6 Circuito RC

8/19/2019 6 Circuito RC

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UNIVERSIDADE ESTADUAL DE MARINGÁ

CENTRO DE CIÊNCIAS EXATAS

DEPARTAMENTO DE FÍSICA

FÍSICA EXPERIMENTAL III

Circuito RC

ACADÊMICO(S): Carla Yuri A !ui RA: "#$#%

Car li&' Ti' i M r a a RA: "#$#"

*ua& RA : TURMA: +$%,-. PROFESSOR:A&/'r0 & R'1i&al/ Sa 2ai

MARINGÁ3 #% /' a4ril /' $#56

1. Introdução



O Cir7ui8 RC 9 u 7a0 2ar8i7ular /' u 7ir7ui8 'l98ri7 7 &8'&/ a2'&a0u a r'0i08 &7ia ' u 7a2a7i8 r; P /'-0' 2'&0ar3 '&8< 3 &'00'0 / i07 2 &'&8'0 li1a/ 0 a8ra=90 /' 0'u0 8'r i&ai0 ' u a 7>a=' !u' 2 /' 2'r i8ir

u &< a 2a00a1' /' 7 rr'&8' & 7ir7ui8 ; N'08' 8i2 /' 7ir7ui8 3 u8ili?a-0' a7 rr'&8' al8'r&a/a (CA)3 !u' 9 u a 7 rr'&8' 7u@ 0'&8i/ =aria 7 8' 2 ; A

r a /' &/a u0ual ' u 7ir7ui8 /' 2 8 &7ia CA 9 0'& i/al 2 r 0'r a r a/' 8ra&0 i00< /' '&'r1ia ai0 'B7i'&8'; E&8r'8a&8 3 ' 7'r8a0 a2li7a '03/i 'r'&8'0 r a0 /' &/a0 0< u8ili?a/a03 8ai0 7 &a r a /' 7 00'& ; 5

O 7ir7ui8 RC '08u/a/ &'08a 2r 8i7a 'H8 'H' 2liB7a/ &a Fi1ura 53 !u'7 &0i08' ' u r'0i08 r /' r'0i08 &7ia R3 u a &8' /' 8'&0< /' 7 rr'&8'al8'r&a/a ' 7a2a7i8 r /' 7a2a7i8 &7ia C3 li1a/ ' 09ri' 7 R;

Fi1ura 5 J Cir7ui8 RC $

1.1- Processo de carga em um capacitor

O 7a2a7i8 r /' 7a2a7i8 &7ia C /a Fi1ura 5 '08 i&i7ial '&8' /'07arr'1a/ ;

Para !u' 'l' 0'@a 7arr'1a/ 3 9 2r'7i0 /iB7ar a 7>a=' S 2ara a 2 0i < a ;Kua&/ i08 7 rr'3 7ir7ui8 0' 8 r&a 7 2l'8 3 u 0'@a3 0ur1' 7 rr'&8'03 a0

!uai0 a7u ula u a 7ar1a q 7a/a ='? ai r &a 2la7a / 7a2a7i8 r3'08a4'l'7'&/ u a /i 'r'& a /' 2 8'&7ial i1ual a:

V c= qC

E! (5)Kua&/ a /i 'r'& a /' 2 8'&7ial 0' i1uala /i 'r'& a /' 2 8'&7ial '&8r' 0

8'r i&ai0 /a &8' ( r a 'l'8r 8ri? - E )3 a 7 rr'&8' 2 ra a 0ua 7ir7ula < ;

A a2li7ar a L'i /a0 al>a0 a 7ir7ui8 3 2'r7 rr'&/ & 0'&8i/ > r ri a2ar8ir / 8'r i&al &'1a8i= /a &8'3 8' -0':

E− iR − qC

= 0

E! ($)Sa4'-0' !u' l8i 8'r / la/ '0!u'r/ /'08a '!ua < r'2r'0'&8a a/i 'r'& a /' 2 8'&7ial '&8r' a0 2la7a0 / 7a2a7i8 r; S'u 8'r 9 &'1a8i= 2 r!u'



a 2la7a /' 7i a J li1a/a a 2 l 2 0i8i= /a &8'- 8' u 2 8'&7ial ai0 al8 /!u' a 2la7a /' 4aiH 3 >a='&/ u a !u'/a /' 2 8'&7ial !ua&/ a 7 rr'&8' 2a00a2'la 2la7a /' 7i a a89 a 2la7a /' 4aiH ; 6

Sa4'&/ !u' 7 rr'&8' 9 i1ual a /'ri=a/a /a 7ar1a ' u& < / 8' 2 :

i= dq

d t

E! (6)C 4i&a&/ (6) 7 ($)3 8' -0'

R dqd t

+ qC

= E

E! (,)Ku' 9 7 &>'7i/a 7 a '!ua < / 2r 7'00 /' 7ar1a3 a !ual /'07r'=' a

=aria < /a 7ar1a q 7 8' 2 3 & 7a2a7i8 r;

Para !u' 0'@a 2 00 ='l r'0 l= -la3 9 2r'7i0 '&7 &8rar a u& <q(t )

!u'2 00a 0a8i0 a?'r '00a '!ua < ; Sa4'-0'3 8a 49 3 !u' 7a2a7i8 r '08

i&i7ial '&8' /'07arr'1a/ 3 u 0'@a3 q= 0 ' t = 0 ;R'0 l='&/ a '!ua < /i 'r'&7ial /' 2ri 'ira r/' 3 8' -0' $:

dqd t

+ q RC

= E R

E! (+)Cu@a 0 lu < 1'ral 9 /a r a

q= q p+k e− at

E! (.)S'&/ q p a 0 lu < 2ar8i7ular /a '!ua < /i 'r'&7ial3 u a 7 &08a&8' a

0'r /'8'r i&a/a a 2ar8ir /a0 7 &/i '0 i&i7iai0 ' a = 1 / RC 3 7 'B7i'&8' /'

q ;

Para /'8'r i&ar q p 3 a?-0'dqd t

= 0 &a '!ua < (+)3 48'&/ q p= C E ;

Su408i8ui&/ '08' =al r /' q p ' (.)3 489 -0'q= C E +k e− at

E! (%)Sa4'-0' !u' q= 0 !ua&/ t = 0 3 2 r8a&8 k =− C E ;

Su408i8ui&/ 0 =al r'0 /' q p ' k ' (.)3 8' -0' !u'

q= C E (1 − e− t / RC )

E! (")



Fi1ura $- Gr B7 /' q(t ) x t & 2r 7'00 /' 7arr'1a '&8

C @ /i8 a&8'ri r '&8'3 0a4'-0' !u' a /'ri=a/a /' q ' u& < /'

t 9 i1ual 7 rr'&8'3 2 r8a&8

i=( E R )e− t / RC

E! ( )

Fi1ura 6 J Gr B7 /' i (t ) x t & 2r 7'00 /' 7arr'1a '&8

O 1r B7 /' i (t ) ' u& < /' t 2 /' 0'r =i08 &a Fi1ura 63 &/' 9

2 00 ='l 40'r=ar !u' =al r /a 7 rr'&8' & i& 7i 9 E R ' !u' a 7 rr'&8' 8'&/'

a ?'r !ua&/ t 8'&/' a i&B&i8 ;



C 4i&a&/ a '!ua < (5) 7 a '!ua < (")3 9 2 00 ='l '&7 &8rar a/i 'r'& a /' 2 8'&7ial '&8r' a0 2la7a0 / 7a2a7i8 r /ura&8' u 2r 7'00 /'7ar1a:

V C = E (1− e− t / RC )

E! (5#)A&ali0a&/ a '!ua < (5#)3 a7i a3 2 /'-0' /i?'r !u' V C = 0 ' t = 0 3

u 0'@a3 7a2a7i8 r '08 8 8al '&8' /'07arr'1a/ ; E V C → E !ua&/

t → ∞ 3 ' a 7ar1a / 7a2a7i8 r 8'&/' 2ara =al r B&al;

1.2- Constante τ C

O 2r /u8 RC !u' a2ar'7' ' (")3 ( ) ' (5#) 2 00ui /i '&0< /' 8' 2 ;I08 2 r!u' ar1u '&8 /' u a 'H2 &'&7ial /'=' 0'r a/i '&0i &al ' 8a 49 3

2 r!u' (1,0 Ω× 1,0 F = 1,0 s) ; O 2r /u8 RC 9 7>a a/ /' constante de

tempo capacitiva ' 9 r'2r'0'&8a/ 2'la l'8ra 1r'1a τ ;

N i&08a&8' t = τ 3 a 7ar1a / 7a2a7i8 r au '&8 u /' ?'r 2ara

q= C E (1 − e− 1)= 0,63 C E

E! (55)

1.3- Processo de descarga de um capacitor Su2 &>a !u' 7a2a7i8 r /' 7a2a7i8 &7ia C '08 7arr'1a/ 3 u 0'@a3 7

u 2 8'&7ial q 0= E ; E t = 0 3 a 7>a=' S 9 /'0l 7a/a 2ara a 2 0i < b ;

I08 a? 7 !u' 7a2a7i8 r 7 '7' a /'07arr'1ar a8ra=90 /' R;A '!ua < /i 'r'&7ial !u' /'07r'=' a =aria < /' q 7 8' 2 9

/'07ri8a 2 r

R dqd t

+ qC

= 0

E!(5$)R'0 l='&/ '08a '!ua < 3 8' -0' !u'

dqq

= − dt RC

E!(56)



I&8'1ra&/ 3 8' -0' !u'ln q= − t

RC +k

E!(5,)

O&/' 9 u a 7 &08a&8' ar4i8r ria !ual!u'r;C /i8 a7i a3 q 0= E ' t = 0 3 2 r8a&8 k = ln q 0

ln q= − t RC

+ln q0

E!(5+)EH2 &'&7ia&/ 3 8' -0'

− ¿ RC t

qq0 = e

¿

P r8a&8− ¿ RC

t

q= q 0 e ¿

E!(5.)O&/' q 0 9 a 7ar1a i&i7ial / 7a2a7i8 r;D'ri=a&/ a '!ua < (5.)3 2 /'-0' /'8'r i&ar a 7 rr'&8' /' u 2r 7'00

/' /'07ar1a:

i= d qdt

=−( q0

RC )e − t RC

E!(5%)P /'-0' 2'r7'4'r !u' a 7 rr'&8' /i i&ui 'H2 &'&7ial '&8' 7 8' 2 3

a00i 7 a 7ar1a 8a 49 2 00ui '00a !u'/a 'H2 &'&7ial; A 7 rr'&8' i&i7ial 9

i1ual a q / RC ; O 0i&al &'1a8i= i&/i7a a /i i&ui < /' 7ar1a & 7a2a7i8 r;

2. Materiais e métodos2.1 Materiais

F &8' /' 8'&0< 3 ul8 '8r 0 (5 a 2'r '8r ' $ = l8 '8r 0)3 7>a='0u&i2 lar'0 /' /ua0 2 0i '03 7r & '8r 3 7a4 03 @a7ar90 ' u 7ir7ui8 RC;

2.2 Montagens experimentais

Pri 'ira '&8' i a/ 8a/a !u' a 7>a=' /a /ir'i8a 9 a 7>a=' S1 ' /a

'0!u'r/a S2 ; E 8a 49 !u'3 !ua&/ a 7>a=' '08a 2ara 7i a '08a &a 2 0i <

53 & 'i &a 2 0i < # ' 2ara 4aiH &a 2 0i < $;O 7ir7ui8 i &8a/ 2ar8i&/ -0' / 2Ql &'1a8i= /a &8' /' 8'&0< ;

Para i00 i u0a/ 7a4 /' 8r 0 =ia03 / 0'1ui&8' / :- O 7a4 ai0 l &1 ' &i7 i 7 &'78a/ &8' 2'l 2Ql &'1a8i=



- O 2ri 'ir 7a4 i 7 &'78a/ a 2i& $ /a 7>a=' S2

- O 0'1u&/ i 7 &'78a/ a 7a2a7i8 r- O 8'r7'ir i 7 &'78a/ a 2i& 5 /a 7>a=' S1 ; Par8i&/ -0' / 2Ql 2 0i8i= /a &8' /' 8'&0< 3 7a4 /' 8r 0 =ia0 i

7 &'78a/ /a 0'1ui&8' a&'ira:- O 7a4 ai0 l &1 i 7 &'78a/ &8' 2'l 2 l 2 0i8i=- O 2ri 'ir 7a4 i 7 &'78a/ a 2i& 5 /a 7>a=' S2

- O 0'1u&/ 7a4 i 7 &'78a/ a 2i& $ /a 7>a=' S 1 ;

F i a7 2la/ u 7a4 ='r 'l> !u' 2ar8ia / 2i& # /a 7>a=' S2 3 ' 'ra

7 &'78a/ a u 2 &8 '&8r' a 2la7a 2 0i8i=a / 7a2a7i8 r ' r'0i08 r; N u8r2lu1 / r'0i08 r3 7 auHili /' u8r 7a4 ='r 'l> 3 a 2'r '8r i7 &'78a/ ' 09ri' 7 7ir7ui8 3 u0a&/ -0' u 7a4 2r'8 3 7 &'78a/ a 2lu1

C u / a 2'r '8r 3 '08' i a7 2la/ a 2i& # /a 7>a=' S 1 3

7 2l'8a&/ a &8a1' / 7ir7ui8 3 7 & r ' Fi1ura ,;

Fi1ura ,; E0!u' a 2ara &8a1' 'H2'ri '&8al / 7ir7ui8 RC

Para a 48'& < /' /a/ 0 ra a7 2la/ 0 / i0 = l8 '8r 03 u 2ara'/ir a !u'/a /' 8'&0< & r'0i08 r ' u8r & 7a2a7i8 r;

A0 2ri&7i2ai0 u& '0 / 7ir7ui8 ra 'H2li7i8a/a0 &a Ta4'la 53 a 0'1uir;

Ta4'la 5; Fu& '0 / 7ir7ui8Funções Chave 1 Chave 2Carga rápida # 5Descargarápida

# $

Carga lenta $ #Descarga lenta 5 #

P r B 3 a &8' i li1a/a ' r'1ula/a 2ara u a 8'&0< /' 5 3+ V; Oa 2'r '8r 3 '&8< 3 i r'1ula/ &a '07ala a/'!ua/a;

A0 7>a='0S1

'S2

ra li1a/a0 ' $ 0u7'00i=a '&8'; F raa& 8a/ 0 0 =al r'0 /' 7 rr'&8' i&i7ial3 /i 'r'& a /' 2 8'&7ial & r'0i08 r ' &



7a2a7i8 r; A 2ar8ir /a 7 rr'&8' i&i7ial3 ra '/i/ 0 ' r'1i08ra/ 0 8' 2 'i&8'r=al 0 /' #3$ A; F i 8 a/ 7ui/a/ /' 0' li1ar 7r & '8r @u&8 7 a

7>a=' S2 &a 2 0i < #; A2Q0 7a2a7i8 r 8'r 0' 7arr'1a/ ra a& 8a/ 0

8' 2 8 8al /' 7ar1a3 a 7 rr'&8' B&al ' a0 !u'/a0 /' 2 8'&7ial & r'0i08 r ' &7a2a7i8 r; O0 /a/ 0 ra a& 8a/ 0 &a Ta4'la $;

E&8< 3 a 7>a=' S1 i l'=a/a a 2 0i < #3 /'iHa&/ 7ir7ui8 a4'r8 '

l 1 /'2 i03 0i ul8a&'a '&8'3 a0 7>a='0 S1 ' S2 ra /'0l 7a/a0 2ara a

2 0i < 5; F ra a& 8a/ 0 a 7 rr'&8' i&i7ial ' a0 /i 'r'& a0 /' 2 8'&7ial &r'0i08 r ' & 7a2a7i8 r; N =a '&8'3 a 2ar8ir /a 7 rr'&8' i&i7ial ra '/i/ 0 'r'1i08ra/ 0 8' 2 ' i&8'r=al 0 /' #3$ A; F i 8 a/ 7ui/a/ /' 0' ?'rar '

li1ar 7r & '8r @u&8 7 a 7>a=' S2 &a 2 0i < #; A2Q0 7a2a7i8 r 8'r 0'

/'07arr'1a/ ra a& 8a/ 0 8' 2 8 8al /' 7ar1a3 a 7 rr'&8' B&al ' a0!u'/a0 /' 2 8'&7ial & r'0i08 r ' & 7a2a7i8 r; O0 /a/ 0 ra a& 8a/ 0 &a Ta4'la 6;

6; Resultados e discussão

Dura&8' 2r 7'00 /' 7ar1a ' /'07ar1a / 7a2a7i8 r ra 48i/ 0 0/a/ 0 2r'0'&8'0 &a0 Ta4'la0 5 ' $3 r'02'78i=a '&8';

i ( A) 8 (0)

53 6 .3%653%6 5$3 653+6 $#3$55366 $"3 55356 6"3%.#3 6 +53."#3%6 . 3##3+6 ,3 , #366 5,,3."#356 6+535"

#3## 6+535" Ta4'la 5: C rr'&8' & 2r 7'00 /' 7ar1a / 7a2a7i8 r Ta4'la $: C rr'&8' & 2r 7'00 /' /'07ar1a /7a2a7i8 r

O0 /a/ 0 /a0 Ta4'la0 5 ' $ ra 2l 8a/ 0 & 0 Gr B7 0 5 ' $3 ' 'i8 u a@u08'/' r'8a i 2 00 ='l 7>'1ar a8ra=90 /' 0 8 ar'0 &a0 '!ua '0 /' i(8);

i (mA) t (s)

-1,93 0

-1,73 6,42

-1,53 12,84

-1,33 20,3

-1,13 29,1

-0,93 39,03

-0,73 51,78

-0,53 69,41

-0,33 93,83

-0,13 143,25

-0,004 337,25



# +# 5## 5+# $## $+# 6## 6+# ,###

5

$

6

(H) 5;". 'H2( -#;#$ H )

t (s)

i (mA)

Gr B7 5: Da/ 0 i H 8 & 2r 7'00 /' 7ar1a / 7a2a7i8 r

# +# 5## 5+# $## $+# 6## 6+# ,##

-$;+-$

-5;+-5

-#;+#

(H) #;+ l&(H) - $;%6

t (s)

i (mA)

Gr B7 $: Da/ 0 i H 8 & 2r 7'00 /' /'07ar1a / 7a2a7i8 r

P /'-0' 40'r=ar !u' Gr B7 $ 9 7 rr'02 &/'&8' a Gr B7 53 2 r9

7 =al r'0 &'1a8i= 03 l 1 3 2 /'-0' '&7 &8rar 2ara u a r'8a a@u08a/ /'0 a 0'1ui&8' '!ua < :

i -53 6' -#3#5"8

C 'ra '02'ra/ 2'la 8' ria;

Sa4'&/ a r'0i08 &7ia / r'0i08 r3 a !ual i '/i/a 7 3 7 ul8 '8r ' a 8'&0< a2li7a/a & 7ir7ui8 3 !u' =al' $#V3 i 2 00 ='l 7al7ular a

7 rr'&8' & 7ir7ui8 ;

i=U R

i= 20

9,99.10 3

i= 2,00 mA

E00a 8'&0< 8a 49 i '/i/a a8ra=90 /' u a 2'r '8r 3 0'&/'&7 &8ra/ =al r /' 53 6 A3 /'08' / 3 2 /' 0 7al7ular /'0=i2'r7'&8ual;



D =i teórico − iexperimenta

i teórico

.100

D = 2,00 − 1,93

2,00 .100

D 63+

E00' /'0=i 2 /' 0'r 'H2li7a/ 2 r al1u&0 au0 7 &8a8 0 'Hi08'&8'0 '&8r'0 7a4 0 ' u a 2 00 ='l 2'!u'&a /'07ali4ra < / =i0 r /a 4a8'ria3 2 r9 &a/a

0i1&iB7a8i= ;

C auH li /a E!; ( ) ' 7 rr'la7i &a&/ -a '!ua < /' r'8a / Gr B7 53

9 2 00 ='l '&7 &8rar =al r 'H2'ri '&8al /a 7 &08a&8' 8' 2 7a2a7i8i= 3 τ C 3

' 0a4'&/ !u' τ C = RC 3 &/' C +###WF3 7al7ula 0 0'u =al r 8'Qri7 3 /'08'

/ 7>'1a&/ a 0 0'1ui&8'0 r'0ul8a/ 0:

τ c experimenta= 1

0,018= 55,556 s

τ c teórico= RC = 9,99.10 3 .5 !10 −3 = 49,95 s

D =|49,95 − 55,5562,0049,95 |.100 = 11,22

O !ual 9 /'7 rr'&8' / 0 'rr 0 a00 7ia/ 0 0 '/i '0 / 0 =al r'0&'7'00 ri 0 2ara 0'u 7al7ul ' / a@u08' /' r'8a;

O40'r=a-0' !u' a 7 &08a&8' /' 8' 2 7a2a7i8i= a2r'0'&8a u&i/a/' /'8' 2 3 03 i00 7 rr' 2 /' 0'r a7il '&8' /' 08ra/ :

[τ C ]= "! F

[τ C ]= V A

! C V

[τ C ]= C C s

= s

O 0i1&iB7a/ 0i7 /'τ C

3 9 8' 2 !u' /'=' 0 '02'rar 2ara !u' 7a2a7i8 r a8i&@a .6 /' 0ua 7ar1a 8 8al3 2 r9 8a 49 2 /' 0 7al7ular 2'la



E!;"3 8' 2 &'7'00 ri 3 u !ua&8ia /' 7 &08a&8'0 7a2a7i8i=a0 &'7'00 ria0 2ara 7a2a7i8 r a8i&1ir /' 0ua 7ar1a 8 8al;

q= C E (1− e− t / RC )

q= 0,99 q #

S'&/ 3 ! a 7ar1a /' '!uil 4ri / 7a2a7i8 r3 u 0'@a3 C E ;

0,99 C E= C E (1− e− t / RC )

0,01 = e− t / RC

EH2 &'&7ia&/ a 4 0 0 la/ 03 48' 0:

ln 0,01 = − t RC

− 4,61 = − t RC

t = 4,61 τ C $ 5 τ C

. Re!er"ncias #i$liogr%&cas

5 alli/a 3 D; 3 R'0&i7 3 R; ' Zal 'r3 *;3 Fu&/a '&8 0 /' F 0i7a 6 -El'8r a1&'8i0 3 '/i8 ra LTC;

$ >882:[[ ;iB;u&i7a 2;4r[\>u1 [a2 08ila0[li=r ;2/ 6 >882:[[ ;7'0'8;u&i7a 2;4r[\l' 4ra= [TT $#6#+[O

$#O07il 07 2i ;2/

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6 Circuito RC