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Centro Universitário Anhanguera de Campo Grande – Unidade II
Engenharia Mecânica 8ºB
DAIE! B"I#$ DE MACIE! "A%&&'(88)(*'
MA#+EU, DA ,I!-A .E"EI"A "A% ('/*)((&0'
A!E1AD"E A!MEIDA "A% &&'(88)0*'
E-E"#I GU##E"E, "A% &02('3&/)2
ATPS ELETRÔNICA E INSTRUMENTAÇÃO
CAMPO GRANDE/MS
NOVEMBRO DE 2015
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SUMÁRIO
Etapa 1 – Passo 1 – Ferramentas de estudo dos Erros.................................3
. Medidas Diretas
. Medidas Indiretas
Etapa 1 – Passo 2 – Método de Keine e M!"into!#.....................................$
Etapa 1 – Passo 3 – Erro em Instrumentos %na&'i!os................................(
. Erro de Paraa)e
. Erro de Interpoa*+o
. Erro em Instrumentos Di'itais
Etapa 1 – Passo $ – item 2 – E)perimento Mutimetros.................................,
. De-ini*+o de Resistores
. O/eti0os
. Reat&rio
Re-eren!ias iio'r-i!as.............................................................................1
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Etapa 1 – Passo 1 – Ferramentas de estudo dos Erros
As ferrae!"as #$e es"$%a &s err&s '&%e ser %()(%(%&s e %$as fa*+(as,
Medidas Diretas4o Me%(%as "&a%as -& $ "('& es'e-(f(-& %e (!s"r$e!"&.
ee'+& 'a#$*e"r&. (-r&e"r&. e"-
Medidas indiretas4o O )a+&r %a e%(%a %e"er(!a%& a 'ar"(r %e $a e%(3& %(re"a
%e &$"ra 4ra!%ea. ee'+& e!sa(& %e fra"$ra
Me%(%as %(re"as s3& $("& $sa%as e +a6&ra"7r(&s %e e"r&+&4(a e
-&!"r&+e %(e!s(&!a+. e es"a +(4a%a %(re"ae!"e a& -&!"r&+e es"a"*s"(-& %&
'r&%$"& &$ 'r&-ess&
Me%(%a I!%(re"a '&%e &6"er a"ra)s %e $a "re!a. $ -r&!8e"r& e $a
6a+a!a. '&ss*)e+ rea+(ar %()ersas e%(9es Iss& &-&rre '&r#$e as
4ra!%eas f*s(-as es"3& re+a-(&!a%as $as :s &$"ras e '&%e&s (!fer(r $a a
'ar"(r %as e%(%as %e &$"ras
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Etapa 1 – Passo 2 – Método de Keine e M!"into!#
M"&%& %e ;+e(!e e M-C+(!"&-
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N&s (!s"r$e!"&s a!a+74(-&s a '&!"e(r&. & err& 4era+e!"e f&r!e-(%&
e "er&s %e f$!%& %e es-a+a S. &$ sea. & )a+&r %e -&rre!"e #$e &r(4(!a a
%ef+e3& "&"a+ %& '&!"e(r& +e)a!%&@& a" & f( %a es-a+a %e e%(3&
Erro de Paraa)e
O-&rre e (!s"r$e!"&s a!a+74(-&s e res$+"a!"e %e $ '&s(-(&!ae!"&
(!-&rre"& %& &6ser)a%&r e re+a3& a& (!s"r$e!"& Ta6 -&!?e-(%& -&&
err& %e fa+sa +e("$ra
Erro de Interpoa*+o
A+ %a '&ss(6(+(%a%e %& err& %e 'ara+ae. &s (!s"r$e!"&s a!a+74(-&s
'er("e a &-&rrF!-(a %& err& %e (!"er'&+a3& Esse err& &r(4(!a@se e f$!3&
%& '&s(-(&!ae!"& %& '&!"e(r& e re+a3& : es-a+a %e e%(%a %& (!s"r$e!"&
Erro em Instrumentos Di'itais
I!%(-a%&res %(4("a(s &s"ra $ +e("$ra !$r(-a & #$e e+((!a & err& %&
&'era%&r e "er&s e 'ara+ae e (!"er'&+a3&. a res&+$3& %esses
(!s"r$e!"&s $%a!a %e "e!s3& #$e fa )ar(ar & 6(" e!&s s(4!(f(-a"()& !&
%(s'+a %& e%(%&r. !3& se '&%e -&!f$!%(r res&+$3& -& err& %e e%(%a. $
(!s"r$e!"& '&%e ser se!s*)e+ a 0.01V
Etapa 1 – Passo $ – item 2 – E5PERIME67O MU87IME7ROS
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De-ini*+o de Resistores
P&%e@se %ef(!(r $ res(s"&r -&& $ -&'&!e!"e #$e "ra!sf&ra
e!er4(a e+"r(-a e e!er4(a "r(-a '&r efe("& H&$+e. $("& $"(+(a%a e
-&'&!e!"es e+e"r8!(-&s. -$a f(!a+(%a%e %e +(("ar a -&rre!"e e+"r(-a e $-(r-$("&
A res(s"F!-(a e+"r(-a &$ ('e%!-(a. !a%a a(s . %& #$e es"a +(("a3&
%a -&rre!"e e $ %e"er(!a%& -(r-$("& O res(s"&r -a$sa $a #$e%a %e
"e!s3& e a+4$as 'ar"es %& -(r-$("&. as !$!-a -a$sar3& #$e%a %a -&rre!"e.
a'esar %& res(s"&r -a$sar a +(("a3& %a -&rre!"e
1. O/eti0os do 7este
Me%(r )a+&res %e res(s"F!-(as %e res(s"&res
Es"(ar err&s %e a'are+?&s a!a+74(-&s e %(4("a(s
2. Reat&rio das medi*9es
Os a'are+?&s %e e%(%a '&%e %()(%(r@se. #$a!"& : f&ra %ea'rese!"a3& %& res$+"a%& %a e%(3&. e a'are+?&s a!a+74(-&s e a'are+?&s
%(4("a(s N$ a'are+?& a!a+74(-& a (!%(-a3& %a%a $a f$!3& -&!"*!$a %a
4ra!%ea e%(%a. -&& !$a r4$a &$ !$ "er8e"r& %e er-Jr(& N$
a'are+?& %(4("a+. a (!%(-a3& f&r!e-(%a s&6 a f&ra !$r(-a e )ar(a '&r
sa+"&s %(s-re"&s. -&& !$ -r&!8e"r& %(4("a+ &$ !$a 6a+a!a e+e"r8!(-&
Os res(s"&res s3& -&'&!e!"es #$e "F '&r f(!a+(%a%e &fere-er $a
&'&s(3& : 'assa4e %e -&rre!"e e+"r(-a. a"ra)s %e se$ a"er(a+ A essa
&'&s(3& %a&s & !&e %e res(s"F!-(a e+"r(-a. #$e '&ss$( -&& $!(%a%e &?
Ca$sa $a #$e%a %e "e!s3& e a+4$a 'ar"e %e $ -(r-$("& e+"r(-&. '&r
aa(s -a$sa #$e%as %e -&rre!"e e+"r(-a Iss& s(4!(f(-a #$e a -&rre!"e
e+"r(-a #$e e!"ra e $ "er(!a+ %& res(s"&r ser= ea"ae!"e a esa #$e
sa( 'e+& &$"r& "er(!a+. '&r ?= $a #$e%a %e "e!s3& U"(+(a!%&@se %(ss&.
'&ss*)e+ $sar &s res(s"&res 'ara -&!"r&+ar a -&rre!"e e+"r(-a s&6re &s
-&'&!e!"es %esea%&s
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N& !&ss& e'er(e!"& f&( fe("& as e%(9es %&s res(s"&res (!%()(%$a(s.
ser(e. e 'ara+e+& Na a"()(%a%e e'er(e!"a+ f&( $sa%& 1 $+"*e"r&. > res(s"&res
%e )a+&res !&(!a(s %(fere!"es. f(&s %e +(4a3&. e 'r&"&6&ar% E f&( e+a6&ra%a
$a "a6e+a -& )a+&res %as -&res %&s es&s
&!"e, ?""',//!er%e+e"r(-&6+&4s'&"-&6r
&( 'es#$(sa%& & err& %& a'are+?& a"ra)s %e se$ a!$a+ !a es-a+a
$"(+(a%a &6"()e&s a se4$(!"e (!f&ra3&. se4$e "a6e+a -& fa(a %e err& !a
es-a+a %e res(s"F!-(as
Pr&-e%(e!"&
"ir!uito
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C& & M$+"*e"r& !a es-a+a e &?*e"r& e 2;K f&( fe("& as 'r(e(ras
+e("$ras %&s res(s"&res (!%()(%$a(s. a"ra)s %& -7%(4& %e -&res f&( fe("& a +e("$ra e
a!&"a%& a res(s"()(%a%e e &6"()e&s &s se4$(!"es )a+&res
Ee'+& %e $ res(s"&r -& as -&res 'ara a +e("$ra !&(!a+ %& res(s"&r
Pro!edimento 8aorat&rio
A se4$(r. ser= %e&!s"ra%a 'ass& a 'ass& e 5 e"a'as & 'r&-e%(e!"&
%& +a6&ra"7r(& #$e fa+ar= s&6re ass&-(a3& %e res(s"&res
Materia 6e!essrio
res(s"&res %e )a+&res %(fere!"es
1 'r&"&6&ar% 1 $+"*e"r&
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Ca+-$+a%&ra Ca!e"a Ca%er!& 'ara a!&"a9es Ta6e+a %e -&res %& res(s"&r e'+(-a%a 'e+& 'r&fess&r
8eitura do R1
"a!uo peas !ores do resistor.
marrom preto marrom DOUR%DO
1 : 1 (;
1: 10
1::< =(;
8eitura instrumento mut>metro4 2K
2K :?:@K ) 1::: @<
Va+&r
0.0;K Q K
Err& K 1 Q 0.
D*4("&s 1
Err& Q√ (2438)5+ (/) 5
Err& Q 1.K
E!"3&. & a'are+?& +e$ K -& $ err& %e /@ 1.K. e & fa6r(-a!"e %& res(s"&r
'e+a s&a"7r(a %e -&res %e$ 100K. e $ err& %e /@ 5 Iss& #$er %(er #$e
1.Q .K $a %(fere!a %e +e("$ra %e 0.02K
8eitura do R2
amareo 0ioeta preto dourado
$ A : (;
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$A10
0
$A< =(;
8eitura instrumento mut>metro4 2K
2K :?:$(K ) 1::: $(<
Err& 5K 1 Q 0.5
D(4("& 1
ERRO ¿√ (0,45) ²+(1 ) ²
Err& Q /@ 1.5
E!"3&. & a'are+?& +e$ 0.05;K -& $ err& %e /@ 1.5K. e & fa6r(-a!"e %&
res(s"&r 'e+a s&a"7r(a %e -&res %e$ K. e $ err& %e /@ 5 Iss& #$er %(er
#$e 5 1.Q .K $a %(fere!a %e +e("$ra %e 0.5>K
8eitura do R3
Es!aa do mut>metro esta0a em 2M
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Err& 2000K 1 Q 20K
D(4("& 1
Err& Q √ (9920 ) ²+(1 ) W
Err&±330/6
E!"3&. & a'are+?& +e$ 0.2MK. &$ sea. 2000K -& $ err& %e /@ 21K.
e & fa6r(-a!"e %& res(s"&r 'e+a s&a"7r(a %e -&res %e$
/2)Ω
. e $ err& %e /@
5 Iss& #$er %(er #$e330222+ 330/=/722/730/6
$a %(fere!a %e +e("$ra %e
121K
"ir!uito 1 Serie R7C R1 R2
O $+"*e"r& es"a)a !a es-a+a %e 2;K. &ra -&+e"a%&s %&(s res(s"&res e
a"ra)s %& -7%(4& %e -&res f&( fe("& a +e("$ra e a!&"a%& a res(s"()(%a%e
R1 Q Marr& 're"&. arr&. %&$ra%&
R2 Q Aare+&. )(&+e"a. 're"&. %&$ra%&
"a!uo peas !ores dos resistores.
RESIS7ORΩ F%RI"%67E MU87ME7RO
ES"%8% 2#
F%7OR B%8OR
R2C $A
R1C 1::R7C 1$A
Ω
:?1$$KΩ ) 1:::
R7C 1$$Ω
N ∗/2 M ∗T
/2∗/2/=/226±*
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&'∗/22=&'6=±*
R"Q R1R2
Rt =/22+ &'=/&'6±*
Err& 1 1 Q 1.
D(4("& 1
Err& Q±04&&Ω
Err& Q√ (/4&&)
0+ (/)0
E!"3&. & a'are+?& +e$ 0.1 ;K. &$ sea. 1K -& $ err& %e /@ 2.K e &
fa6r(-a!"e %& res(s"&r 'e+a s&a"7r(a %e -&res %e$ 1K. e $ err& %e /@ 5
Iss& #$er %(er #$e 1 2. Q 1.K $a %(fere!a %e +e("$ra %e 0.5K
Se'unda eitura em serie4
O $+"*e"r& es"a)a !a es-a+a %e 2MK
Va+&r -&r
0.1MK R1 Q Marr&. 're"&. arr&. %&$ra%&
2433/∗/2)=33/2226
R> Q Marr&. 're"&. )er%e. %&$ra%&
Ca+-$+& 'e+as -&res %&s res(s"&res
RESIS7ORΩ F%RI"%67E MU87ME7RO
ES"%8% 2M < F%7OR B%8OR
R1C 1::
R3C @@1:::R7C @@11::
Ω
:?@@1MΩ ) 1:::
R7C @@1::::Ω
10∗101=100Ω±5
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10∗105=10
6Ω±5
R"Q R1R2
R"Q 100 106
R"Q 100001X 106
K ±5
Err& 10000 1 Q 100
D(4("& 1
Err& Q √ (33/2)
0
+ (/)0
Err& Q±33//6
E!"3&. & a'are+?& +e$ 0.1MK. &$ sea. 1000K -& $ err& %e /@ 11K e
& fa6r(-a!"e %& res(s"&r 'e+a s&a"7r(a %e -&res %e$ 1000100K. e $ err& %e
/@ 5 Iss& #$er %(er #$e 1000K 11K Q 100011K $a %(fere!a %e
+e("$ra %e 11K a a(s 'e+a s&a"7r(a %e -&res
7er!eira eitura em série.
O $+"*e"r& es"a)a !a es-a+a %e 2MK
Va+&r -&r
0.0MK R2 Q Aare+&. )(&+e"a. 're"&. %&$ra%&
0,990∗106=990.000 Ω
R> Q Marr&. 're"&. )er%e. %&$ra%&
"a!uo peas !ores dos resistores.
47∗100=10Ω±5
10∗105
=106
Ω±5
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R"Q R2R>
R"Q 10 106
R"Q 100001X 106
K ±5
Err& 0000 1 Q 00
D(4("& 1
Err& Q√ (3322)0+ (/)0
Err& Q±3732/6
E!"3&. & a'are+?& +e$ 0.0MK. &$ sea. 0000K -& $ err& %e /@ 01K
e & fa6r(-a!"e %& res(s"&r 'e+a s&a"7r(a %e -&res %e$ 100010K. e $ err& %e
/@ 5 Iss& #$er %(er #$e 0000K 01K Q 01K $a %(fere!a %e
+e("$ra %e 10K 'ara a"(!4(r a s&a"7r(a %a es-a+a %e -&res
"ir!uito 1" Paraeo. RSC1
R2
1
R3
O $+"*e"r& es"a)a !a es-a+a 2;K. &ra -&+e"a%&s %&(s res(s"&res e a"ra)s
%& -7%(4& %e -&res f&( fe("& a +e("$ra e a!&"a%& a res(s"()(%a%e
Pr(e(ra +e("$ra,
Va+&r -&r
0.05;K R2 Q Aare+&. )(&+e"a. 're"&. %&$ra%&
242&*∗/222=&*6
R> Q Marr&. 're"&. )er%e. %&$ra%&
Ca+-$+& 'e+as -&res %&s res(s"&res
47∗100=47Ω±5
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10∗105=10
6Ω±5
R"Q R1R2
R"Q 106
R"Q 100000X 106
K ±5
Y$a!%& ass&-(a&s res(s"F!-(as e 'ara+e+&. & res$+"a%& !3& ser= a s&a
"&"a+. as s( a s&a a"ra)s %a se4$(!"e f7r$+a,
RT = R
1∗ R
2
R1+ R2
RT =47∗10
6
47+106
RT =47000000
1.000 .047
RT =46,9977911
Ω±5
Err& 5 1 Q 0.5
D(4("& 1
Err& Q√ (27&*)0+ (/)0
Err& C
±/4&*Ω
E!"3&. & a'are+?& +e$ 0.05;K. &$ sea. 5K -& $ err& %e /@ 1.5K e &
fa6r(-a!"e %& res(s"&r 'e+a s&a"7r(a %e -&res %e$ .11K. e $ err& %e
/@ 5 Iss& #$er %(er #$e 5K 1.5K Q .5K $a %(fere!a %e +e("$ra %e
0.511 K 'ara a"(!4(r a s&a"7r(a %a es-a+a %e -&res
Se'unda eitura em paraeo o mut>metro esta0a na es!aa de 2K.
Va+&r -&r
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0.0; R1 Q Marr&. 're"&. arr&. %&$ra%&
24233∗/222=336
R> Q Marr&. 're"&. )er%e. %&$ra%&
"a!uo peas !ores dos resistores.
N ∗/2 M ∗T
/2∗/2/=/226
/2∗/2*=/2)Ω
Y$a!%& ass&-(a&s res(s"F!-(as e 'ara+e+&. & res$+"a%& !3& ser= a s&a
"&"a+. as s( a s&a a"ra)s %a se4$(!"e f7r$+a,
RT = R1∗ R2
R1+ R2
RT =100∗10
6
100+106
RT =33433222/Ω±*
Err& 1 Q 0.
D(4("& 1
Err& Q√ (2733)0+ (/)0
Err& Q±/433Ω
E!"3&. & a'are+?& +e$ 0.0;K. &$ sea. K -& $ err& %e /@ 1.K e &fa6r(-a!"e %& res(s"&r 'e+a s&a"7r(a %e -&res %e$ .0001K. e $ err& %e
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/@ 5 Iss& #$er %(er #$e K 1.K Q 100.K $a %(fere!a %e +e("$ra %e
0. K a a(s 'e+a s&a"7r(a %e -&res
7er!eira eitura em paraeo o mut>metro esta0a na es!aa de 2K1;K R1 Q Marr&. 're"&. arr&. %&$ra%&
242(/∗/222=(/6
R2 Q Aare+&. )(&+e"a. 're"&. %&$ra%&
"a!uo peas !ores dos resistores.
N ∗/2 M ∗T
/2∗/2/=/226
&'∗/22=&'6
Y$a!%& ass&-(a&s res(s"F!-(as e 'ara+e+&. & res$+"a%& !3& ser= a s&a"&"a+. as s( a s&a a"ra)s %a se4$(!"e f7r$+a,
RT = R
1∗ R
2
R1+ R2
RT =100∗47
100+47
RT =4700147
RT =(/43'0'83/0Ω±*
Err& >1 1 Q 0.>1
D(4("& 1
Err& Q√ (27(/)
0+ (/)0
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Err& Q±/4(/Ω
E!"3&. & a'are+?& +e$ 0.>1;K. &$ sea. >1K -& $ err& %e /@ 1.>1K e &
fa6r(-a!"e %& res(s"&r 'e+a s&a"7r(a %e -&res %e$ >1.212K. e $ err& %e
/@ 5 Iss& #$er %(er #$e >1K 1.>1K Q >2.>1K $a %(fere!a %e +e("$ra %e
0.>>2 K a a(s 'e+a s&a"7r(a %e -&res
"on!us+o do E)perimento
C&!-+$*&s #$e & a'are+?& %(4("a+ #$e $sa&s &fere-e $a 're-(s3& %e
err& 1 !a es-a+a %e res(s"()(%a%e. e a"ra)s %&s -=+-$+&s &6"()e&s as
%(fere!as %e +e("$ra
N&s "rFs res(s"&res a!a+(sa%&s. &6ser)&$@se #$e &s )a+&res e%(%&s e &s
-a+-$+a%&s "()era '&$-a )ar(a3&. -&'r&)a!%& #$e &s 'r&-e%(e!"&s f&ra
efe"$a%&s %e f&ra -&rre"a e 'e+a )ar(a3& =(a e *!(a e!-&!"ra%a e!"re
&s )a+&res e%(%&s e -a+-$+a%&s es"es es"a)a se're %e!"r& %a "&+er!-(a
Z5 'ara a -&r &$r&. -&'r&)a!%& #$e "&%&s &s res(s"&res es"a)a %e!"r&
%e s$a fa(a %e "&+er!-(a (!f&ra%a 'e+& fa6r(-a!"e
Etapa 1 – Passo $ – item 3 – Es!oa do Pro/eto
N&ssa e#$('e (r= -&!s"r$(r & "e'&r(a%&r -& CI 555 se!s*)e+ a&
T$e)ers3& A.
Para rea+(ar es"e 'r&e"& )a&s 're-(sar %&s -&'&!e!"es +(s"a%&s a6a(&,
01 [ PC [ P&"e!-(8e"r& 100;
01 [ PC [ P&"e!-(8e"r& 50< s&e!"e es"e %(s'&!*)e+
01 [ PC [ Res(s"&r 1;
01 [ PC [ Res(s"&r 10;
01 [ PC [ Ca'a-("&r 100\
01 [ PC [ Ca'a-("&r 100!
01 [ PC [ CI 555
01 [ PC [ D(&%& N1
01 [ PC [ Re+
01 [ PC @ LDR
Re-eren!ias iio'r-i!as
8/18/2019 261205408 Atps Eletronica Revisado
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