Fisica3 - TP5 “CIRCUITOS EN CORRIENTE ALTERNA”

8/17/2019 Fisica3 - TP5 “CIRCUITOS EN CORRIENTE ALTERNA”

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UNIVERSIDAD NACIONAL DE ROSARIOFACULTAD DE CIENCIAS EXACTAS, INGENIERIA Y AGRIMENSURA

FISICA IIIDEPARTAMENTO DE FÍSICA Y QUÍMICA (E.F.B.)

ACTIVIDAD DE LABORATORIO Nº5

TITULO “CIRCUITOS EN CORRIENTE ALTERNA”

RESUMEN: En el !"#!en$e $%&'& *%+$!, !n$en$&%e- '$ene% l& &%!&!ne/e l& n/!!ne /e 0#n!n&-!en$ /e !%#!$ &*&!$! e!n/#$!, #&n/ l& 0%e#en!& /e en$%&/& &%1&, 2 l& e3&l /e en$%&/&e #n& n/& &l$e%n& !n#!/&l.

0

PROFESOR:

• Te%1&4 PROF. CARLOS ABECASIS• P%+$!& 4 PROF. MARICEL MATAR• L&'%&$%!4 PROF. CARMELO CELAURO

ALUMNOS:• CAPELLO, N!l+ C567789:• GIO;ANON, B%#n G56:669<• MARCU==I, F&'! M567>9:• ;ENTICINQUE, P&'l ;5@67@97

HORARIO DE LABORATORIO:

;!e%ne /e @@4?? @64??


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OBJETIVOS

An&l!&%e- el -*%$&-!en$ /e l !%#!$ RL, RC, LRC, en %"!-en /e%%!en$e &l$e%n&.

INTRODUCCIÓN TEÓRICA

CIRCUITO SERIE EN CORRIENTE ALTERNA

L& !"#!en$e 0!"#%&, n -#e$%& l& e$%#$#%& l+!& /e #n "ene%&/% !n/#$%!&len l& #&l e &*%e!& l& e$%#$#%& /el !n/#$% 2 /el !n/#!/. Al%e/e/% /e l&!%#n0e%en!& !n$e%n& /el e$&$% e$+n /!$%!'#!/ !e%$ n-e% /e *&%e /e*l. C- &/& n/#$% !$#&/ '%e l& #*e%0!!e

/el !n/#!/ %$% %$& el &-* -&"n$!, e*%/#e en l #n& 0e- !n/#!/&, en /e$e%-!n&/ en$!/#&n/ el n/#$% *&& *% #n *l n%$e 2 en en$!/*#e$ #&n/ *&& *% #n *l #%. L& 0e- !n/#!/&e, *% n!"#!en$e, &l$e%n&, 2 el n-e% /e !l-*le$ en &/& #el$& e !"#&l &l n-e% /e *&%e /e*l. E$& /!*!!n -#l$!*l&% *e%-!$e &l&n&% #n&0%e#en!& #0!!en$e-en$e "%&n/e !n #e e& nee&%!#$!l!&% #n& el!/&/ &n"#l&% *el!"%&-en$e ele&/&.L& 0e- !n/#!/& /e #n &l$e%n&/% !n/#$%!&l *#e/e /!0e%!% /e l& 0%-& !n#!/&l*e%0e$&, *e%, & -en #e n e /!"& e*%e&-en$e $%& &, #*n/%e-#e #$!l!&- #n &l$e%n&/% #e -&n$!ene en$%e # '%ne #n& /!0e%en!& /e*$en!&l !n#!/&l /&/& *%4

)( t senV v m ω = (@)

!en/ l& /!0e%en!& /e *$en!&l !n$&n$+ne&, V m l& /!0e%en!& /e *$en!&l-+!-& 2 ω l& 0%e#en!& &n"#l&%, !"#&l &l n-e% /e %el#!ne *% e"#n//el %$% -#l$!*l!&/ *% el n-e% /e *&%e /e *l. En N%$e&-%!&, *&%&-#H /e l &l$e%n&/%e, 0


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!en/ !, /! 9 /$ 2 l& !n$en!/&/ !n$&n$+ne& /e l& %%!en$e, # /e%!&/& %e*e$&l $!e-* 2 l& &%"& /el n/en&/%, %e*e$!&-en$e. De%!&n/ e$& e#&!n%e*e$ & $, 2 #$!$#2en/ / 9 /$ *% !, e '$!ene4

iC dt

id L

dt

di Rt V m .

1..)cos(

2

2

++=ω ω

E$& e #n& e#&!n /!0e%en!&l /e e"#n/ %/en, #2& l#!n e4

bt m At sen

C L R

V i −+−

−+

= ε ϕ ω

ω ω

.)(.

)1

( 22

/n/e

R

C L

Tg ω ω

ϕ

1−

=

E$& e#&!n *&%ee -*l!&/& *e% # !n$e%*%e$&!n n e /!01!l.

Cn!/e%e- en *%!-e% l#"&% el $%-!n A.ε5'$. L& -&"n!$#/e A 2 ' /e*en/en /el& n$&n$e /el !%#!$ 2 /e l& n/!!ne !n!!&le, e$ e, /e l &l%e /e;, !, /!9/$ 2 en el !n$&n$e /e e%%&% el !%#!$. El 0&$% ε5'$ /e%eee*nen!&l-en$e n el $!e-* 2 e H&e /e*%e!&'le &l &' /e #n $!e-*#0!!en$e (/e %/!n&%! -#2 *e#e3). E$e 0&$% e $%&n!$%! 2 n#e en l&*%+$!& l& /!0e%en!& /e *$en!&l 2 l& %%!en$e $%&n!$%!& *#e/en &/#!%!% &l%e *el!"%&-en$e "%&n/e, n l $en/%e- en #en$& 2 ln!/e%&%e- el *%!-e% $%-!n, #e e /en-!n& l#!n /el e$&/e$&!n&%!.

Se e #e l& %%!en$e %%e*n/!en$e &l e$&/ e$&!n&%! &%1&!n#!/&l-en$e n el $!e-*, l -!- #e el l$&e en$%e l '%ne. S# &l% -+!- e4

22)

1(C

L R

V I mm

ω ω −+

=

L& !n$en!/&/ /e l& %%!en$e en el e$&/ e$&!n&%! *#e/e e%!'!%e, *% $&n$,

)(. ϕ ω −= t sen I i m (:)

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L& 0%e#en!& /e l& !n$en!/&/ /e l& %%!en$e e, *% $&n$, l& -!-& #e l& /ell$&e, *e% &-'& /!0!e%en en l& 0&e, e&, e$+n /e0&&/& #n +n"#l ϕ.

In$%/#&- l& !"#!en$e !-*l!0!&!ne4

Z X R

X X X C

L

X C

X L

C L

C

L

=+

=−=−

=

=

22

1

1

ω ω

ω

ω

En$ne,

Z

V

X R

V

X X R

V I mm

C L

mm =

+

=

−+

=2222 )(

(6)

R

X Tg =ϕ (8)

L& -&"n!$#/ = e /en-!n& !-*e/&n!& /el !%#!$K X e l& %e&$&n!&, 2 X L 2 XCn l& %e&$&n!& !n/#$!& 2 l& %e&$&n!& &*&!$!&, %e*e$!&-en$e. L&!-*e/&n!& 2 l& %e&$&n!& e e*%e&n en OH-.

L& !n$en!/&/ -+!-& /e %%!en$e e$+ %el&!n&/& n l& -+!-& /!0e%en!& /e*$en!&l *% #n& e#&!n #e $!ene l& -!-& 0%-& #e l& le2 /e OH-, *&%& l&

%%!en$e n$!n#&, %%e*n/!en/ l& !-*e/&n!& = & l& %e!$en!& R.

MEDIAS CUADRÁTICAS O VALORES EFICACES

L &l%e !n$&n$+ne /e #n& !n$en!/&/ /e %%!en$e, 0e- /!0e%en!& /e*$en!&l &l$e%n&, &%1&n /e #n -/ n$!n# /e/e #n &l% -+!- en #nen$!/, *&&n/ *% e%, H&$& #n -+!- en en$!/ *#e$, 2 &1#e!&-en$e. E -+ -/ e$#/!&% l& %%!en$e &l$e%n& n!/e%&n/ #valores cuadráticos medios en l#"&% /e # &l%e -+!-.

El &l% #&/%+$! -e/! /e l& !n$en!/&/ /e #n& %%!en$e &%!&'le e /e0!ne- el &l% /e l& !n$en!/&/ /e #n& %%!en$e n$&n$e #e /e&%%ll&e l&-!-& &n$!/&/ /e &l% en !"#&l $!e-* 2 en l& -!-& %e!$en!&K 2 *% e$&%&n e /en-!n& &l &l% #&/%+$! -e/!, valor eficaz /e l& %%!en$e &%!&'le.L& /e%!&/& %e*e$ &l $!e-* /e l& &n$!/&/ /e &l% /e&%%ll&/& en #n&%e!$en!& R, #e $%&n*%$& #n& %%!en$e &l$e%n& !n#!/&l )(. t sen I i m ω = , e4

)(.. 222 t sen R I Ri m ω =

L& &n$!/&/ $$&l /e &l% /e&%%ll&/& en #n $!e-* T, !"#&l & #n *e%1/, e4

3


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RT I t sen R I Rdt i H m

T

m

T

2

0

22

0

2

2

1)(.. === ∫ ∫ ω

L& &n$!/&/ /e &l% /e&%%ll&/& *% #n& %%!en$e /e !n$en!/&/ n$&n$e I e enel -!- $!e-* e4

RT I H e .2

=

P#e$ #e *% /e0!n!!n /e I e l& &n$!/&/e /e &l% n !"#&le,

2.

2

1.

22 meme

I I RT I RT I =⇒=

P% n!"#!en$e, ! l& !n$en!/&/ /e #n& %%!en$e &%1& !n#!/&l-en$e, # &l% e0!& e 2/1 ≈ ?,? ee # &l% -+!-. A!-!-, el &l% e0!& /e #n&/!0e%en!& /e *$en!&l #e &%1e !n#!/&l-en$e e 2/1 ee # &l% -+!-. S! /!!/!en/ *% 2/1 el *%!-e% 2 el l$!- -!e-'% /e l& e#&!n(3), '$ene-4

Z

V I mm 2/

2=

e&,

Z

V I ee = (>)

De &H%& en &/el&n$e, e !n$e%*%e$&%+ #e l& le$%& I , ε V !n #'1n/!e, e%e0!e%en & l &l%e e0!&e /e l& -&"n!$#/e %%e*n/!en$e. L& e#&!n(5) e e%!'!%+, *% $&n$,

Z

V I =

Cn!/e%e- &H%& l 0&$%e #e /e$e%-!n&n l& %e!$en!&, %e&$&n!& e!-*e/&n!& /e #n !%#!$. En *%!-e% l#"&%, l& %e!$en!& /e #n n/#$% #e$%&n*%$& #n& %%!en$e &l$e%n& *#e/e n e% l& -!-& #e l& %e!$en!& /el

-!- n/#$% #&n/ $%&n*%$& #n& %%!en$e n$&n$e. L& /!0e%en!& e/e'e &l HeH /e #e l& /en!/&/ /e %%!en$e en #n H!l #e $%&n*%$& #n&%%!en$e &l$e%n& n e #n!0%-e en $/& l& e!n /el -!-, !n -&2% #n$ &l& #*e%0!!e. E$e 0en-en e ne n el n-'%e /e e0e$ %$!&l “e0e$!n”. L& e!n e0e$!& /el n/#$% e %e/#e 2 # %e!$en!& -en$&. Ele0e$ %$!&l e %!"!n&/ *% l& 0e- $!n/#!/& %e&/& *% l& &%!&!ne /el0l# !n$e%n en #n n/#$%, 2 e -&2% #&n$ -+ ele&/& e l& 0%e#en!&. A#n#e e$e e0e$ e #n 0&$% !-*%$&n$e *&%& l& 0%e#en!& #$!l!&/& en%&/!, *#e/e /e*%e!&%e /e %/!n&%! *&%& l& 0%e#en!& /e


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#n& $!n/#!n, X L :π0.L, e *%*%!n&l & l& e &l e0!!en$e /e$!n/#!n 2 & l& 0%e#en!&. S! H&2 #n nle /e H!e%% &!&/ &l !n/#$%,en$ne el e0!!en$e /e $!n/#!n n e n$&n$e, *e% /e n#e *&%&-&2% en!lle n $en/%e- en #en$& e$& &%!&!n.

L& %e&$&n!& &*&!$!&, X C @ 9 :π0.C, e !ne%&-en$e *%*%!n&l & l&&*&!/&/ 2 & l& 0%e#en!&.

L& %el&!n en$%e l& !-*e/&n!& = /e #n !%#!$ en e%!e 2 l &l%e /e R, X L 2XC *#e/e %e*%een$&%e "%+0!&-en$e n!/e%&n/ $/& e$& -&"n!$#/e -e$%e. L& %e!$en!& R e %e*%een$& *% #ne$% !$#&/ '%e el ee X, 2 #2 en$!/!n!/e n el en$!/ *!$! /el -!-K 2 l&%e&$&n!& XL 2 XC *% e$%e !$#&/ '%eel ee Y 2 en l en$!/ *!$! 2 ne"&$!,%e*e$!&-en$e. L& !-*e/&n!& e el e$% #-& "e-$%!& %e#l$&n$e /e e$ $%ee$%e, - e e en l& !"#!en$e 0!"#%&. E$&0!"#%& e H& /!'#&/ *&%& el & X L XC 2, *% $&n$, X e *!$!&. S! XL XC, %e#l$& X ne"&$!&2 e /!%!"e H&!& &'& en e /e H&!& &%%!'&.

RELACIÓN ENTRE LAS FASES DEL VOLTAJE Y DE LA INTENSIDAD DECORRIENTE

L& !n$en!/&/ e0!& en #n !%#!$ en e%!e e !"#&l & l& %&n /el l$&ee0!& & l& !-*e/&n!& /el !%#!$. Cn!/e%e- &H%& l& 0&e /e l& !n$en!/&//e %%!en$e %e*e$ & l& /el l$&e. L& e#&!ne (1), (2) 2 (4) *#e/ene%!'!%e #n$& *&%& -&2% -/!/&/,

R

X Tg

t sen I i

t senV v

m

m

=

−=

=

ϕ

ϕ ω

ω

)(.

)(.

El &l% ω %e*%een$& #n +n"#l (en %&/!&ne), 2 # &l% en #&l#!e% !n$&n$e $ e/en-!n& 0&e /el ;l$&e. An+l"&-en$e, l& -&"n!$#/ (ω$5ϕ), e /en-!n& 0&e/e l& !n$en!/&/ /e l& %%!en$e. Se /!e #e l& %%!en$e *%een$& #n& /!0e%en!&/e 0&e n el l$&e, #e e$+ /e0&&/& #n +n"#l ϕ %e*e$ &l l$&e.P#e$ #e l& %e&$&n!& X *#e/e e% *!$!& ne"&$!&, l -!- le #e/e &l+n"#l ϕ. S! XL XC, X e en$ne *!$!&, ϕ e *!$!, 2 l -+!-,-1n!-, e$., /e l& !n$en!/&/ /e l& %%!en$e &*&%een en !n$&n$e *$e%!%e#e l #e %%e*n/en &l l$&e. Se /!e #e l& !n$en!/&/ e$+ %e$%&&/&

%e*e$ &l l$&e. P% el n$%&%!K ! XL XC, X e ne"&$!&, ϕ $&-'!n ene"&$! 2 l& !n$en!/&/ e$+ &&n&/& %e*e$ &l l$&e.

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El +n"#l ϕ *#e/e /e$e%-!n&%e !n-e/!&$&-en$e -e/!&n$e el /!&"%&-& /el e$% !-*e/&n!&, *#e$ #e R X Tg /=ϕ . C- & e*e!&l, e e!/en$e #e ! #n!%#!$ e$+ 0%-&/ *% #n& %e!$en!& *#%& ne$&/& & #n& /!0e%en!& /e*$en!&l &l$e%n&, X ?, = R, ϕ ?, 2 l& !n$en!/&/ 2 el l$&e e$+n en 0&e,

- !n/!& l& !"#!en$e 0!"#%&.

S! el !%#!$ e -*ne /e #n& $!n/#!n *#%&, R ?, = X L, 2/π ϕ += , 2 l&!n$en!/&/ e$+ %e$%&&/& %e*e$ &l l$&e #n +n"#l /e π 9 : %&/!&ne, 7?,e"n e e en l& !"#!en$e 0!"#%&.

S! el !%#!$ n$!ene l &*&!/&/, R ?, = X C, 2/π ϕ −= 2 l& !n$en!/&/ e$+&&n&/& %e*e$ &l l$&e #n +n"#l /e 7?, - !n/!& l& 0!"#%&

L& !n$en!/&/ /e l& %%!en$e $!ene l& -!-& 0&e en $/& l& *&%$e /e #n !%#!$

en e%!eK e&, e -+!-& en l& %e!$en!&, l& $!n/#!n 2 el n/en&/% &l

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-!- $!e-*K n#l& en l $%e #n !n$&n$e /e*#K -+!-&, *e% /e en$!/*#e$, $% !n$&n$e $/&1& *$e%!%, 2 &1 #e!&-en$e.

DIFERENCIA DE POTENCIAL ENTRE LOS PUNTOS DE UN CIRCUITORECORRIDO POR UNA CORRIENTE AL TERNA

L& /!0e%en!& /e *$en!&l e0!& en$%e / *#n$ #&le#!e%& /e #n!%#!$ en e%!e e !"#&l &l *%/#$ /e l& !n$en!/&/ e0!& *% l& !-*e/&n!& /el!%#!$ en$%e l / *#n$ n!/e%&/, !e-*%e #e n e!$& n!n"#n& 0e--*%en/!/& en$%e ell4

abab Z I V .=

L& /!0e%en!& /e 0&e ϕ en$%e V ab e I e4

ab

ab

R

X Tg =ϕ

En l& 0!"#%&, l& !-*e/&n!& Z ab en$%e & 2 ' e !"#&l & R, *#e$ #e n H&2 $%ele-en$ /e !%#!$ en$%e e$ *#n$. P% n!"#!en$e, V ab I.R 2 ϕ &% $"? ?. E$ e, l& /!0e%en!& /e *$en!&l en$%e l $e%-1n&le /e #n& %e!$en!&*#%& e$+ en 0 &e n l& !n$en!/&/ /e l& %%!en$e en l& %e!$en!&. En$%e l

*#n$ ' 2 , Z bc X L, V bc = I.X L, ϕ &% T" ∞ π 9 :. L& /!0e%en!& /e *$en!&len$%e l e$%e- /e #n& $!n/#!n *#%& e$+ &&n&/& 7? %e*e$ & l&!n$en!/&/. En$%e l *#n$ 2 /, Z cd X C , V cd I.X C , ϕ &% $" (5∞) 5 π9:. L&/!0e%en!& /e *$en!&l en$%e l '%ne /e #n n/en&/% e$+ %e$%&&/& 7?%e*e$ & l& %%!en$e en el n/en&/%.

L& #-& /e l& /!0e%en!& /e *$en!&l e0!&e en$%e l e$%e- /e!e%$ n-e% /e ele-en$ /e #n !%#!$ en, e%!e, n e !"#&l & l& /!0e%en!& /e*$en!&l e0!& en$%e l e$%e- /el !%#!$ en n#n$. E$& &n-&l1& e

e*l!&, n '$&n$e, en!ll&-en$e, ! e $!enen en #en$& l& %el&!ne /e 0&een$%e l& /!0e%en!& /e *$en!&l /e l& /!$!n$& *&%$e.

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L& l1ne& llen& %e*%een$& l& !n$en!/&/ !n$&n$+ne& /e l& %%!en$e, l& -!-& en$/& l& *&%$e /el !%#!$, 2 #e $!ene #n &l% -+!- /e 2.e I A. L& $%&$%e #%& %e*%een$&n l& /!0e%en!& /e *$en!&l !n$&n$+ne& en$%e & 2 'K ' 2, 2 2 /, #2 &l%e -+!- n 2.abV , 2.bcV 2 2.cd V %e*e$!&-en$e, 2 #2& /!0e%en!& /e 0&e n %el&!n & i n l& %e5*%een$&/&.

L& /!0e%en!& /e *$en!&l !n$&n$+ne& v ad e !"#&l & l& #-& /e l& /!0e%en!& /e*$en!&l !n$&n$+ne& v ab, v bc 2 v cd . S! e #-&n l& $%e #%& /e $%&, l& #%&'$en!/& %e*%een$&, *% $&n$, l& /!0e%en!& /e *$en!&l !n$&n$+ne& en$%e & 2 /.

DIARAMAS DE VECTOR ROTATORIO

L& /!0!#l$&/ e!/en$e /e /!'#&% e !n$e%*%e$&% /!&"%&-& $e-*%&le -el &n$e%!%, H&e /ee&'le !n$%/#!% &l"n -$/ "%+0! -+ en!ll *&%&%e*%een$&% l& %el&!ne /e 0&e en$%e !n$en!/&/e 2 /!0e%en!& /e *$en!&l enl !%#!$ /e %%!en$e &l$e%n&, l #e *#e/e ne"#!%e - !"#e.

S#*n"&- #e e /ee& %e*%een$&% #n& %%!en$e #e &%1e !n#!/&l-en$e,/e 0%e#en!& 0 2 &l% -+!- I m. Cn$%#2&- #n e$% I m, - el /e l& 0!"#%&& !e%$& e&l& nen!en$e, e !-&"!ne- #e e$e e$% e$ "!%&n/ &l%e/e/% /e O en en$!/ n$%&%! &l /e l& &"#& /e #n %el n #n& el!/&/ &n"#l&% #n!0%-e ω :π.0 %&/9e".

S! el e$% #*& l& *!!n H%!n$&l en el !n$&n$e $ ?, # *%2e!n -*nen$e '%e #n ee e%$!&l, en #&l#!e% !n$&n$e $, e%+ !"#&l &l &l% /e l&%%!en$e en /!H !n$&n$e, *#e$ #e e"n l& 0!"#%& l& -*nen$e e%$!&l e4

i ft sen I sen I mm == π θ 2

8


10/28

N&$#%&l-en$e, el /!&"%&-& l %e*%een$& el &l% /e i en #n !n$&n$e/e$e%-!n&/, *e% el le$% *#e/e #*l!% l& %$&!n -en$&l-en$e, 2 e"#!% l&0l#$#&!ne /e i #&n/ I m "!%&. E$e -$/ e e#!&len$e &l #e e #$!l!&*&%& %e*%een$&% #n -!-!en$ &%-n! !-*le *% l& *%2e!n '%e #n

/!+-e$% /e #n *#n$ #e e -#ee en #n& !%#n0e5

%en!& n el!/&/ &n"#l&% n$&n$e. S! e /ee&%e*%een$&% en el -!- /!&"%&-& l &l%e!n$&n$+ne /e #n& /!0e%en!& /e *$en!&l /&/&

)2( ϕ π −= ft senV v m #e $en"& l& -!-& 0%e#en!&

#e l& %%!en$e, *e% %e$%&&/& %e*e$ & $& #n+n"#l ϕ, e n$%#2e #n e"#n/ e$% /e ln"!5

$#/ V m & !e%$& e&l& nen!en$e, *e% /e*l&&/ %e*e$ & I m #n +n"#l ϕ enel en$!/ /e l& &"#& /el %el. C#&n/ &-' e$%e "!%&n en en$!/n$%&%! &l /e l& &"#& /el %el, e e!/en$e #e l &l%e !n$&n$+ne /e v *%een$&%+n !e-*%e #n %e$&%/ /e 0&e ϕ %e*e$ & l /e i .

;l!en/ &l !%#!$ LRC &n$e%!%, %e*%een$&- *% e$e -$/ /el e$% %$&$%! l& !n$en!/&/ 2 l& /!0e%en!& /e *$en!&l en$%e l e$%e- /e l&/!$!n$& *&%$e /el !%#!$.

P&%& %e*%een$&% l& !n$en!/&/ /e l& %%!en$e '&$&%+ #n l e$% I m, 2& #e$e $!ene el -!- &l% 2 l& -!-& 0&e en $/& l& *&%$e /el !%#!$. L&/!0e%en!& /e *$en!&l en$%e l '%ne /e l& %e!$en!& e$+ %e*%een$&/& *% ele$%

abmV #e $!ene l& -!-& /!%e!n #e I m, *#e$ #e v ab e i e$+n en 0&e,

2 #2& ln"!$#/ e V V abe 2. . An+l"&-en$e, l e$%e

bcmV /e ln"!$#/

V V bce

2. 2cd m

V /e ln"!$#/ V V cd e

2. %e*%een$&n l& /!0e%en!& /e *$en!&l&&n&/& en$%e l '%ne /e l& $!n/#!n 2 l& /!0e%en!& /e *$en!&l%e$&%/&/& en$%e l '%ne /el n/en&/%. C#&n/ l e$%e "!%&n, #-*nen$e e%$!&le e*e%!-en$&n l& -!-& &%!&!ne #e l& %/en&/&/e l& #&$% #%& /el /!&"%&-& $e-*%&l &n$e%!%.

9


11/28

Q# #e/e n l& /!0e%en!& /e *$en!&l en$%e & 2/. U$!l!&n/ el /!&"%&-& /el e$% %$&$%!, e$ e'$!ene #-&n/ l& -*nen$e e%$!&le /e

abmV ,

bcmV

cd mV . Pe% l& #-& /e l& -*nen$e

e%$!&le /e e$ e$%e e !"#&l & l& -*nen$ee%$!&l /e # #-& "e-$%!& %e#l$&n$e. P% $&n$,! e$& %e#l$&n$e e '$!ene *% #&l#!e% -$/&/e#&/, # -*nen$e e%$!&l %e*%een$& l&/!0e%en!& /e *$en!&l !n$&n$+ne& en$%e l e$%e-/el !%#!$, 2 el +n"#l ϕ, #e 0%-& n I m, !n/!& l&/!0e%en!& /e 0&e /el !%#!$ en n#n$. L& *%*!&

%e#l$&n$e %e*%een$&, *% $&n$, l& /!0e%en!& /e *$en!&l -+!-& en$%e & 2 /, e&

abmV . A#n#e el /!&"%&-& /el e$% %$&$%! e een!&l-en$e #n -$/

*&%& %e*%een$&% &l%e !n$&n$+ne, en l& *%+$!&, e #$!l!& &! !e-*%eel#!&-en$e n l &l%e e0!&e 2 l& /!0e%en!& /e 0&e. S! !-&"!n&-#e e -/!0!& l& e&l& /e l /!&"%&-& 0&%!&le en el 0&$% 2 , l -!-e$%e #e %e*%een$&n &l%e -+!-, %%e*n/e%+n en l& n#e& e&l& &&l%e e0!&e, *e%-&ne!en/ !n&%!&'le l +n"#l # %e*%een$&n/!0e%en!& /e 0&e. P% ell e *%+$!& n%-&l n$%#!% e$ /!&"%&-& n le$%e #e %e*%een$&n l &l%e e0!&e en l#"&% /e l &l%e -+!-. S!e /ee&n l &l%e !n$&n$+ne l e nee&%! !-&"!n&% -#l$!*l!&/& *%

2 l& ln"!$#/ /e $/ l e$%e 2 #*ne% el /!&"%&-& en %$&!n.

E -*le$&-en$e &%'!$%&%!& l& %!en$&!n #e e / &l /!&"%&-& e$%!&l. En #n!%#!$ en e%!e e -!en& /e %/!n&%! *% /!'#&% el e$% !n$en!/&/0%-&n/ #n +n"#l #&l#!e%& 2 e n$%#2en l $% e$%e n l&%!en$&!n %el&$!& &/e#&/&. Se -!$en "ene%&l-en$e l ee X e Y. A-'&0!"#%& n !"#&le, &l #e el e$% !n$en!/&/ e H%!n$&l 2 #e l& e&l& eH& -/!0!&/ *&%& #e l e$%e %e*%een$en &l%e e0!&e. P#e$ #e V ab IR , V bc = IX L, V cd = IX C 2 V ad = IZ , l e$%e l$&e e$+n %el&!n&/e&$&-en$e /el -!- -/ #e l e$%e en #n /!&"%&-& /e e$% !-*e/&n!& $&l - el /!&"%&-& /e !-*e/&n!&. En e0e$, el /!&"%&-& /ele$% l$&e /e #n !%#!$ en e%!e *#e/e '$ene%e & *&%$!% /e # /!&"%&-& /ee$% !-*e/&n!&, -#l$!*l!&n/ &/& e$% %e!$en!&, %e&$&n!& !-*e/&n!&

*% l& !n$en!/&/.

10


12/28

CIRCUITOS EN PARALELO

Cn!/e%e- &H%&, el &*l&-!en$ en *&%&lel /e l ele-en$ /el!%#!$ /e l& 0!"#%&. L& /!0e%en!& /e *$en!&l !n$&n$+ne& v ab en l e$%e- /el& / /e%!&!ne e l& -!-&. L& !n$en!/&/ i 1 en l& /e%!&!n #*e%!% (&*&!$!&) e$&%+ &&n&/& %e*e$ & v abK l& /e l& /e%!&!n !n0e%!% (!n/#$!&)e$&%+ %e$&%/&/&. Se"n l& le2 /e l n#/ /e !%HH00, l& !n$en!/&/ !n$&n$+ne&I l /e l& l1ne& e !"#&l & l& #-& /e l& !n$en!/&/e !n$&n$+ne& i 1 e i 2 . El/!&"%&-& e$%!&l /el !%#!$ e$+ !n/!&/ & #n $&/. El e$% V ab %e*%een$&

l& /!0e%en!& /e *$en!&l -n en$%e l e$%e- /e &/& /e%!&!n, 2 le$%e I 1 e I 2 , l& !n$en!/&/e. I 1 e$+ &&n&/& %e*e$ & V , #n +n"#l ϕ@ &%$" X l /R l K I 2 e$+ %e$%&&/& %e*e$ & ; #n +n"#l ϕ: &% $" X 2 /R 2 . L& !n$en!/&/en l& l1ne& e$+ %e*%een$&/& *% I l , #-& "e-$%!& /e I 1 e I 2 , 2 ϕ e l&/!0e%en!& /e 0&e en$%e l& !n$en!/&/ en l& l1ne& 2 V .

Se /e0!ne l& !-*e/&n!& e#!&len$e /el !%#!$ - l& %&n /e V ab & l&!n$en!/&/ en l& l1ne& I l . E e!/en$e #e ! V ab 2 l& n$&n$e /el !%#!$ nn!/& (/&$), el +l#l /e I l lle& n!" el +l#l /e l& !n$en!/&/e

!n/!!/#&le en &-'& /e%!&!ne, 2 # /!0e%en!& /e 0&e. P% n!"#!en$e,l& !-*e/&n!& e#!&len$e *#e/e e*%e&%e en 0#n!n /e l& %e!$en!& 2%e&$&n!& /e l& /e%!&!ne. L& e*%e!n #e %e#l$& e &l" -*l!&/&,n#e *#e/e /e/#!%e 0+!l-en$e -e/!&n$e l& "%&0!& &n$e%!%e.

RESONANCIA

Un & *&%$!#l&% /e !n$e% e *%een$& en #n !%#!$ en e%!e #e n$!ene$!n/#!n 2 &*&!/&/, #&n/ L, C 2 f $!enen &l%e $&le #e

11


13/28

fC fL π π 2/12 = , e$ e, #&n/ X L X C . En$ne X ?, Z = R 2 ϕ &% $" X 9 R ?. L& !-*e/&n!& /e !%#!$ e !-*le-en$e !"#&l & # %e!$en!&, 2 l&!n$en!/&/ e$+ en 0&e n l& /!0e%en!& /e *$en!&l en$%e l '%ne /el !%#!$.L& %%!en$e #e &$%&!e& #n !%#!$ %en&n$e en e%!e, ! # %e!$en!& e*e#e3&, e%+ "%&n/e, 2 l& /!0e%en!& /e *$en!&l en$%e l '%ne /e l&

$!n/#!n 2 /e l& &*&!/&/ *#e/e e% -#H -&2% #e l& #e e!$e &$%& /e $/ el !%#!$.

;e&- &H%&, el 0en-en n #n !%#!$ RLC e%!e /e ee-*l.

Cn!/e%e- #n !%#!$ en e%!e en el #&l $ene- R , X L X C , ne$&/ & #n&

/!0e%en!& /e *$en!&l &l$e%n& #2 &l% e0!& e ε. L& !n$en!/&/ /e l& %%!en$een el !%#!$ e4

R

V

Z

V I ==

L& /!0e%en!& /e *$en!&l en$%e l '%ne /e l& %e!$en!&,

IRV R =

L& /!0e%en!& /e *$en!&l en$%e l '%ne /e l& $!n/#!n,

L L IX V =

12

I

ε

V R

V L

V C

V X

R XLX

C


14/28

L& /!0e%en!& /e *$en!&l en$%e l& &%-&/#%& /el n/en&/%,

C C IX V =

Y l& /!0e%en!& /e *$en!&l en$%e l e$%e- /e @& -'!n&!n $!n/#!n5

&*&!/&/ (V X ) e4 IX V X =

Se 'e%& #e l& /!0e%en!& /e *$en!&l !n$&n$+ne& en$%e l e$%e- /e l&$!n/#!n 2 /el n/en&/% e$+n /e0&&/& @?, 2 n#e l &l%ee0!&e /e &/& #n& *#e/en e% "%&n/e, # %e#l$&n$e en $/ !n$&n$e e n#l&.En ne#en!& #n l$1-e$% &*l!&/ en$%e ' 2 /, !n/!&%+ e%.L& 0!"#%& %e*%een$& #n !%#!$ en *&%&lel en el #&l X L X C , !en/ R l& -!-&en &/& /e%!&!n. L& !n$en!/&/ e0!& e, *% n!"#!en$eK !"#&l en &/&/e%!&!n, e$&n/ #n& /e e$& %%!en$e %e$&%/&/& 2 l& $%& &/el&n$&/& el

-!- +n"#l %e*e$ & l& /!0e%en!& /e *$en!&l. S! X L 2 X C n -#H-&2%e #e R , l& /!0e%en!& /e 0&e n &*%!-&/&-en$e 7? 2, - %e#l$&e!/en$e, l& !n$en!/&/ I l en l& l1ne& e -#H -en% #e l& !n$en!/&/ en &/&/e%!&!n. De $%& 0%-&, l& !-*e/&n!& e#!&len$e, V 9 I l , /el !%#!$ en n#n$e -#2 ele&/&, -#H -&2% #e l& /e #n& #&l#!e%& /e l& /e%!&!ne. De-/ '&$&n$e *&%&/!, #&n$ -en% e l& %e!$en!&, -&2% e l&!-*e/&n!&, 2& #e #&n/ R $!en/e & e%, l& /!0e%en!& /e 0&e $!en/en & 7?,2 l& %%!en$e /e l& l1ne& $!en/e & e%. Se /!e #e el !%#!$ e$+ en %en&n!&*&%&lel&.

De'e e!$&%e l& %en&n!& en l& l1ne& /e $%&n*%$e /e ene%"1&, *#e$ #e,!n/#/&'le-en$e, %e#l$&%+n !n$en!/&/e /e %%!en$e 2 /!0e%en!& /e *$en!&l

ele&/& en !e%$& *&%$e /el !%#!$. P% el n$%&%!, en l !%#!$ /e %&/! e&*%eH& l& en$&& /e l& %en&n!& en el *%e /e !n$n!&!n. El !%#!$/e &n$en& /e #n %&/!%%ee*$% n$!ene #n& $!n/#!n 2 #n n/en&/% ene%!e. L& e$&!ne e-!%& -*%en/!/& /en$% /el !n$e%&l /e 0%e#en!&/el %ee*$% !n/#en en e$e !%#!$ 0#e%& ele$%-$%!e /e 0%e#en!&!"#&le & l& 0%e#en!& *%$&/%& /e /!H& e$&!ne. C#&n/ eln/en&/% /e !n$n1& e &#$& /e -/ #e el !%#!$ e$ en %en&n!& nl& 0%e#en!& /e #n& e$&!n /ee&/&, l& !n$en!/&/ /e %%!en$e #e %%e5*n/e & &#ell& 0%e#en!& *&%$!#l&% e "%&n/e, 2 e '$!ene #n& /!0e%en!& /e*$en!&l $&-'!n "%&n/e en$%e l& &%-&/#%& /el n/en&/%K *e%, - #nn/en&/% l *#e/e e$&% en %en&n!& *&%& #n& 0%e#en!&, l& $%&e$&!ne n *%/#!%1&n -+ #e !n$en!/&/e 2 /!0e%en!& /e *$en!&l/e*%e!&'le, 2, *% n!"#!en$e, n e%+n 1/&.

13


15/28

L& n/!!n nee&%!& *&%& l& %en&n!& e4

C L X X

LC ω

ω 1

=⇒=

/e l& #&l /e/#!-4

L

C

LC f

/1.

2

11.

2

1

π π == (


16/28

ELEMENTOS UTILI"ADOS

O!l*!K Gene%&/% /e n/&K C!%#!$ /e P%#e'& (e"n 0!"#%&), #2&l%e n4

R#$%$'%$ C*%&+,#$ I'-.&'%$R@ @>? Ω C@ ?,?8 µF L@ 8, -J2R: 6,6 Ω C: ?,@ µF L: >?? µJ2 99 @


17/28

CIRCUITO R3L1FRECUENCIA: 3/0H

seg rad Hz f

seg T Hz f

T

5

5

10.45,239000..2..2

10.5,239000

11

=⇒==

=⇒== −

ω π π ω

( )mA

V

Z

V I teorica 53,0

)107,41045,2(680

5,02

2352=

⋅⋅⋅+Ω

⋅==

−

t ! $!e-* /e /e0&&e ⇒ Se '$!ene /e l& "%+0!& /e l& e3&le en el!l*!

E*e%!-en$&l-en$e, -e/!-4 t = 8 µe".

ϕ 4 +n"#l /e /e0&&e

º2,5698,010.4.10.45,2. 65 =⇒=== − ϕ ω ϕ rad seg seg

rad t

C-*&%+n/l n el &l% $e%!, $ene-4

º6003,1680

7,4.10.45,2 5

=⇒=Ω

=== ϕ ω

ϕ rad mHy seg

rad

arcTg R

LarcTg

R

X acrTg L

mAdiv

V div

I practico 47,0680

2,06,1

=Ω

⋅

=

RAFICA Y V R (I ) VS TIEMPO

16


18/28

DIARAMA FASORIAL

FRECUENCIA: 130H

seg rad Hz f

seg T

Hz f

T

4

5

10.2,813000..2..2

10.7,7

13000

11

=⇒==

=⇒== −

ω π π ω

( )mA

V

Z

V I teorica 90,0

)107,4102,8(680

5,02

2342=

⋅⋅⋅+Ω

⋅==

−

E*e%!-en$&l-en$e, -e/!- el /e0&&e4 t = V9/!

V: 6,8 /!V

R: @,< /!

D#$: ?, /!

ε

i

VR

VL

φ


19/28

º2,285,010.6.10.2,8. 64 =⇒=== − ϕ ω ϕ rad seg seg

rad t

C-*&%+n/l n el &l% $e%!, $ene-4

º5,2952,0680

7,4.10.2,8 4

=⇒=Ω

=== ϕ ω

ϕ rad mHy seg

rad

arcTg R

LarcTg

R

X acrTg L

mAdiv

V div

I practico 79,0680

2,07,2

=Ω

⋅

=


DIARAMA FASORIAL

FRECUENCIA: !0H

18

13KHz

V ( ): ?,: ;9/!V

R (): ?,: ;9/!

&: @?V9/!

V: 6,: /!

VR: :, /!D#$: ?,< /!

ε

i

VR

VL

φ


20/28

seg rad Hz f

seg T Hz f

T

4

4

10.8,36000..2..2

10.7,16000

11

=⇒==

=⇒== −

ω π π ω

( )mA

V

Z

V I teorica 01,1

)107,4108,3(680

5,02

2342=

⋅⋅⋅+Ω

⋅==

−

E*e%!-en$&l-en$e, -e/!- el /e0&&e4 t = µe".

ϕ 4 +n"#l /e /e0&&e

º3,1527,010.7.10.8,3. 64 =⇒=== − ϕ ω ϕ rad seg seg

rad t

C-*&%+n/l n el &l% $e%!, $ene-4

º1,1526,0680

7,4.10.8,3 4

=⇒=Ω

=== ϕ ω

ϕ rad mHy seg

rad

arcTg R

LarcTg

R

X acrTg L

mAdiv

V div

I practico 88,0

680

2,03

=

Ω

⋅

=


DIARAMA FASORIAL

19

6KHz

V ( ): ?,: ;9/!V

R (): ?,: ;9/!

&: :?V9/!

V: 6,: /!V

R: 6 /!

D#$: ?,6> /!


21/28

CIRCUITO R1C1FRECUENCIA: 460H

seg rad Hz f

seg T Hz f

T

5

5

10.52,240000..2..2

10.5,240000

11

=⇒==

=⇒== −

ω π π ω

( )

mAV

Z

V I teorica 11,4

)10047,01052,2

1(150

5,02

2

65

2

=

⋅⋅⋅+Ω

⋅==

−

t ! $!e-* /e /e0&&e ⇒ Se '$!ene /e l& "%+0!& /e l& e3&le en el!l*!

E*e%!-en$&l-en$e, -e/!-4 t = : µe".

ϕ 4 +n"#l /e /e0&&e

º92,2851,010.2.10.52,2. 65 =⇒=== − ϕ ω ϕ rad seg seg rad t

C-*&%+n/l n el &l% $e%!, $ene-4

º3,2952,0047,0.150.10.52,2

11

5=⇒=

Ω

=== ϕ µ

ω ϕ rad

F seg

rad arcTg

R

C arcTg R

X acrTg C

mAdiv

V div

I practico 10,3150

2,03,2

=Ω

⋅

=

20

ε

i

VR

VL

φ


22/28


DIARAMA FASORIAL

FRECUENCIA: 130H

seg rad

Hz f

seg T Hz f

T

4

5

10.2,813000..2..2

10.7,713000

11

=⇒==

=⇒== −

ω π π ω

21

40KHz

V ( ): ?,: ;9/!V

R (): ?,: ;9/!

&: >V9/!

V: :, /!V

R: :,6 /!

D#$: ?,8 /!

ε

i

VR

VC

φ


23/28

( )

mAV

Z

V I teorica 36,2

)10047,0102,8

1(150

5,02

2

64

2

=

⋅⋅⋅+Ω

⋅==

−

E*e%!-en$&l-en$e, -e/!- el $!e-* /e /e0&&e4 t = @6 µe".

ϕ 4 +n"#l /e /e0&&e

º3,6107,110.13.10.2,8. 64 =⇒=== − ϕ ω ϕ rad seg seg

rad t

C-*&%+n/l n el &l% $e%!, $ene-4

º6005,1047,0.150.10.2,8

11

4=⇒=

Ω

=== ϕ µ

ω ϕ rad F

seg rad

arcTg RC arcTg

R X acrTg C

mAdiv

V div

I practico 00,2150

2,05,1

=Ω

⋅

=


DIARAMA FASORIAL

22

13KHz

V ( ): ?,: ;9/!V

R (): ?,: ;9/!

&: @?V9/!

V: 6,@ /!V

R: @,> /!

D#$: @,6 /!

ε

i

VR

VC

φ


24/28

FRECUENCIA: 70H

seg rad Hz f

seg T Hz f

T

4

4

10.1,58000..2..2

10.25,18000

11

=⇒==

=⇒== −

ω π π ω

( )

mAV

Z

V I teorica 6,1

)10047,0101,5

1(150

5,02

2

64

2

=

⋅⋅⋅+Ω

⋅==

−

E*e%!-en$&l-en$e, -e/!- el $!e-* /e /e0&&e4 t = :8 µe".

ϕ 4 +n"#l /e /e0&&e

º2,7023,110.24.10.1,5. 64 =⇒=== − ϕ ω ϕ rad seg seg

rad t

C-*&%+n/l n el &l% $e%!, $ene-4

º3,7023,1047,0.150.10.1,5

11

4=⇒=

Ω

=== ϕ µ

ω ϕ rad

F seg

rad arcTg

R

C arcTg R

X acrTg C

mAdiv

V div

I practico 33,1150

2,01

=Ω

⋅

=


23

8KHz

V ( ): ?,: ;9/!V

R (): ?,: ;9/!

&: :?V9/!

V: 6,: /!

VR: @ /!D#$: @,: /!


25/28

DIARAMA FASORIAL

OBSERVACIONES

N$&- #e, en el !%#!$ R L1, #&n/ l& 0%e#en!& /!-!n#2e, el +n"#l/e /e0&&e e &H!&, /e'!/ & #e /!-!n#2e l& %e&$&n!& !n/#$!& X L, 2& #el& -!-& e /!%e$&-en$e *%*%!n& & l& 0%e#en!&

P% n$%&*&%$e, e- #e #&n/ /!-!n#!- l& 0%e#en!&, el +n"#l/e /e0&&e -en$&, /e'!n/e e$, & #e X C e !ne%&-en$e *%*%!n&l &l& 0%e#en!& /e $%&'&.

C&'e &l&%&% #e l& /!0e%en!& '$en!/& en$%e l &l%e $e%!&l#l&/ 2 l &l%e *%+$!, n /e'!/& & e%%%e /e -e/!!n, /e&*%e!&!n, -&l n$&$, *&&e /e l& "%+0!& /el !l*! & l&#&/%!#l&, e$.

24

ε

i

VR

VC

φ


26/28

CIRCUITO R1R3L1C1

P&%& */e% /e$e%-!n&% l& 0%e#en!& /e %en&n!&, $ene- / 0%-&4

- Enn$%&% l& I I -&- J&ll&% #n /e0&&e n#l (ϕ ?)

U&- l& l$!-& /e l& *!ne *#e$ #e e -& *%e!& 2 -+ en!ll&,2& #e e -+ !-*le &*%e!&% #n /e0&&e en el !l*!, #e /e$e%-!n&% en#e --en$ l& %%!en$e I , e H&ll& en # &l% -+!-.

E$e -$/ n!$e en &%!&% l& 0%e#en!& /el "ene%&/% /e e3&le, H&$&#e l& "%+0!& (/e ε 2 V R ) en el !l*! !n!/&n. E$& 0%e#en!&enn$%&/& e, en$ne, l& ll&-&/& 0%e#en!& /e %en&n!&.

E$e 0en-en e /& #&n/ X L X C , 2& #e4

? /e0&&(e =⇒=−

= ϕ ϕ R

arcTg R

X X arcTg C L

0

e- #e #&n/ e$ #e/e4 V L V C ⇒ ε R 1..I R 2 .I X L.I 5 X C .I

⇒ el !%#!$ e *#%&-en$e %e!$!

CÁLCULO TEÓRICO DE f 0

sT kHz f

T

kHz f kHz f kHz f

seg rad

f f seg

rad

F mHy

LC LC C L X X X

T!RIC!T!RIC!

T!RICA

C L

T!RICA

5

0

000

4

4

2

10.34,971,10

11

07,165,135,55,071,10

.2

10.8,6

2210.8,6

047,0.7,4

1

1110

−=⇒==

=⇒=⇒=

⇒==⇒=⇒==

⇒=⇒=⇒=⇒=⇒=

π π

ω π ω

µ ω

ω ω ω

ω

CALCULO PRÁCTICO DE f 0

C#&n/ l& "%+0!& /e ε 2 V R !n!/en, el *e%1/ -e/!/ /el !l*! e4

" #R$C"IC% 78 µe".

kHz f seg T

f "RACTIC!

"RACTIC!

"RACTIC! 64,10

9411 =⇒== µ

25

X ?


27/28

RAFICA Y V R VS TIEMPO

C- *#/!- &*%e!&% en l& "%+0!&, e- #e #&n/ &%!&- l&0%e#en!& /e %en&n!& f & & ?,>f & , e- #e l& %%!en$e &/el&n$& & l& $en!n,

26

f 0

V ( ): ?,: ;9/!V

R (): ?,: ;9/!

&: @?V9/!

V: 6,: /!V

R: :,< /!

D#$: ? /!

0,5 · f 0

V ( ): ?,: ;9/!V

R (): ?,: ;9/!

&: :?V9/!

V: 6,: /!V

R: :,: /!

D#$: ?, /!

1,5 · f 0

V ( ): ?,: ;9/!V

R (): ?,: ;9/!

&: @?V9/!

V: 6,: /!V

R: :,> /!

D#$: ?,6 /!


28/28

*%e/-!n&n/ #n -*%$&-!en$ &*&!$!K -!en$%& #e #&n/ l& 0%e#en!&/e %en&n!& f & l& &%!&- & @,>f & , e 'e%& #e l& %%!en$e &$%&&%+ & l&$en!n, *%e/-!n&n/ #n -*%$&-!en$ !n/#$!.

El -*%$&-!en$ /e l& %%!en$e en #n !%#!$ en e%!e /e %%!en$e&l$e%n&, #&n/ &%1& l& 0%e#en!& /e l& e3&l /e en$%&/&, e e&$&-en$e

&n+l" & l& %e*#e$& /el !$e-& -&&5%e%$e, #e $!ene 0#e%& /e&-%$!"#&-!en$ !, &l &%!&% l& 0%e#en!& /e l& 0#e%& !-*#l%&.

OBSERVACIONES

P&%& l& 0%e#en!&, !"#&l & l& 0%e#en!& /e %en&n!&, X L X C , *% l #eV L V C , en$ne el !%#!$ e%+ *#%&-en$e %e!$! ε R 1.i R 2 .i

Al /!-!n#!% l& 0%e#en!& &*&%ee #n +n"#l /e /e0&&e, &/el&n$&n/ l&%%!en$e & l& $en!n, 2 el !%#!$ $en/%+ #n -*%$&-!en$ &*&!$!. M!en$%&#e &l -en$&% l& 0%e#en!&, n %e*e$ & l& 0%e#en!& /e %en&n!&,

$&-'!n &*&%ee%+ el +n"#l /e /e0&&e, -!en$%& #e l& %%!en$e %e$%&&%+ & l&$en!n, 'e%+n/e #n -*%$&-!en$ !n/#$!.

CONCLUSIONES

Cn l !$ &n$e%!%-en$e */e- /e/#!%, #e n e nee&%! &-'!&% l -*nen$e /e #n !%#!$, *&%& &-'!&% # 0#n!n, e /e!%, *&%& &%!&% #-*%$&-!en$. P% ee-*l /e &*&!$! & !n/#$! e *#e/e l"%&% -e/!&n$el& &%!&!n /e l& 0%e#en!& /e l& e3&l /e en$%&/&. W$e -*%$&-!en$ e -#2$!l, *% ee-*l, en l &*&%&$ /e %&/! %ee*!n !n nee!/&/ /e $ene% #e&-'!&% l ele-en$ n$!$#$! /e l !%#!$ /e l &*&%&$. L -!-#e/e, ! #e%e- &-'!&% # -*%$&-!en$ /e !n/#$! & &*&!$!.

T&-'!n !- #e e *#e/e %e"#l&% el +n"#l /e /e0&&e en$%e l&e3&le /e en$%&/& 2 /e l& %%!en$e #e !%#l& & $%& /e #n !%#!$, !n-/!0!&% l -*nen$e /el -!-. E$ e %e&l!& -e/!&n$e el &-'! /e0%e#en!&.

BIBLORAFIA

• '()IC* +IV-R)I"*RI*, /e SEARS5=EMANSY5YOUNG, Se$& e/!!nEDIT. A//!n5ele2 I'e%&-&%!&n& S.A., !l-!n"$n, Del&&%e, E.U.A. @7C&*1$#l 6

Fisica3 - TP5 “CIRCUITOS EN CORRIENTE ALTERNA”

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Transcript of Fisica3 - TP5 “CIRCUITOS EN CORRIENTE ALTERNA”