UNIVERSIDADE FEDERAL DE UBERLÂNDIA FACULDADE DE ENGENHARIA ELÉTRICA ELETRICIDADE E MAGNETISMO
RELATÓRIO EXPERIMENTO Nº 3 LABORATÓRIO DE FÍSICA EXPERIMENTAL II
BÁRBARA FLAVIANA LUTHULI PEDRO RAFAELA WILLIAM
UBERLÂNDIA 2011
BÁRBARA FLAVIANA LUTHULI PEDRO RAFAELA WILLIAM
RELATÓRIO EXPERIMENTO Nº 3 CAPACITORES
Relat!"# a$!e%e&ta'# a# $!#(e%%#! Wa)&e! Ut"el S"l*a !e(e!e&te + '"%,"$l"&a 'e F-%",a E.$e!"/e&ta 2 '# 2 $e!-#'# 'e E&)e&a!"a Elt!",a 'a U&"*e!%"'a'e Fe'e!al 'e U3e!l4&'"a5
UBERLÂNDIA 2011
SUMÁRIO
CONTEÚDO 15 INTRODU67O 555555555555555555555555555555555555555555555555555555555555555555555555555 5555555555555555555551 25 OB8ETIVO 55555555555555555555555555555555555555555555555555555555 5555555555555555555555555 5555555555555555555552 95 PROCEDIMENTO E:PERIMENTAL55555 5555555555555555555555555555555555555555555555555555552 951 MATERIAL NECESSÁRIO55555555555555555555555555555555555555555555555555555555555555555555552 952 METODOLOGIO555555555555555555555555555555555555555555555555555555555555555555555555 5555555555555559 ;5 RESULTADO E DISCUSS ;59 CÁLCULO PARA LINEARI=A67O555555555555555555555555555555555555555555555555555555555555? ;5; RESULTADO DA LINEARI=A67O55555555555555555555555555555555555555555555555555555555551; ;5@ ERRO5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555 555555555555555551> @5 CONCLUS7O555555555555555555555555555555555555555555555555555555555555555555555555555555 55555555555555555551
1
1. INTRODUÇÃO O ,a$a,"t#! (#!/a'# $#! 'a% $la,a% # elet!#'#% e te/ ,#/# (&# a!/ae&a/e&t# 'e ,a!)a% #$#%ta% %e&'# ela% %e$a!a'a% $#! "%#la&te # $#! / '"elt!",# e $!"&,"$al/e&te ,#&'t#!a% e te/ %a ,a!)a a!/ae&a'a
C#&%"'e!e # ,"!,"t# /#%t!a'# &a (")!a 15 E%ta&'# # ,a$a,"t#! "&","al/e&te 'e%,a!!e)a'# %e a ,a*e S (#! (e,a'a a (#&te 'e te&%# V ,!"a! /a ,#!!e&te elt!",a "JtK at e # ,a$a,"t#! ("e ,#/$leta/e&te ,a!!e)a'# ,#/ /a ,a!)a CV5 D!a&te # $!#,e%%# 'e ,a!)a '# ,a$a,"t#! te/#% ε =
R
d q d t
+
S
q C
J1K
R
V
o
C
Figu! 1" ,"!,"t# $a!a ,a!)a e 'e%,a!)a 'e / ,a$a,"t#!
#
2
Pa!a / "&%ta&te 'e te/$# t0% te/#% e a ,a!)a '# ,a$a,"t#! a te&%# &# ,a$a,"t#! e a ,#!!e&te elt!",a '# ,"!,"t# elt!",# %e!# 'a'a% $#! q
=
C ε (1 − e
(1 −e
V
=ε
i
ε
=
R
e
t RC
−
t RC
−
)
)
t RC
−
E%ta&'# # ,a$a,"t#! ,a!!e)a'# e a3!"&'# e&t# a ,a*e S &# te/$# t 0% a$a!e,e! /a ,#!!e&te e/ %e&t"'# ,#&t!!"# + a&te!"#! at e # ,a$a,"t#! 'e%,a!!e)e ,#/$leta/e&te5 E%ta ,#!!e&te #3e'e,e + !ela# Jle" 'a% /ala%K5 dq dt
+
q R C
=
0
A ,a!)a &# ,a$a,"t#! a te&%# &# ,a$a,"t#! e a ,#!!e&te e/ (&# '# te/$# '!a&te # $!#,e%%# 'e 'e%,a!)a %e!# 'a'a% $#! q
=
V
i
#&'e
qo a
q0 e e
ε
=
=−
t R C
−
t R C
−
qo
R C
e
t R C
−
,a!)a '# ,a$a,"t#! ,a!!e)a'#5
$. OB%ETI#O Dete!/"&a! e.$e!"/e&tal/e&te a ,!*a 'e 'e%,a!)a 'e / ,a$a,"t#! J'e ,a$a,"t4&,"a CK %#3!e / !e%"%t#! J'e !e%"%t&,"a RK ,al,la! a ,#&%ta&te 'e te/$# ,a$a,"t"*a Q RC e ta/3/ a ,a$a,"t4&,"a '# ,a$a,"t#!5
3. PROCEDIMENTO EXPERIMENTAL !. MATERIAL NECESSÁRIO
F#&te DC @00V Mlt-/et!# A&al)",# Pla,a 'e $!#t#3#a!' Ca3#% $a!a ,#&e.e%
3
Ca*e l")a e 'e%l")a C!#&/et!# Ca$a,"t#! 'e 1 . >90V5
Figu! $ Ca$,"t#! l")a'# a (#&te e a# /lt"/et!#
&. METODOLO'IA
1 Ve!"(",#%e "&","al/e&te %e # ,a$a,"t#! e%ta*a 'e%,a!!e)a'#5
2 O ,a$a,"t#! e e%ta*a e/ / ,"!,"t# (#" a,"#&a'# /e'"a&te a /a (#&te e e%ta*a ,#&e,ta'# a ele5
9 A&te% 'e l")a! a ,a*e S 'a (#&te l")#%e # /lt-/et!# ,#/ # *#lt-/et!# ,#/ (&'# 'e e%,ala 'e 1000 V5
; A&#t#%e # *al#! 'a !e%"%t&,"a '# *#lt-/et!# $a!a e%,ala5
@ L")a! a ,a*e S e ,#/ # ,!#&/et!# %"/lta&ea/e&te $a!a te&ta! /e'"! # te/$# ,#/ a /a"#! e.at"'# $#%%-*el '# !e,e3"/e&t# 'e ,a!)a $el# ,a$a,"t#!5
4
> F#" ,#&%ta'# # *al#! 'e%ta ,a!)a a%%"/ ,#/# # te/$# 'e ,a!!e)a/e&t#5
X C#/ # ,a$a,"t#! ,a!!e)a'# 'e%l")#%e a ,a*e S e %"/lta&ea/e&te "&","# # ,!#&/et!#5
E/ 'ete!/"&a'# "&te!*al# 'e te/$# JtK %e t#/a*a #% *al#!e% '# te/$# e '# *al#! 'a ,a!)a !e%ta&te &# ,a$a,"t#! t#/a'# &# /lt-/et!# at %e t#tal 'e%,a!!e)a/e&t#5
? E%te e.$e!"/e&t# (#" !e$et"'# t!% *ee% $a!a e a #3%e!*a# '# ,#/$#!ta/e&t# '# ,a$a,"t#! (#%%e /el#! e%t'a'#5
(. RESULTADOS E DISCUSS)ES O% 'a'#% ,#leta'#% $#! e%te )!$# e/ !ela# +% a/#%t!a% %# a$!e%e&ta'#% &a% ta3ela%5
(.1 C*+,-! /, /!/* A 0 Pi,i* Te/$# 'e ,a!!e)a/e&t# 0000;; % De%,a!!e)a/e&t#
Me'"'a
VJ*K
TJ%K
1
@?0
0
2
9@0
10
9
220
20
;
1;0
90
5
@
100
;0
>
>0
@0
X
;0
>0
90
X0
?
20
0
T!&,+! 21" Me'"'a% 'e V . t 'a $!"/e"!a ,#leta
B S,gu4/* Te/$# 'e ,a!!e)a/e&t# 0000@@ % De%,a!!e)a/e&t# Me'"'a
VJ*K
TJ%K
1
@0
0
2
9>0
10
9
210
20
;
1;0
90
@
?0
;0
>
@0
@0
X
;0
>0
90
X0
?
20
0
T!&,+! 2$ Me'"'a% 'e V . t 'a %e)&'a ,#leta
C 0 T,5,i* Te/$# 'e ,a!!e)a/e&t# 0000;0% De%,a!!e)a/e&t# Me'"'a
VJ*K
TJ%K
1
@0
0
2
9>0
10
6
9
220
20
;
1;0
90
@
?0
;0
>
>0
@0
X
;0
>0
90
X0
?
20
0
T!&,+! 23" Me'"'a% 'e V . t 'a te!,e"!a ,#leta
(.$ Li4,!i6!78, /* /!/* u!4/* ,g,9* +i4,! O E%t'# 'e%te ,#/$#!ta/e&t# $#'e!"a %e! (e"t# $#!
−t
V = ε 5e Rc −t
l& V = l& ε + l&Je
Rc
5t RC ↑ 1
l& V = l& ε + −
↑
↑
y
a
b
Então N
= l& V x = t a = l& ε y
b =−
K
1 RC
O&'e
C Ca$a,"t4&,"a
← x
7
R Re%"%t&,"a V V#lta)e/ t Te/$#
C#/ a !e)!e%%# l"&ea! $#%%-*el (ae! /a $!e*"%# '# ,#/$#!ta/e&t# '# )!(",# 'a !ela# e&t!e 'a% *a!"*e"% &# ,a%# e&t!e # te/$# e a *#lta)e/ ,#/$a!a&'# a%%"/ ,#/ # ,#/$#!ta/e&t# !eal 'a *a!"a#5 O /t#'# /a"% %a'# $a!a e%t"/a! #% $a!4/et!#% A e B # /t#'# '#% /-&"/#% a'!a'#%5 E%te /t#'# )a!a&te e a !eta #3t"'a aela $a!a a al %e te/ a% /e&#!e% '"%t4&,"a% Ja# a'!a'#K e&t!e #% *al#!e% #3%e!*a'#% 'e Y e a $!$!"a !eta5 O ,#e(","e&te a&)la! e%t"/a'# $ela (!/la
n
b = ∑J x1 − xKJ yi − y K i =1 n
∑J x
1
− xK
2
i =1
sendoG
x =
y =
1
n 1
n
n
∑ x
1
i =1
n
∑ y
1
i =1
O "&te!,e$t# e%t"/a'# $ela (!/la
a = y −b x
P#'e&'# %e! *"%ta ,#/# /a ea# 'a !eta '# (#!/at#
8
: ; ! < &.= U%a&'# #% ,#&,e"t#% e (#!/la% a,"/a $#%%-*el (ae! # ,al,l# 'e l"&ea!"a# '#% 'a'#% ,#l"'#%5
(.3 C>+5u+* ?!! +i4,!i6!79*
A Pi,i*
x =
x =
x =
1 n 1 ?
n
∑ x
1
i =1
?
∑0 + 10 + 20 + 90 + ;0 + @0 + >0 + X0 + A0 i =1
9>0 ?
x = ;0
n
y =
1
y =
1
y =
1@@0
∑ y
n i =1
1
?
∑@?0 + 9@0 + 220 + 1;0 + 100 + >0 + ;0 + 90 + 20
? i =1
?
y = 1X2G22
9
?
J0 −;0KJ@?0 −1X2G 22K +J10 −;0KJ9@0 −1X2G22K +J 20 −;0KJ 220 −1X2G22K + ∑ i= 1
J90 −;0KJ1;0 −1X2G22K +J ;0 −;0KJ100 −1X2G22K +J@0 −;0KJ>0 −1X2G 22K + J>0 −;0KJ ;0 −1X2G22K +JX0 −;0KJ90 −1X2G 22K +JA0 −;0KJ 20 −1X2G22K
b =
?
J0 −;0K ∑
2
+J10 −;0K
2
2
+J>0 −;0K +JX0 −;0K
+J20 −;0K
2
+J90 −;0K
2
2
+JA0 −;0K
i= 1
+J@0 −;0K
2
−9>A00
b =
>000
b =−>G1999
a = y −b x a =1X2G22 −J −>G1999K5;0 a =1X2G22 +2;@G992 a =;1XG@@2
B S,gu4/*
x =
x =
x =
1 n 1 ?
n
∑ x
1
i =1
?
∑0 + 10 + 20 + 90 + ;0 + @0 + >0 + X0 + A0 i =1
9>0 ?
x = ;0
2
+J ;0 −;0K
2
10
y
y
=
=
1 n 1 ?
n
∑ y
1
i =1
?
∑@A0 + 9>0 + 210 + 1;0 + ?0 + @0 + ;0 + 90 + 20 i =1
1@20
y
=
y
= 1>AGA?
?
?
J0 −;0KJ@A0 − 1>AGA?K +J10 −;0KJ9>0 − 1>AGA?K +J 20 −;0KJ 210 − 1>AGA?K ∑ i= 1
J90 −;0KJ1;0 − 1>AGA?K +J ;0 −;0KJ?0 − 1>AGA?K +J@0 −;0KJ@0 − 1>AGA?K + b
J>0 −;0KJ ;0 − 1>AGA?K +JX0 −;0KJ90 − 1>AGA?K +JA0 −;0KJ 20 − 1>AGA?K = ? J0 −;0K ∑
2
+J10 −;0K
2
+J 20 −;0K
2
+J90 −;0K
2
i= 1
+J@0 −;0K 2 +J>0 −;0K 2 +JX0 −;0K 2 +JA0 −;0K 2
b
− 9>>00 = >000
b
=− >G1
a = y −b x a =1>AGA? −J −>G1K5;0 a =1>AGA? +2;; a =;12GA?
C T,5,i*
x =
x =
x =
1 n 1 ?
n
∑ x
1
i =1
?
∑0 + 10 + 20 + 90 + ;0 + @0 + >0 + X0 + A0 i =1
9>0 ?
x = ;0
+J;0 −;0K
2
11
y
y
=
=
1 n 1 ?
n
∑ y
1
i =1
?
∑@A0 + 9>0 + 220 + 1;0 + ?0 + >0 + ;0 + 90 + 20 i =1
1@;0
y
=
y
= 1X1G1
?
?
J0 −;0KJ@A0 − 1X1G1K ∑ i
+J10 −;0KJ9>0 − 1X1G1K +J20 −;0KJ 220 − 1X1G1K
= 1
J90 −;0KJ1;0 − 1X1G1K +J;0 −;0KJ?0 − 1X1G1K +J@0 −;0KJ>0 − 1X1G1K + b
J>0 −;0KJ;0 − 1X1G1K +JX0 −;0KJ90 − 1X1G1K +JA0 −;0KJ20 − 1X1G1K = ? J0 −;0K 2 ∑ i
+J10 −;0K 2 +J 20 −;0K 2 +J90 −;0K 2 +J ;0 −;0K 2
= 1
+J@0 −;0K 2 +J>0 −;0K 2 +JX0 −;0K 2 +JA0 −;0K 2
b
−9>X00 = >000
b
=− >G11>X
a = y −b x a =1X1G1 −J −>G11>XK5;0 a =1X1G1 +2;;G>>A a =;1@G>>A
(.( R,u+-!/* /! +i4,!i6!79* A Pi,i*
12
Voltagem
Linear
650 600 550 500 ) 450 v ( 400 m e 350 g a 300 t l o 250 V 200 150 100 50 0 0
20
40
60
Tempo(s)
: ; 0@1333= < (1$
B0 S,gu4/*
80
100
13
Voltagem Linear (Voltagem)
) v ( m e g a t l o V
650 600 550 500 450 400 350 300 250 200 150 100 50 0 0
20
40
60
Tempo (t)
: ; 0@1= < (1$
C T,5,i*
80
100
14
Voltagem(v)
Linear 650 600 550 500 450
) V ( 400 m350 e g a 300 t l o 250 V 200 150 100 50 0
0
20
40
60
Tempo(t)
: ; 0@11@= < (1@@ (. E* P,+! -,*i! /, '!u /* ,*" ?
∑ J y
i
∆ x =
− yK
1
nJn − 1K
A Pi,i!
2
80
100
15
J@?0 − 1X2G22K2 + J9@0 − 1X2G 22K2 + J220 − 1X2G22K2 + J1;0 − 1X2G22K2 + J100 − 1X2G22K2
?
∆ x =
∑ + J>0 − 1X2G22K2 + J ;0 − 1X2G22K2 + J90 − 1X2G22K2 + J20 − 1X2G22K 2 1
? J? − 1K
∆ x =>952>2>
O ,* u!/>-i5* G @3$@$@
B S,gu4/!
?
J@A0 − 1>AGAK2 + J9>0 − 1>AGAK 2 + J210 − 1>AGAK 2 + J1;0 − 1>AGAK 2 + J?0 − 1>AGAK 2
1
+ J@0 − 1>AGAK + J;0 − 1>AGAK + J90 − 1>AGAK + J20 − 1>AGAK
∑ ∆ x =
2
2
2
2
?J? − 1K
x =>950X?; ∆
O ,* u!/>-i5* G @32(
C T,5,i!
?
J@A0 − 1X1G1K 2 + J9>0 − 1X1G1K 2 + J220 − 1X1G1K 2 + J1;0 − 1X1G1K 2 + J?0 − 1X1G1K 2
1
+ J>0 − 1X1G1K + J;0 − 1X1G1K + J90 − 1X1G1K + J20 − 1X1G1K
∑ ∆ x =
2
2
2
2
?J? − 1K
x =>25?2@ ∆
O ,* u!/>-i5* G @32(
. CONCLUSÃO A&al"%a&'# #% )!(",#% $e!,e3e/#% e &# ,a$a,"t#! a&al"%a'# &aela% ,#&'"e% a$!e%e&ta /a $ee&a *a!"a# *"%t# a '"%$#%"# 'a% ta3ela% e '#% )!(",#%5 C#/ # $a%%a! '# te/$# a # ,a$a,"t#! *a" %e 'e%,a!!e)a&'# (#!/a&'# #% )!(",#% *"%t#% a,"/a5 A,!e'"ta/#% e e%%e 'e%,a!!e)a/e&t# a,#&te,e l"&ea!/e&te a# l#&)# '# te/$#5 Ot!# (at#! a %e! #3%e!*a'# a "/$#!t4&,"a '# %# 'e !e)!e%%# l"&ea! $a!a e&te&'e! # ,#/$#!ta/e&t# 'a *a!"a# 'e 'a% *a!"*e"%
16
