Labo Cir 2 Informe Resonancia

8/20/2019 Labo Cir 2 Informe Resonancia

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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%-?(,-&#5-&.

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+ ,&+%+()# '

"-$#+ +( +$ #%-?(,-&#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/

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