UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD ACULTAD DE INGENIERI INGE NIERIA A CURSO BASICO
LABORATORIO DE FISICA BASICA III
INFORME 9 OSCILACIONES ELECTROMAGNÉTICAS
ESTUDIANTE: MONTAÑO SAAVEDRA MAURICIO DANIEL CARRERA: ING. QUIMICA GRUPO: B DOCENTE: ING. MAMANI FECHA DE PRACTICA: 12 NOVIEMBRE FECHA DE ENTREGA: 19 NOVIEMBRE
OSCILACIONES ELECTROMAGNÉTICAS OBJETIVO -
Ver!"#r $%& 're& '(%& )e re&(*e&'# e+ e$ "%,(%r'#,e+'% )e *+ "r"*'% RLC &ere e-"'#)% (%r *+ %$'#/e "%+&'#+'e.
FUNDAMENTO TEÓRICO Se# e$ "r"*'% )e $# F0*r# 1 *e 3# (er,#+e")% "%,% &e ,*e&'r# (%r ,*"3% 'e,(%. S e+ '45 e$ "%+,*'#)%r S &e (# )e $# (%&"6+ 1 # $# 2 # (#r'r )e e&e +&'#+'e &e 'e+)r7: V
=v +v +v R
L
C
(1)
% &e#: V
= R i + L
di dt
+ vC (2)
D#)% *e: i
=
C
dvC dt
(3)
$# e"*#"6+ 82 (*e)e e&"rr&e: d2vC dt 2
+
R dvC L dt
+
1 LC
vC
=
V LC
(4)
% e+: d 2 vC dt
2
+ 2α
dvC dt
+ ωO2 vC = ωO2 V (5)
)%+)e ω5 re"e e$ +%,re )e ;re"*e+"# +#'*r#$ +% #,%r'0*#)# < "%+&'#+'e )e #,%r'0*#"6+ &e+)%:
ω = O
1 LC
α=
α
e$ )e
R 2L
(6)
P#r# $# e"*#"6+ 8= )e(e+)e+)% )e $# +#'*r#$e># )e $#& r#?"e& )e &* e"*#"6+ "#r#"'er?&'"# (*e)e+ )#r&e 're& '(%& )e &%$*"%+e& % re&(*e&'#& )e C@ e&'#& &e )e&"re+ # "%+'+*#"6+:
α > ω0
ó
R
L
>2
C
1. R!"#!$% !&'%&$*+#%,%. S $# e"*#"6+ 8= re&*$'# &er: vC
= V 1 + 1τ
1
1
τ
−t
2
e
− 1τ 2
$# &%$*"6+ )e 1
τ1
+
1τ
2
τ
−t
1
e
τ2
− 1τ 1
()
)%+)e:
τ = 1
1
α− α −ω
τ = 2
2
2
O
1
α+ α −ω
2
2
O
()
α = ω0
ó
R = 2 L
C
2. R!"#!$% /&0 %&$*+#%*0$& /$*/&. S 8#$%r "%+%")% "%,% re&&'e+"# "r?'"# $# &%$*"6+ )e $# e"*#"6+ 8= e&: − t 1 − t v C = V1 − e τ − e τ
τ
()
)%+)e:
τ=
1
α
(1 )
α < ω0 3. R!"#!$% !#'%&$*+#%,% # &!/*%$&*%. S &%$*"6+ )e 8= e&:
ωO − t τ − ω v C = V 1 − e sen ωt + tg 1 α ω )%+)e:
ó
R < 2 L
C $#
(11)
τ=
1
α
(12)
<
ω= ω −α 2
2
O
(13)
e&'# $',# e& $# ;re"*e+"# +#'*r#$ #,%r'0*#)#@ $*e0% e$ (er%)% )e %&"$#"%+e& e+e )#)% (%r: T=
2π
ω
(14)
E+ $# !0*r# 2 &e re(re&e+'#+ $%& 're& '(%& )e re&(*e&'# )e C.
C VCMM Re&(*e&'# &*#,%r'0*#)#
e-"'#"6+
V
Re&(*e&'# "%+ #,%r'0*#,e+'% "r?'"% Re&(*e&'# &%re#,%r'0*#)#
T
$ F*+#% 2.
P#r# e$ #+7$&& (r7"'"% )e *+ "r"*'% "%,% e$ )e $# F0*r#1 $# ;*e+'e )e 'e+&6+ "%+'+*# V < e$ "%+,*'#)%r S (*e)e+ ree,($#>#r&e (%r *+ 0e+er#)%r )e ;*+"%+e& *e e+'re0*e *+# %+)# "*#)r#)# %&"$#+)% e+'re 5 < V@ )e e&'# ,#+er# e$ %$'#/e &%re e$ "#(#"'%r &e 3#"e (er6)"% < (*e)e &er e&'*)#)% (%r *+ %&"$%&"%(%. E+ '#$ "#&% (*e)e &er +e"er% "%+&)er#r $# re&&'e+"# )e $)# )e$ 0e+er#)%r )e ;*+"%+e& R 5 #&? "%,% $# re&&'e+"# 63,"# )e$ +)*"'%r RL.
RL C
E+ $# F0*r# &e 'e+e *+ "r"*'% *e e,($e# *+ 0e+er#)%r )e ;*+"%+e& "%+ &* re&&'e+"# )e $)# R O ,%&'r#)# e-($?"'#,e+'e. De$ ,&,% ,%)% &e ,*e&'r# $# re&&'e+"# 63,"# )e$ +)*"'%r R L. S $#& re&&'e+"#& (re&e+'e& &e re+e+ e+ *+# re&&'e+"# '%'#$ R T4RORLR e$ "r"*'% e& &,$#r #$ )e $# F0*r# 1 < '%)% e$ #+7$&& re#$>#)% (#r# #*e$ "#&% e& 7$)% (#r# &'e &e,(re *e &e &*&''*<# R (%r R T.
E+ e$ "#&% %&"$#'%r% α < ω (*e)e+ )e'er,+#r&e e-(er,e+'#$,e+'e ,)e+)% e$ (er%)% T < e$ (r,er ,7-,% )e$ %$'#/e &%re e$ "#(#"'%r )e&0+#)% CMM "%+ $#& &0*e+'e& e"*#"%+e&:
α EXP =
2 T
ln
V v CMM
−V
ω EXP =
2π
ω (15)
TRATAMIENTO DE DATOS C7LCULOS R!"#!$% !&' %&$*+#%,% 1 E0 '%! % % $%'% 1 , % 8&9% , ,%$&!: %'&% #0% $%'% $-/;"/$&. E!$% #$*% %+0*$#, ,' %#%! 0 '%! % % /#%/*<0 /&!"&0,*0$ , =#0,%0$& $&*/& > /&0!*,%0,& % !*!$0/*% $&$% , /*/#*$&. D*'#9% % /#% /$& ! $ > 0 *!& +%?/& #'*/% &! "#0$&! /&!"&0,*0$! % /;" '8*&
V" e-( 8V
'8& 5
5
5
25
555552
5
5
55555
52
5
55555
1
155
55551
1
V" 'e% 8V 5 5229 59=2 1 152=9 2595= 9
#$;# R'%'#$ 8%3,
1291
%,e0#
=
1559=
'#* 1
555512=92
'#* 2
95E5
15
55551
1
255
55552
2
55
5555
292
55
5555
2
=55
5555=
55
5555
2=2 1 59529 =22 2 =155 1 2 1 = 1
1J'#*1
9111=
1J'#*2
2=15519
V/ 0 R!"#!$% !&'%&$*+#%,% .= .= 2.=
V/ (V)
e-( 'e%
2 1.= 1 5.= 5 5
155
255
55
55
=55
55
55
T*"& (*/&!+#0,&!)
R!"#!$% /&0 %&$*+#%*0$& /*$*/& 2. R"$* "#0$& %0$*& "%% % $%'% 2 '8*&
V" e-( 8V
'8& 5
5
15 25
555551 555552
V" 'e% 8V 5
5 52912 5 92 59 515
#$;# '#*
== 229E 5=
5
55555
1=
5
55555
212
=5
55555=
2=
5
55555
29
5
55555
155
55551
12= 555512=
2
255
9
55552
== 1=12 =9 2595 =2 2=5== 12 295525 22 12=5 =9 = 22 91 1
V/ 0 R!"#!$% /&0 %)&($*+#%)*0$& /(*$*/& .= .= 2.=
e-% 'e%
V/ (V) 2 1.= 1 5.= 5 5
=5
155
1=5
T*"& (*/&!+#0,&!)
255
2=5
R!"#!$% !#'%&$*+#%,% 3. R"$* "#0$& 1 "%% % $%'% 3 '8*&
V" e-( 8V
'8& 5
5
5
55555
=2 55555=2
=
2 555552
2
155
55551
=5
15
55551
2
1 55551
12
212 5555212
=5
25
55552
5555
=2
25
55552
5
9 55559
2
= 5555=
1
5555
1
V" 'e% 8V 5 1151 1= =5 1 155 2 =591 52 255 5 ==99= =11= 12 =95 92 = 9=55 = 29=1 21= 51 2 1195 9
#$;# '#*
19 55551=
%,e0#
11=22
%,e0# %
=
V/ 0 !"#!$% !#'%&$*+#%,% = e-( 'e%
V/ (V) 2 1 5 5
155
255
55
55
=55
55
55
55
T*"& (*/&!+#0,&!)
4. C&"%% &! %&! ;"*0$%! > $&*/&! , %=% > &+%. @%% !$&: ;$% &! %&! ;"*0$%! , VCMM > T ,*/$%0$ , % $%'% 3 C%,% e,%&: T =
2 π ω
D%+)e T e& e$ 'e,(% +)"#)% e+ $# 0*?# *e e+ +*e&'r% "#&% e& 55551& A)e,7& V" MM e& 2V C%+ e&'%: K e-( 9=
K 'e%
); 151 19 99
e-(
'e%
); 1 99 11=22
CUESTIONARIO 1. E0 /%!& , % !"#!$% &!/*%$&*%. @& # /%#!% =!*/% &$%9 !&' /%"%/*$& /&0$*0% %#0$%0,& ,!"#! , # 8% %/%0%,& &$%9 , ;/*$%/*<0 -E&'% e& (%&$e e+ *+ "#(#"'%r )e *+ 0r#+ )e$"'r"% < ($#"#& "%+)*"'%r#& "%,% e$ "#(#"'%r e&'7 "#r0#)% <# (%r $ 'e+)r7 *+ %$'#/e V" )e & ,&,%. Y "%,% V (# (%r $# re&&'e+"# R < $# %+# L e&'# $$e0#r "%+ ,e+%r "#r0# );ere+"#$ )e (%'e+"#$ #$ "#(#"'%r e$ "*#$ #*,e+'#r# &* "#r0# < e&'# (er,#+e"er7 #&? "#r0#)# (%r *+ +&'#+'e (e*e%. 2. E0 /%!& , % !"#!$% &!/*%$&*%. @& # /%#!% =!*/% ,*!*0#> % %"*$#, , %! &!/*%/*&0! L# #,($'*) )e $#& %&"$#"%+e& &e ,#+'e+)r?# "%+&'#+'e & $# %&"$#"6+ ;*er7 )e#$ #$e )e"r (%r e/e,($% e+ *+ "r"*'% LC )e#$ )%+)e +% e-&'e (r))# )e e+er0?# (er% e+ e$ "r"*'% RLC &e (r%)*"e (er))#& )e e+er0?# )e)% # *e e+ $# re&&'e+"# &e (r%)*"e e;e"'% %*$e < '#,+ #*+*e ,e+%r e+ e$ +)*"'%r <# *e '#,+ (%&ee re&&'e+"# R L. 3. C#%0,& % !% , +0%,& /% % HV (& # #*% % +!% /&0#$%,& , % F*+#% 1: , % "&!*/*<0 2 % % 1) $%'*0 ! "!0$%0 =0<0&! $%0!*$&*&! 0 C. A # ! ,' !$& -C*#+)% &e (r%"e)e # "#r0#r *+ "r"*'% e+ +*e&'r% "#&% RCL &e 'e+e *e '%,#r ,*< e+ "*e+'# *e $# "#r0# +% &e 3#"e e+ *+ ,%,e+'% & +% *e e& ,*< (#*$#'+#,e+'e. P%r e&'e "#&% "*#+)% e$ %$'#/e )e $# ;*e+'e )&,+*
CONCLUSIONES Se #r,% *+ "r"*'% RLC &ere "%+ *+# re&&'e+"# #r#$e (#r# (%)er er $# re&(*e&'# &*#,%r'0*#)# &%re#,%r'0*#)# < "%+ #,%r'0*#,e+'% "r'"% )e$ "r"*'%. Se %&er% ,e)#+'e e$ %&"$%&"%(% e$ %$'#/e )e$ "%+)e+)%r "%,% ;*+"6+ )e$ 'e,(% +%'7+)%&e $#& "*r#& "#r#"'er?&'"#& )e $#& re&(*e&'#& &*#,%r'0*#)# &%re#,%r'0*#)# < "%+ #,%r'0*#,e+'% "r'"%. Se 0r#!"#r%+ $#& re&(*e&'#& &*#,%r'0*#)# &%re#,%r'0*#)# < "%+ #,%r'0*#,e+'% "r'"% e-(er,e+'#$e& "%,(#r7+)%$#& "%+ $#& "*r#& 'e%r"#& %&er#+)% &* &,$'*) < (%"# #r#"6+.
Se "%,(#r#r%+ K < e-(er,e+'#$e& "%+ &*& #$%re& 'e%r"%& %'e+e+)% *+# ,*< #/# );ere+"# (%r"e+'*$ $# "*#$ +%& +)"# e$ *e+ (r%"e),e+'% e-(er,e+'#$.