = 5 ⋅ 10 = 50 BV L4 3+64 ,9 #43 '(3 ,49*43 * )#'4 */& *4(&)3 # )#'4 4#-,4*) V' = V1 + V2 + V = W0 + 100 + 50
= 220BVC
12% R3-3'&,-4 & 4(4##)
FIGURA B P4(4 ,)&,'4( (3-3'&,-43 & 4(4##)? 3 ,)&,'4 & 8)(64 * (46-8-,4,-)&3 * 6)*) + ,4*4 <'(6) * ##43 3'> +&-*) 4 ,)&*+,')(3 * (3-3'&,-4 *3(,-4/# C)&,'4*43 #43 (3-3'&,-43 * 3' 6)*)? # )#'4 4#-,4*) 3 ,)6& 4(4 ')*43 ##43 = #4 ,)((-&' 3 (4(' ())(,-)&4#6&' * 4,+(*) 4# 4#)( (,9(),4 * ,4*4 (3-3'&,-4 ,)&,'4*4 & 4(4##4 D #4 8-7+(4B? #43 ,)((-&'3 3(@&:
I 1
V 1
=
R1
− I 2 =
V 2 R2
− I =
V R
() V1 V2 V P)( #) '4&') I 1
V
=
R1
− I 2 =
V R2
− I =
V R
, L= * C)((-&'3 * J-(,;;)88 BLCJ L4 3+64 4#7/(4-,4 * ')*43 #43 ,)((-&'3 + ##74& 4 +&4 +&-.& 3 -7+4# 4 #4 3+64 4#7/(4-,4 * ')*43 #43 ,)((-&'3 + 34#& * >3'43 A#-,4&*) LCJ 4# ,-(,+-') * #4 8-7+(4 ? '&6)3: I T
= I 1 + I 2 + I
E& )'(43 4#4/(43? #4 ,)((-&' ')'4# * +& ,-(,+-') 8)(64*) )( (3-3'&,-43 & 4(4##)? 3 -7+4# 4 #4 3+4'4 * #43 ,)((-&'3 * ,4*4 (464 G&(4#-4&*)? 4(4 N (3-3'&,-43 ,)&,'4*43 & 4(4##) I T
= I 1 + I 2 + I +
B20
+ I
N
E<(34&*) #43 ,)((-&'3 )( #43 (4643 & 8+&,-.& * #4 #= * );6 4(4 +& ,-(,+-') ,)& N (3-3'&,-43 ,)&,'4*43 & 4(4##) V
1 1 1 1 = V ⋅ + + + + R R1 R2 RL
R
+
+
V
I T
R2
+
V
=
R1
+
V
I T
R N
N
S4/6)3 +: R
=
V I T
V
= V
1 1 1 1 ⋅ + + + + R R1 R2 RL
N
B21 R
=
1
1 1 1 + + + + 1 R R1 R2 RL
N
1 1 1 1 = + + + + R R R1 R2 RL 1
N
B22
P)*6)3 ,)&,#+-( +: E& +& ,-(,+-') 8)(64*) )( BN R3-3'&,-43 & 4(4##)? # 4#)( (,9(),) * #4 (3-3'&,-4 ')'4# 3 -7+4# 4 #4 3+64 * #)3 4#)(3 (,9(),)3 * #43 R3-3'&,-43 4(,-4#3
1 C43)3 E3,-4#3 1 C43) * *)3 (3-3'&,-43 & 4(4##): 1 R
=
1 R1
+
1 R2
R ⋅ R + R2 = ⇒ R = 1 2 R1 ⋅ R2 R1 + R2
B2
R1
F-7+(4 [ 2 C43) * *)3 R3-3'&,-43 -7+4#3 ,)&,'4*43 & 4(4##): P)( #)? '4&') R
=
R1 ⋅ R2 R1
+ R2
⇒ R =
R1
2
2 R1
⇒ R =
R1
2
L4 R3-3'&,-4 ')'4# * +& ,-(,+-') 8)(64*) )( *)3 (3-3'&,-43 -7+4#3 ,)&,'4*43 & 4(4##)? 3 -7+4# 4 #4 6-'4* *# 4#)( * +&4 * ##43 P4(4 # ,43) * BN (3-3'&,-43 -7+4#3 ,)&,'4*43 & 4(4##): B2 R =
R N
P)( #) '4&')? #4 (3-3'&,-4 ')'4# * +& ,-(,+-') 8)(64*) )( 4(-43 (3-3'&,-43 -7+4#3 ,)&,'4*43 & 4(4##)? 3 -7+4# 4# 4#)( * +&4 *--*-*) )( # &6() * ##43 1% C)&<-.& 6-<'4 * R3-3'&,-4 C+4&*) & +& 6-36) ,-(,+-') 3 ,)&,'4& (3-3'&,-43 & 3(- = & 4(4##)? 3 *-, + 3 '-& +& 4,)#46-&') 6-<') * (3-3'&,-43 P4(4 (3)#( 3')3 ,-(,+-')3 = *'(6-&4( # 4#)( * #4 (3-3'&,-4 ')'4#? 3 (3+#& (-6() #)3 7(+)3 & 4(4##) E& 3'43 ,)&*-,-)&3? ,+4#+-(4 + 34 # &6() * (3-3'&,-43 ,)&,'4*43 & 4(4##)? 3 4 ')64&*) 4(4 (3)#(#43 * *)3 & *)3 = 3 4 3-6#-8-,4&*) # ,-(,+-') ;43'4 ##74( 4 3)#) +&4 (3-3'&,-4 +-4#&' 4(4##) D 3'4 64&(4? 3 3+64& ')*43 #43 (3-3'&,-4 & 3(- 4 + 3 ;4=4 (*+,-*) # ,-(,+-') = '&*(6)3 # 4#)( * #4 (3-3'&,-4 ')'4# E6#)? R3)#( # 3-7+-&' ,-(,+-'):
S)#+,-.&
R A = R1 ⋅ R2 Q BR1 + R2 = 5 ⋅ QB5 + = 2?W2 Ω RC
= Ρ 4 ⋅ Ρ 5 / ( Ρ 4 + Ρ 5) = 7 ⋅ 8/(7 + 8) = 3,73Ω
E# ,-(,+-') &)3 +*4 (*+,-*) 4
RT"TA#
= R + R + R A!
C
= 2W2 + + W = 105Ω
E# ,-(,+-') *# 6#) 1 +*4 (*+,-*) 4
R3)#+,-.& * #4 (* )( (*+,,-)&3 3+,3-43 R FG
=
10 2
= 5Ω
E# ,-(,+-') +*4:
REl
=
RL ⋅ BRM
+ R5 = W?5 B RL + BRM + R5
E# ,-(,+-') +*4 (*+,-*) 4
RA R1 Y R2 Y REl 1W?5 F-&4#6&' # ,-(,+-') *# 6#) 2? +*4 (*+,-*) 4:
1%M>')*) * 3)#+,-.& )( ,)((-&'3 * 64##43
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
F-7+(4 10 N+*)3 E3 # +&') * #4 R* *)&* ,)&(7& '(3 ) 6@3 ,)&*+,')(3 BF-7+(4 11
F-7+(4 11 R7#4 * #)3 N+*)3K L4 3+64 4#7/(4-,4 * #43 ,)((-&'3 + 3 *-(-7& 4 ,+4#+-( &+*) * #4 (* 3 ,()
∑
i
=0
B25
R7#4 * #43 64##43: L4 3+64 4#7/(4-,4 * #43 %F6? & +&4 64##4 ,+4#+-(4 * +&4 (*? 3 -7+4# 4 #4 3+64 4#7/(4-,4 * #43 ,49*43 * )#'4
∑ =∑ $
⋅ =0
B2
R i
L4 (-6(4 (7#4 <(34 + #43 ,)((-&'3 &) 3 4,+6+#4& & +& +&')? 3-&) + &'(4& = 34#& A 3' (3,')? ,)&&,-)&4# 6&' #43 ,)((-&'3 + &'(4& 4# &+*) 3 #43 E& '4&') + #43 ,)((-&'3 + 34#& 3 #43 *3-7&4 ,)& # 3-7&) $%$ I1 % I2 % IL % IM = 0
BFIGURA 11
A 6&+*)? # 3&'-*) * #43 ,)((-&'3 3 *3,)&), ,+4&*) 3 #4&'4 +& ()/#64 * 64##43 E# (-6( 43) & #4 3)#+,-.& * +& ()/#64 6*-4&' #4 4#-,4,-.& * #43 (7#43 * J-(,;;)88? 3 43-7&4( +& 3&'-*) * #43 86 = ,)((-&'3 P4(4 # ,43) * #43 ,)((-&'3? 3- # 3&'-*) 43-7&4*) 3 ((.&)? # (3+#'4*) &+6>(-,) 4 + 3 ##74 3-6( 3 # 6-36) E# 3&'-*) (4# & + ,-(,+#4 #4 ,)((-&' 3 )/'-& * #4 3)#+,-.& 4#7/(4-,4 *# ()/#64 S- # 4#)( &,)&'(4*) 4(4 #4 ,)((-&' (3+#'4 ,)& 3-7&) &74'-)? 43-7&4*) +-( *,-( + # 3&'-*) (4# 3 ,)&'(4(-) 4# 43-7&4*) E& (#4,-.& 4 #43 (7#43 * #43 64##43? 3-6#6&' )'(4 4#-,4,-.& * #4 #= * O;6 E3 -*&'? + 3- 3 4(' * +& +&') & +& ,-(,+-') = 3 3-7+ )( #)3 ,)&*+,')(3 + 8)(64& #4 64##4 ;43'4 4#,4&4( * &+) # 6-36) +&')? *-,;) +&') */ &,)&'(4(3 4# 6-36) )'&,-4# + '&94 4# (-&,--) *# (,)((-*) P)( #) '4&')? #43 86 + 3 4=4& &,)&'(4&*)? */& 3( &,34(-46&' -7+4#3 4 #43 ,49*43 * '&3-.& & #43 (3-3'&,-43? *4&*) 4 ,4*4 +&4 * ##43 # 3-7&) 4*,+4*) P4(4 #4 8-7+(4 12? ^C+@# 3(@ #4 ,)((-&' = #4 '&3-.& & #)3 *-3'-&')3 +&')3 *# ,-(,+-')_
F-7+(4 12 C)6) #43 /4'(943 3'@& & ))3-,-.&? #4 ,)((-&':
E1 E2 = R1 I =
⋅I+
R2 ⋅ I
+
RL
⋅
I
− e2 10 − = = 05 A R1 + R2 + R 1+ 2 + 5 e1
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p ,)((-&' = )#'43 4(4 #)3 &+*)3 = 64##43 ())(,-)&4& # &6() * ,+4,-)&3 -&*&*-&'3 &,34(-43 4(4 (3)#( #)3 4#)(3 * ,)((-&' = )#'4 *3,)&),-*)3 E# &6() * ,+4,-)&3 -&*&*-&'3 * ,)((-&' 3 -7+4# 4# ')'4# * &+*)3 6&)3 +&) E& #4 8-7+(4 Íl? 3 '&*(@& '(3 ,+4,-)&3 * ,)((-&' -&*&*-&'3? +3') + ;4= ,+4'() &+*)3 4? /? ,? *: 4 / C
i
− i1 − i 2 = 0
i1
− iL − i M = 0
i2
− iL + i5 = 0
E6#)3 * R3)#+,-.&
M4##4 1
E4
% E/ F6 ')'4# 4#-,4*4 4 64##4 1
EA % E = R1 ⋅ I1 + R2 ⋅ I1 + R ⋅ I1 % R2 ⋅ I2 EA % E = I1BR1 + R2 + R I2 ⋅ R2 D3-7&4*) )(: R11 = R1 + RL + RL
R12 % R2
BR3-3'&,-4 ()-4 * #4 64##4 1
? B(3-3'&,-4 6+'+4 &'( 64##43
EA % E E1? F6 T)'4# 4#-,4*4 4 #4 64##4 1 P)( #) '4&'): E1 = I1⋅ R11 + R12 ⋅ I2
#º E,+4,-.& * 64##4
M4##4 2 E % EC
=
R2 ⋅ I2 + RM ⋅ I2 + R5 ⋅ I2 % R2 ⋅ I1
E % EC E A&@#)746&':
E % EC = I2BR2 + R + R5 I1⋅ R2 R2 + R + R5 = R22 % R2 = R21 E2 = R21 ⋅ I1 + R22 ⋅ I2
2*4 E,+4,-.& * 64##4
P#4&'4&*) 3-3'64 * ,+4,-.& E1 E2
= =
R11 ⋅ I1 + R12 ⋅ I2 R21 ⋅ I1 + R22 ⋅ -2
N)3 (6-' *'(6-&4( I1 I2 ? (3)#-&*) )( *'(6-&4&'3: I 1 =
=
P()
1 R11
R12
R 21
R 22
= R11 ⋅ R 22 − R12 ⋅ R 21 = R11 ⋅ R 22 − R12 2
R21R12%R2 S-&*) 1 =
I 2
=
E 1
R12
E 2
R 22
= E 1 ⋅ R 22 − E 2 ⋅ R12
2
D)&* 2
=
I 1 = I 2
=
R11
E 1
R 22
E 2
= E 2 ⋅ R11 − E 1 ⋅ R 21
E 1 ⋅ R 22 − E 2 ⋅ R12 R11 ⋅ R 22 − R12
2
E 2 ⋅ R11 − E 1 ⋅ R 21 R11 ⋅ R 22 − R12
2
R3)#(
E,+4,-.& * 64##43: E1 = R11 f I1
+ R12 f I2
E1 = R21 f I1
+ R22 f I2
D)&*: R11 R1 Y R R22 R2 Y R R12 R21 R L43 ,+4,-)&3 * 64##43:
%E1 B R1 Y R f I1 aRfI2 64##4 1 E2 B R2 Y R f I2 aRfI1 64##4 2 R6#44&*) 4#)(3: %10 10 I1 % [ I2 2O % [ I1 Y 10 I2 R3)#-&*) *'(6-&4&'3 I1
I2
− 10 − [ 20 10 − 100 + 1Z0 Z0 = = = MA2 A 100 − Z1 1[ 10 − [ − [ 10
10 − [ 10 − [
− 10 20 200 − [0 110 = = = 5 A − [ 100 − 1 1[ 10
L4 ,)((-&' * 64##43? 3 -7+4# 4 #4 ,)((-&' * (464? 3-&*): I2 -2 5? BA I1 %-1 Y ?2 BA d -1 % ?2 A#-,4&*) #4 (-6(4 LJC 4# &+*) A
L4 3+64 4#7/(4-,4 * #43 ,)((-&'3 O P)( ,)&&,-.& 3-&*) #43 ,)((-&'3 + ##74&BY = B % #43 + 34#&? 15?% $T)(64 D T;&-&$ E# T)(64 * ';&-& 3 )'() * #)3 ,)&),-*)3 + &)3 (6-' ,)&('-( +& ,-(,+-') ,)6#) & +& ,-(,+-') +-4#&' 3&,-##) E3' ')(64 &)3 *-, + +&4 (* 4,'-4 ,+4#+-(4 6-(4*4 *3* *)3 '(6-&4#3 * ##4? 3 -7+4# 4 +&4 8+&' * '&3-.& ,)& +&4 (3-3'&,-4 & 3(-? &
*)&* #4 8+&' * '&3-.& 3 -7+4# 4# )#'4 + (3&'4 #4 (* & ,-(,+-') 4/-('4 &'( #)3 '(6-&4#3 #7-*)3 = #4 (3-3'&,-4 & 3(- 3 -7+4# 4 #4 (3-3'&,-4 + (3&'4 #4 (*? 6-(4*4 *3* #)3 '(6-&4#3 & (8(&,-4 C-(,+-') )(-7-&4#
C-(,+-') * '(4/4)
C-(,+-') +-4#&'
C@#,+#) * V';
C@#,+#) * R'; 1?% C-(,+-') E+-4#&' * N)(')& L4 3,,-.& +-4#&' * N)(')& 3 3-6-#4( 4# +-4#&' * T;&-&? <,') + ,)&3'4 * +&4 8+&' * ,)((-&' *&)6-&4*4 ,)((-&' * N)(')& E# ')(64 * N)(')& 3 +34 4(4 3-6#-8-,4( +& ,-(,+-') & '>(6-&)3 ,9 ,)((-&' & #+74( * )#'4 E# +-4#&' * N)(')& +* *'(6-&4(3 *# +-4#&' * T;&-& = -,(34? )( 6*-) * #4 3-7+-&' (#4,-.&: ZN)(')& ZT;&-& IN)(')& ET;QZT;
E6#)3
1 D'(6-& VT; = RT; = *-/+ # &+) ,-(,+-') 2
∗ + R 2 + R5 R1 + R M Rth = = 2Ω R1 ∗ R M + R 2 + R5 R1 + R M R1 R M
R';115
V'; 1V I 1 =
5 5
= 10 A
I2?A V4/ RfI2 V4/ 5f? 1?V
E!EMPLO 4
/
1W% T(4&38)(64,-.& E3'(##4 T(-@&7+#) C-(,+-')3 6@3 ,)6#)3 + #)3 ,)6+3')3 * ,)6/-&4,-)&3 3&,-##43 & 3(- = 4(4##)? +*& (*+,-(3 4 8)(643 6&)3 ,)6#43 +'-#-4&*) #43 '(4&38)(64,-)&3 3'(##4o'(-4&7+#) 1 $C)&(3-.& T(-@&7+#) 4 E3'(##4$
D 4,+(*) 4 8-7+(4 1K R1 =
Ra ⋅ Rb Ra + Rb + Rc
R 2 =
Rc ⋅ Rb Ra + Rb + Rc
R =
Ra ⋅ Rc Ra + Rb + Rc
2 $C)&(3-.& E3'(##4 4 T(-@&7+#) D 4,+(*) 4 %8-7+(4 1K Ra = Ra =
Rc =
R1 ⋅ R 2 + R2 ⋅ R + R ⋅ R1 R 2 R1 ⋅ R 2 + R 2 ⋅ R + R ⋅ R1 R R1 ⋅ R2 + R2 ⋅ R + R ⋅ R1 R1
S- ')*43 #43 (4643 * +&4 3,,-.& & '(-@&7+#) 4 & 3'(##4 '-&& -6*4&,-43 -7+4#3? #4 3,,-.& 3 *&)6-&4 '(-@&7+#) ) 3'(##4 +-#-/(4*4 P)( #) '4&') '&6)3 +:
∆ = L R%
R
B2[
E6#)
D 4,+(*) 4 #4 ,+4,-.& B2 R B10 B10 Y 10 B10 Y 10 B10Q 10 00Q10 0 R2 00Q10 0 R 00Q10 0 PROLEMAS PROPUESTOS
1 C4#,+#4( #4 (3-3'&,-4 ')'4# *# ,-(,+-') * #4 8-7+(4 3-7+-&'
2 P4(4 # 3-7+-&' ,-(,+-')
D'(6-&4(: 4 L4 (3-3'&,-4 * &'(4*4 / L4 ,)((-&' ')'4# + ,-(,+#4 )( # ,-(,+-') , # )#'4 & #4 (3-3'&,-4 * 5 E& # ,-(,+-') * #4 8-7+(4
C4#,+#4( # )#'4 &'( q4%/d = #43 ,)((-&'3 O/'&74 # ,-(,+-') +-4#&' * #4 8-7+(4 3-7+-&'? 4 '(4>3 * #43 '(4&38)(64,-)&3 3'(##4 '(-@&7+#) ('-&&'3
5 E&,)&'(4( # +-4#&' T;&-& *# ,-(,+-') 3-7+-&' &'( #)3 '(6-&4#3 4 = /
TEST DE EVALUACIÓN 1 L4 (3-3'&,-4 * +& ,)&*+,')( * A#+6-&-) * ,-('4 #)&7-'+* 3 0 4 0"C ^C+@# 3 # @(4 * #4 (3-3'&,-4 4 20º C_
2 D'(6-&4( #4 (3-3'&,-4 * +& ,)&*+,')( * 4#+6-&-) * +&4 #)&7-'+* * 5 6 ,+=4 3,,-.& '(4&3(34# (,'4&7+#4( 3 * 066 )( 2066 D'(6-&4( # *-@6'() * +& ,)&*+,')( * ,)/( * 1?5 J6 * #4(7) = ,+=4 (3-3'&,-4 3 * 1?5 D'(6-&4( # +-4#&' * #43 3-7+-&'3 (3-3'&,-43 ,)&,'4*43 & 3(-: ?10?5?0 5 E# +-4#&' * 3-3 (3-3'&,-43 ,)&,'4*43 & 3(- 3 * 10 J S- #)3 4#)(3 * ,-&,) * #43 (3-3'&,-43 3)&: 1000K 200? 100? 000 = 500 (3,'-46&'? *'(6-&4( # 4#)( .;6-,) * #4 3<'4 (3-3'&,-4 U'-#-4&*) #4 8.(6+#4 4*,+4*4? *'(6-& #4 (3-3'&,-4 +-4#&' & ,4*4 +&) * #)3 3-7+-&'3 ,)&+&')3 * (3-3'&,-43 & 4(4##) 4 #00 = 0 / 5 = 500 K , 2 J = 2 J K * 0?01 = 100 W V-&' (3-3'&,-43 * 12 3'@& ,)&,'4*43 & 4(4##) 4 +&4 8+&' * OV D'(6-&4( #4 ,)((-&' ')'4# &'(74*4 )( #4 8+&' L4 (3-3'&,-4 * +& &()##4*) 4 #4 '6(4'+(4 46/-&' * 20ºC 3 * 5K *3+>3 * +& 6)6&') * 3'4( ,)&,'4*) 3 ;4 +#') 4 6*-( = 3+ 4#)( 3 * ?5 ^C+@# 3 # 4+6&') * Tº + ;4 <(-6&'4*)_ [ U& 3)#*4*)( #>,'(-,) +'-#-4 Jj%; * &(794 & 12;(3? ,+4&*) 3 ,)&,'4 4 +&4 8+&' * 120 D'(6-&4(: 4 #4 )'&,-4 *# 3)#*4*)(K / #4 ,)((-&'K ,d #4 (3-3'&,-4 *# 3)#*4*)( 10 E& # ,-(,+-') 3-7+-&'? ,4#,+# #4 )'&,-4 &'(74*4 )( #4 8+&' 6*-4&' # 6>')*) * #43 64##43
11 R3)#( #4 64##4 * #4 8-7+(4 3-7+-&' & 3+3 *-3'-&')3 4#)(3 * ,)((-&'
