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ÍNDICE
• OBJETIVOS………………………………………………………. 3
• MATERIALES UTILIZADOS ……………………………………. 3
• CIRCUITOS A UTILIZAR …………………………………………6
• PROCEDIMIENTO ………………………………………………. 7
o CASO I ………………………………………………… 7
o CASO II………………………………………………… 8
o CASO III……………………………………………….. 9
•
CUESTIONARIO ………………………………………………… 10• CONCLUSIONES Y RECOMENDACIONES ………………… 28
o CONCLUSIONES…………………………………….. 28
o RECOMENDACIONES……………………………… 29
• BIBLIOGRA!A ………………………………………………….. 29
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RESONANCIA EN CIRCUITOS ELÉCTRICOS
LINEALES
I. OBJETIVOS
• E"#$%#& ' #(#$)*#& +( ,-&# +/+&)+(#$ $#
#+&4)# 5+ &+-(#()# +( )&%)- +$&)-
$)(+#$+.
II. MATERIALES UTILIZADOS
• 1 +(+-& 5+ -(5# )(%-)5#$+.
Figura 1 Generador de ondas.
• 1 #(+$ 5+ -(5+(#5-&+.
Figura 2 Condensadores.
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• 1 %$4+&- 5))#$ AC VR.
Figura 3 Multímetro digital.
• 3 %$4+&- 5))#$+ AC VC: VL: V.
Figura 4 Multímetros digitales.
• 1 ;-;)(# 5+ 87.2< =.
Figura 5 Bobina.
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• 1 &+)+()# 5+ .
Figura 6 Resistencia variable.
• J%+- 5+ -(5%-&+.
Figura Cable conductores.
• 1 A%-?(,--&.
Figura ! "uto#trans$ormador.
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III. CIRCUITOS A UTILIZAR
VV v vc
Autotransfora!or
C"
VR VL
L"R"
#$% &'.(#)
Circuito %& 1
VV v vc
*+n+ra!or
!+on!as
C"
VR VL
L"R"
#$%&'.(#)
$."u,
V"
Circuito %& 2
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VV v vc
*+n+ra!or
!+ on!as
C"V"
$."u,
L"
&'.(#)
V
VR
Circuito %& 3
IV. -ROCEDIMIENTO
P# $# &+)+()# + )+(+@
Ω= 3.50 R
P# $# ;-;)(# + )+(+@
mH L 86.112=
Ω= 2.13r
CASO I
". Arar + c/rcu/to N0 " 1 r+2uar + auto3transfora!or a ($$V u
otro vota4+ 5u+ + /n!/5u+ + 6rof+sor.
V V 4.113=
(. D+t+r/nar ana7t/ca+nt+ a ca6ac/tanc/a !+ con!+nsa!or 8C$9
6ara a cua ocurr+ r+sonanc/a.
F C µ 3.620 =
:. Con+ctar os con!+nsa!or+s +n s+r/+ 1;o 6ara+o u+2o +!/r a corr/+nt+ I 1 os
vota4+s VC> VL 1 VR.
?. Var/ar a ca6ac/tanc/a !+ =anco !+ con!+nsa!or+s 6ara ca!a
caso +!/r corr/+nt+ I 1 os vota4+s VC> VL 1 VR.
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T#;$# 1
C VC V VL V VR V I A10.0< 128.7< 22.2 2.2 0.8<20.3 13
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". Arar + c/rcu/to N0 :> ant+n/+n!o a /2ua 5u+ +n + c/rcu/to
ant+r/or> #V a a +ntra!a !+ c/rcu/to> ca/=rar + con!+nsa!or a
un vaor !+ $.",.
Hz f 65.2790 =
F C µ 87.2=
(. Var/ar a fr+cu+nc/a !+ sa/!a !+ 2+n+ra!or !+ on!as !+s!+
$.") 2raf/car VL> VC + I
+n func/@n !+ FCG.
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Gr'$ico 1. ( ) vs C
Gr'$ico 2. ( C vs C
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Gr'$ico 3. * vs C
=. D+t+r/nar t+@r/ca+nt+ + vaor !+ FCG n+c+sar/o 6ara 5u+ s+6ro!uca a r+sonanc/a 1 co6araro con os r+suta!os
+H6+r/+nta+s. M+nc/onar co+ntar/os.
P# %( )&%)- RLC +&)+ +( &+-(#()# + 5+;+ %$)& $# )%)+(+
&+$#)(@
C L X X =
C L ⋅=⋅
ω
ω 1
)+(5-@ f ⋅⋅= π ω 2
D++#(5- C@
( ) L f C
⋅⋅⋅
=2
2
1
π
R++$#*#(5- "#$-&+@
F C teórico µ 34.62=
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E$ CF &+#$ $- -;+(+- 5+ $# &,)# 3. L# &+-(#()# >#+ H%+ $#
-&&)+(+ +# /)#: -& $- H%+ 5+;+- >#$$#& +$ %(- /)- 5+ $#
&,)#.
D+ $# +%#)( 5+ $# &,)#@
2649.00425.00003.0 2
+⋅+⋅−= C C I
D+&)"#(5-@
0425.00006.0 +⋅−= C dC
dI
I + /)# %#(5- $# 5+&)"#5# + )%#$ # +&-: -& $- #(-@
004250.00006.0 =+⋅−= C dC
dI
F C real µ 83.70=
=#$$#- +$ +&&-& -;+()5-@
100% ⋅−
=
teórico
teóricoreal
C
C C e
%62.13% =e
E$ +&&-& + %+5+ 5+;+& # 5)"+&- -)"-: +(&+ $- %#$+ -5+-
+()-(#& $- +&&-&+ +( $# +5))( - $# "#&)#)-(+ 5+ ,&+%+()# '
"-$#+ +( +$ #%-?(,--&.
c. Cacuar t+@r/ca+nt+ + FG !+ c/rcu/to r+sonant+ a cont/nuac/@n> a
6art/r !+ 2raf/co !+ I vs C +!/r os vaor+s !+ ca6ac/!a!corr+s6on!/+nt+s a os 6untos !+ +!/a 6ot+nc/a. Con +stos vaor+s
+vauar as corr+s6on!/+nt+s fr+cu+nc/as !+ +!/a 6ot+nc/a 8o
+Htr+os !+ a =an!a f" 1 f(9 1 f/na+nt+ cacuar + FG
+H6+r/+nta> usan!o a forua
21 f f
a fresonanci
−
+ara el circuito 2
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C$%$- 5+$ +&)- 5+$ )&%)- 2@
)a energía total almacenada es constante ,ara un circuito en resonancia-
cuando el voltae de la ca,acitancía es cero- la corriente ,or la
inductancia es m'/ima 0 toda la energía almacenada est' en la
inductancia. Cuando el voltae de la ca,acitancia es m'/imo- la corriente
,or la inductancia es cero 0 toda la energía almacenada est' en la
ca,acitancia.
)a $uncin de e/citacin de la corriente es
)a m'/ima energía almacenada es
)a energía disi,ada ,or ciclo es la ,otencia ,romedio dividida entre la
$recuencia $ o- entonces
R++$#*#(5- "#$-&+ +( @
3.1228Q =
C#$%$- 5+$ +/+&)+(#$ # #&)& 5+ $# ,)# I " , 5+$ )&%)- 2@
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Gr'$ica 4. * vs $
P-& $- #(-@
556.5018.22335.273
65.27912
0 =
−
=
−
=
f f f Q
E$ +&&-& + 5+;+ # H%+ +( $# &,)# ' +( $- $%$- + -()5+ # $#
-&&)+(+ /)# # $# -&&)+(+ /)# -#5# +( +$ $#;--&)- 0.018A
+&- +# (- + $# "+&5#5+ $# /)# -&&)+(+ +( &+#$)5#5 + 0.02A.
E(-(+: -- $# -&&)+(+ /)# "+&5#5+ + #$#: +$ #(>- 5+
;#(5# +& # +H%+K- ' -& +(5+ +$ F +/+&)+(#$ 5))(%)& ' +
#&-/)# #$ +&)-.
!. A 6art/r !+ os r+suta!os o=t+n/!os +n + caso II> 2raf/car R> KL> KC>
φ > I> VR> VL 1 VC +n func/@n !+ a fr+cu+nc/a f 8φ +s + n2uo !+
!+sfasa4+ +ntr+ I 1 V9.
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Gr'$ica 5. R7r- 8 ) 0 8 C vs $
I%#$#(5- $# +%#)( 5+ +(5+()# 5+ $# &+##()# ##))"#
155455 −⋅ X ' $# +%#)( 5+ +(5+()# 5+ $# &+##()# )(5%)"#
X ⋅7091.0 + %+5+ -;+(+& $# ,&+%+()# 5+ &+-(#()#@
X X ⋅=⋅ −
7091.055455 1
Hz X 65.279=
N-#@
R&@ &+)+()# -#$ 5+$ )&%)-
L@ &+##()# )(5%)"#C@ &+##()# ##))"#
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Gr'$ica 6. 9ngulo vs $
E( ++ ,)- -5+- -+(#& H%+ $# $4(+# 5+ +(5+()# 5+$ (%$-
>) %- )(+&+# #$ ++ / +( $# ,&+%+()# 5+ &+-(#()# '# H%+ %#(5-
+$ )&%)- +# +( &+-(#()# )+(+ %( --&#)+(- &+))"- #;)(
-;+&"#- H%+ +$ (%$- 5+ 5+,##+ + 5)&+#+(+ &--&)-(#$ # $#
,&+%+()# '# H%+ $# &+##()# )(5%)"# #%+(# ' $# ##))"#
5))(%'+ %#(5- $# ,&+%+()# #%+(#.
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Gr'$ica . * vs $
E( ++ ,)- -5+- -+(#& H%+ $# -&&)+(+ + /)# %#(5-
-%&&+ $# &+-(#()# '# H%+ $# &+##()# )(5%)"# ' ##))"# +
#(+$#( +(-(+ $# )+5#()# -#$ + 4()#.
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Gr'$ica !. ( R - ( ) vs $
E( ++ ,)- -5+- -+(#& H%+ $# &+-(#()# + 5# +( $#
)(+&+)( 5+ $- "-$#+ ##))"- + )(5%)"-. E- "-$#+
5+;+&4#( )(+&+#&+ +( % /)- "#$-&+ +&- +( +$ ,)- (-
%+5+ +- $# $4(+# -# +# # #&&);# 5+;)5- # H%+ $# ;-;)(#
)($%4# %(# &+)+()# &-)# -& +$$- +$ "-$#+ +5)5- + %( --
5+ $- H%+ 5+;+&4# +& +(-(+ ) $+ H%)#- $# #45# 5+ +()( 5+;)5-
# $# &+)+()# )(+&(# &+)( %$)&4# H%+ $- "-$#+ + 5+;#(
)(+&+#& +( % /)- "#$-&+.
N-#@
L4(+# -#@ "-$#+ 5+ $# ;-;)(#
L4(+# ##&)$$#@ "-$#+ 5+$ ##)-&
L4(+# #*%$@ "-$#+ 5+ $# &+)+()#
+. A 6art/r !+ os r+suta!os o=t+n/!os +n + c/rcu/to N :> +vauar IR> IL
+ IC. *raf/car +stos vaor+s +n func/@n !+ a fr+cu+nc/a. En a /sa
2raf/car os vaor+s !+ VC +n func/@n !+ a fr+cu+nc/a.
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C'lculo de la corriente :ue ,asa ,or la resistencia
T#;$#
R -> VR
V 1000 R
VR
)RA
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, =*C*f * pi*2
1C-> VCV
1000 XC
VC )A
100.0<
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;-;)(# (- "#&)# %>- -- -5+- -;+&"#& +( $# $4(+# ##&)$$#.
T#;)( -;+&"#- H%+ $# -&&)+(+ 5+ $# &+)+()# +( $# &+-(#()#
+ +&- 5+;)5- # H%+ $# )+5#()# +H%)"#$+(+ 5+ $# # #$+$# +
)(,)()- ' &+#$ '# (- + -$+- ' + -& +- H%+ $# -&&)+(+ + +&-.
f. Cacuar t+@r/ca+nt+> a fr+cu+nc/a !+ r+sonanc/a 1 co6arara con
a o=t+n/!a +H6+r/+nta+nt+. Co+ntar as causas 5u+ or/2/naron
a !/f+r+nc/a +ntr+ !/c- 5+ -&- -5-
$# &+##()# ##))"# + )(5%)"# 5+;+( #(%$#&+.
T-#(5- ,#-&)#$+(+ $# I+5#()# +(+-@
E( R+-(#()#@
*
A5+@
. **
R+$#*#(5- 5+ I ' II: +(+-@
LC a fresonanci
π 2
1=
=#)+(5- %(# #;$# # $- "#$-&+@
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T#;$# 7
NQ L= C , 0=* 01 112.86 10.0< 19.
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D+ $- #(+&)-& +(+-: -#(5- ,#-&)#$+(+@
A($-#+(+ H%+ +( +$ #- RLC +( +&)+@
***
A5+@
. *(
R+$#*#(5- 5+ III ' IV: +(+-@
E(-(+ # +$ #- II Y III + )+(+@
O;+&"#)(@
A )$+ ")# $- "#$-&+ 5+ &+-(#()# -( $- )- +&- +( #5#
#- #(- +( +&)+ -- +( #$+$- )+(+( 5),+&+(+ +,+- '
#$)#)-(+: '# H%+ +( +$ &)+&- >#' #(#()# 5+ +()( ' +( +$
+&+&- >#' #(#()# 5+ -&&)+(+
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2. Evauar t+@r/ca+nt+ + FG !+ c/rcu/to r+sonant+> /n!/can!o +
to!o s+2u/!o 1 co6araro con + vaor o=t+n/!o a 6art/r !+ os
r+suta!os +H6+r/+nta+s.
S#;+- H%+ +$ ,#-& 5+ #$)5#5 + $# +5)5# 5+ $# ##)5#5 5+
#$#+(#)+(- 5+ +(+&4# 5+ %( )&%)- +( &+$#)( -( % ##)5#5
5+ 5))#)( 5+ +(+&4#: #+)#+(+ +(+-@
D-(5+ -;+&"#- H%+ + %( -)+(+ #5)+()-(#$.
P# +$ #- 5+ &+-(#()# +( +&)+
L# +(+&4# -#$ #$#+(#5# + -(#(+ # %( )&%)- +( &+-(#()#:
%#(5- +$ "-$#+ 5+ $# ##)#()# + +&-: $# -&&)+(+ -& $#
)(5%#()# + /)# ' -5# $# +(+&4# #$#+(#5# + +( $#
)(5%#()#. C%#(5- +$ "-$#+ 5+ $# ##)#()# + /)-: $# -&&)+(+
-& $# )(5%#()# + +&- ' -5# $# +(+&4# #$#+(#5# + +( $#
##)#()#.
L# ,%()( 5+ +/)#)( 5+ $# -&&)+(+ +@
L# /)# +(+&4# #$#+(#5# +@
L# +(+&4# 5))#5# -& )$- + $# -+()# &-+5)- 5)")5)5# +(&+ $#
,&+%+()# , -: +(-(+@
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P# +$ #- 5+ &+-(#()# +( P#$+$-
C-- $# +(+&4# %+5+ #$#+(#&+ -$#+(+ +( +$ )(5%-& - +( +$
##)-&: ' %+5+ 5))#&+ -$- +( +$ &+)-&: %+5+ +/&+#&+ +(
&)(- 5+ $# +(+&4# )(#((+# #-)#5# -( #5# %(- 5+ $-
+$++(- &+#)"-: ' -( $# -+()# &-+5)- 5))#5# -& +$ &+)-&@
S) $# ,%()( 5+ +/)#)( 5+ $# -&&)+(+ +@
E$ "-$#+ +&@
L# +(+&4# #$#+(#5# +( +$ ##)-& +@
L# +(+&4# )(#((+# +( +$ )(5%-& +@
L# +(+&4# -#$ )(#((+# #$#+(#5# +@
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E+ "#$-& + -(#(+ ' #5+ + #;)( +$ "#$-& /)-: +( +$
&+)-& $# -+()# &-+5)- #;-&;)5# +@
P# %( +&)-5-@
R++$#*#(5- # +$ #-& 5+ C#$)5#5@
C-( #$%(# %)%)-(+ + -;)+(+( +/&+)-(+ +H%)"#$+(+
O;+&"#)(
P# >#$$#& +$ R+#$ : #$)#-@
D-(5+@
A(#$)*#- # +$ #- II@
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A(#$)*#- # +$ #- III@
V. CONCLUSIONES RECOMENDACIONES
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CONCLUSIONES
• P# $- #- I ' II: +$ "-$#+ VL +5)5- (- &+&++(# #$ "-$#+ 5+ $#
)(5%#()# %: )(- 5+ $# )(5%#()# # % &+)+()# )(+&(#. P-& $-
#(- #$ #(#$)*#& VR +( $# &+-(#()#: # +$ )&%)- +&)+: ++ (-
%$+ -( $# &+$#)( VR- V )(- H%+ + #$- +(-& # H%+ 5)>#
&+$#)( + %$# 5+;+- -()5+& #5+ 5+ VR $# #45# 5+
-+()#$ +( $# &+)+()# )(+&(# 5+ $# ;-;)(# V& .
• P# +$ #- III: $# &++()# 5+ $# &+)+()# )(+&(# 5+ $# ;-;)(# (- +
#( )(),)#)"#: 5+;)5- # H%+ $# ;-;)(# ' +$ ##)-& +( -(+#5-
+( #$+$- ' $# )+5#()# 5+ &+-(#()# 5+ $# # +( #$+$- +(
-(%(- )+(5+ # )(,)()-.
• E( -5- )&%)- RLC +( +&)+: %#(5- + &++(# $# &+-(#()#
&+##()# +H%)"#$+(+ + >#+ (%$#: -& $- H%+ $# -&&)+(+ +( +$ )&%)-
+ /)#. E- #;)( $- -5+- )(+&&+#& -- H%+ +( $#
&+-(#()#: +$ "-$#+ ' $# -&&)+(+ +( +( ,#+ -&&)+(+ )&%$# $-
-& R.
• E( -5- )&%)- RLC +( #$+$-: %#(5- + &++(# $# &+-(#()#: $#
&+##()# +H%)"#$+(+ )+(5+ #$ )(,)()-: -& $- H%+ $# -&&)+(+ +( +$
)&%)- + 4()#. T#;)( +$ "-$#+ ' $# -&&)+(+ +( +( ,#+-&&)+(+ )&%$# $- -& R. P# +$ #- ++)#$ 5+$ )&%)- NQ 3 +
-;+&"# H%+ # $# &+-(#()#: 5+;)5- H%+ $# &+##()# +( #$+$-
)+(5+ #$ )(,)()-: $# -&&)+(+ # " 5+$ )&%)- +& (%$#.
• E( &+-(#()#: +$ ,#-& 5+ #$)5#5 F + )("+&#+(+ &--&)-(#$ # C
' R +( %( )&%)- +&)+ + 5)&+#+(+ &--&)-(#$ # C ' R +( %(
)&%)- #$+$-.
RECOMENDACIONES
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• P# -&-;#& $# &+$#)( VR- V -#& +( %+(# #;)( $# #45# 5+
-+()#$ +( &.
• B%#& $# #'-& &+))( -);$+ #$ &+%$#& +$ +(+-&.
VI. BIBLIO*RA,IA
• LINEAR CIRCUITS R-$#(5 E. S-
• >@+.))+5)#.-&
• >@+.));--.-&
• A%(+ 5+ A($)) 5+ C)&%)- E$&)- II
http://es.wikipedia.org/http://es.wikibooks.org/http://es.wikipedia.org/http://es.wikibooks.org/