laboratorio 4 de fisica 3 FIEE

INDICE: 1. Objetivos………………………………………...………..……..….pág. 2

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Carga y descarga de un condensador en un circuito RC

2. Equipos y materiales……………………………….……………..pág. 2

3.Resumen………………………………………………….……..……pág. 5

4. Introu!!i"n………………………………………………….…......pág. #

5. $unamento %e %e"ri!o…………….................. "ri!o…………….............................. ........................…. ............…..pág.& .pág.&

#.'iagrama e (lujo…………………………………….……..…......pág. 12

&. )ro!eimiento E*perimental……………………….………......pág. 13

+. ,ál!ulos y Resultaos………………………….…………….......pag.1#

-. Observa!iones…………………………………………………….pág. 2&

1. ,on!lusiones…………………………………………………......pag.2+

11. /ibliogra(0a….…………………………………………………….pag.2-

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Carga y descarga de un condensador en un circuito RC

Calcul cular ar los val valores ores expe experim riment entale aless de los con condens densador adores es y com compar parar ar los  Cal resultados con los valores nominales obtenidos

Materiales.     

Un osciloscopio de dos canales Elenco modelo S-1!". Un generador de #unci$n Elenco %#-&'!(. Un mult)metro *igital. Una caja con condensadores y resistencias. Cables de conexi$n.

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Carga y descarga de un condensador en un circuito RC

GENERADOR DE FUNCION ELENCO GF8026

CAJA DE CONDENSADORES Y RESISTENCIAS

CABLES DE CONEXIONES

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Carga y descarga de un condensador en un circuito RC

MULTIMETRO DIGITAL

OSCILOSCOPIO DE DS CANALES ELENCO MODELO S -1325

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Carga y descarga de un condensador en un circuito RC

El circuito RC constituye básicamente una asociación de resistencias y  capacitores. El proceso de carga y descarga del capacitor es el tema fundamental de este informe. El generador de onda se comportó como una batería al cumplir con la condición de que su periodo sea mayor que el tiempo de carga del capacitor. El osciloscopio se utilizó para medir el voltaje del capacitor y el voltaje de la resistencia para así hallar la carga del capacitor y la corriente respectivamente. odas las grá!cas son de naturaleza e"ponencial. #or $ltimo% las mediciones de la capacitancia% resistencia y constante temporal &RC' resultaron con poco porcentaje de error. #alabras claves( Circuito RC% osciloscopio% carga% corriente% generador de onda% voltaje.

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Carga y descarga de un condensador en un circuito RC

+ntroducci$n. En palabras simples un circuito el)ctrico es el camino por el cual *uye la corriente el)ctrica% la cual sale de una fuente de poder% pasa a trav)s de resistencias condensadores% diodos% o cualquier elemento que contenga el circuito y regresa al punto de partida. +e otra forma% un circuito el)ctrico está compuesto por dos importantes implementos% una fuente de poder &,em.'% y elementos que ocupan la energía el)ctrica. En nuestro caso de hoy utilizaremos un condensador% elemento del cual a continuación lo e"plicaremos y analizaremos brevemente. El condensador es un dispositivo que almacena carga el)ctrica. En su form fo rma a má máss se senc ncil illa la%% un co cond nden ensad sador or es está tá fo form rmado ado po porr do doss pl plac acas as metá me táli lica cass &a &arm rmad adur uras' as' se separ parad adas as po porr un una a lá lámi mina na no co cond nduc ucto tora ra o diel)ctrico. -l conectar una de las placas a un generador% )sta se carga e induce una carga de signo opuesto en la otra placa. a botella de eyden es un condensador simple en el que las dos placas conductoras son so n !n !nos os re reve vest stim imie iento ntoss me metá táli lico coss de dent ntro ro y fu fuer era a de dell cr cris ista tall de la botella% que a su vez es el diel)ctrico. a magnitud que caracteriza a un condensador es su capacidad% cantidad de carga el)ctrica que puede almacenar a una diferencia de potencial determinado. os condensadores tienen un límite para la carga el)ctrica que pueden alma al mace cenar nar%% pa pasa sado do el cu cual al se pe perf rfora oran. n. #u #ued eden en co cond nduc ucir ir co corri rrien ente te cont co ntin inua ua du dura rant nte e só sólo lo un in inst stan ante te%% au aunq nque ue fu func ncio iona nan n bi bien en co como mo cond co nduc ucto tore ress en ci circ rcui uito toss de co corri rrien ente te al alte tern rna. a. Es Esta ta pr prop opie ieda dad d lo loss

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Carga y descarga de un condensador en un circuito RC

os condensadores se fabrican en gran variedad de formas. El aire% la mic ica% a% la cer erám ámiica ca%% el pa pape pell% el ac acei eite te y el vac acío ío se usa san n com omo o diel)ctricos% seg$n la utilidad que se pretenda dar al dispositivo.

#undamento ,e$rico. En los circuitos RC &resistor R% condensador C'. anto la corriente como la carga en el circuito son funciones del tiempo. Como se observa en la !gura( En el circuito cuando el interruptor está en la posición /. a dife di fere renc nciia de po pote tenc nciial es esttab able leci cida da po porr la fu fuen entte% pr pro odu duce ce el desplazamiento de cargas en el circuito% aunque en verdad el circuito no está cerrado &entre las placas del condensador'. Este *ujo de cargas se estab es table lece ce ha hast sta a qu que e la di dife fere renc ncia ia de po pote tenc ncia iall en entr tre e la lass pl plac acas as de dell condensador es 0% la misma que hay entre los bornes de la fuente. ue u ego de es esto to la cor orri rien entte de dessap apar arec ece. e. Es de deccir% ha hast sta a qu que e el condensador llega al estado estacionario.

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Carga y descarga de un condensador en un circuito RC i=

+e la de!nición de

dq dt 

 . -l reacomodar &/./' obtenemos( q − VC

dq = −    ÷ RC dt    

 

3nvirtiendo( dq

dt  

=−

q − VC

RC  

#ara #a ra ha hall llar ar la ca carg rga a en fu func nció ión n de dell ti tiem empo po to toma mamo moss en cu cuen enta ta la lass t

=

t

'- q = '

condiciones iniciales. En

 y en

q.

dq

= t .- q = q .

t .

dt  

∫ q − VC = ∫ − RC '

 . Entonces(

'

 

Equivalente a( [ ln/q

t 

−

q q.

−

VC 0 ] q

=

=

'

=

 RC 

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Carga y descarga de un condensador en un circuito RC

#or lo tanto% la función de carga es( t   RC  −

q /t 0

=

V C /1

−

e

0

(12!

 → ∞ t  →

En do dond nde e 0C re repr pres esen enta ta la ca carg rga a !n !nal al cu cuan ando do . 4 al de deri riv var  respecto del tiempo se obtiene la corriente cor riente en el circuito(

i /t 0

V   =

−

e

t 

 RC 

 R

(13! V   R

 -quí  representa la corriente inicial en el circuito. ass ec a ecua uaci cion ones es &/ &/.5 .5'' y &/ &/.6 .6'' re repr pres esen enta tan n la lass fu func ncio ione ness de ca carg rga a e intensidad de corriente durante la carga del condensador. V q / 0./ 0 =  s  A V 

 -l obtener las dimensiones de RC( 7R8. 7C8 9 . &Como debería ser' se r'.. En Ento tonc nces es se de de!n !ne e la cons % o ti tiem empo po de constante tante de tiemp tiempo o relajación como( τ  

=

 RC    (14!

:eg$n las grá!cas de la !gura 5 se observa% que a mayor valor de RC el

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Carga y descarga de un condensador en un circuito RC − t 

i /t 0

q/t 0 = VC /1 − e RC  0

V   =

−

t 

e  RC 

 R

FIGURA 2

 -l conectar el interruptor : en la posición 5% vemos que el circuito se compone solo de la resistencia y el condensador% entonces si tomamos el mismo sentido del corriente anti horario% horar io% de &/./.' tenemos que( iR

−

−

q C 

=

'

(15!

Reordenando( q=−

dq dt 

RC 

Entonces( dq

=−

q

dt   RC 

#ara este caso hallar la función de carga% las condiciones iniciales son que para un cierto tiempo t 9 t /%/% q 9 q ; 9 0C< y para otro tiempo t 9 t= q 9 q= . 3ntegrando( q.

dq

∫q

q'

t .

= ∫ − t 1

dt   RC 

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Carga y descarga de un condensador en un circuito RC

En donde al derivar q &t' respecto del tiempo la corriente será(

i /t 0 = −

V   R

− / t −t 1 0

e

 RC 

 

(1"!

El signo negativo indica que la corriente es en el sentido opuesto al que t

se tomó en &/.>'. -l analizar los limites lim q /t 0 = ' t →∞

i/'0 = −

V   R

= '- t  → ∞

 vemos que( q &;' 9 0C

lim i /t 0 = ' t →'

 y  % tambi)n % .:eg$n las grá!cas para este caso vemos que la carga almacenada en el condensador se disipa% durante la descarga del condensador(

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Carga y descarga de un condensador en un circuito RC

FIGURA 4

#ara lo cual el periodo de la onda debe ser  debe ser mucho mayor que la constante τ   para el circuito estudiado y se obtendrán en el monitor del osciloscopio gra!cas de la forma(

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Carga y descarga de un condensador en un circuito RC

*iagrama de lujo.

REALI$AR LA INSTALACION DEL CIRCUITO RC

MEDIR LA RESISTENCIAS Y CAPACITANCIAS CON EL MUL RC TIMERO

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Carga y descarga de un condensador en un circuito RC

2rocedimiento experimental. /.? Enc Encend endimo imoss el oscilos osciloscop copio io y se conectó conectó con un cab cable le coa"ial coa"ial al generador gener ador de funci función% ón% coloc colocando ando el sele selector ctor del gener generador ador en sali salida da de onda cuadrada. 5.? :e ajustó ajustó la frecuenc frecuencia ia de la ond onda% a% a 5@ 5@; ; Az apr apro"i o"imad madame amente nte%% tambi)n se ajustó el tiempo del osciloscopio a ;.@ msBdivisión% además se adecuo el tamao de la onda para que ocupara D cuadritos en la  posición horizontal. 6.?? :e mo 6. mont ntó ó el ci circ rcui uito to de la !g !gur ura a pa para ra el co cond nden ensa sado dorr C/  y la resistencia R/ de la caja(

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Carga y descarga de un condensador en un circuito RC

>.? Cambiando el selector de canal en el osciloscopio% se obtuvieron en el monitor del osciloscopio las grá!cas que se muestran en la !gura @. @.? -decuando los controles del osciloscopio de manera que permanezca estacionario% se midió el tiempo en el cual la carga del condensador era el 6F de su valor !nal. ambi)n se midió para la descarga% el tiempo en el cual la carga era el 6GF de su valor inicial. .? Cambiando el selector de canal del osciloscopio se midió el tiempo en que la corriente decae al 6GF de su valor inicial. D.? :e realizaron los pasos% de >.6 a >.% para todas las combinaciones  posibles de resistencias y condensadores condensadores disponibles en la cajita. H.? Con el multímetro se midió el valor de las resistencias( R/% R 5 y R 6 de la cajita. cajita. Con los dat datos os de tie tiempo mpo τ   % y valores de tiempo hallados se calculó e"perimentalmente la capacitancia C / y C 5 de cada condensador. uego con el multímetro volvió a medir C / y C5. /;.? #ara el circuito de la !gura G% se calculó los valores de( &a' Corriente en t 9 ;% cuando el interruptor : se coloca en /. &b' a corriente para un tiempo t 9 ∞  .  . &c'os valores má"imo y mínimo de corriente al poner : en la posición posición 5. &d' El voltaje voltaje má"imo en el condensador condensador%% obteniendo obteniendo las respuestas(

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Carga y descarga de un condensador en un circuito RC FIGURA 7

//.? :e montó el circuito de la !gura D% para veri!car las respuestas halladas en >./;.

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Carga y descarga de un condensador en un circuito RC

C3lculos y resultados. c 1− R

2

FRECUENCIA 24# %+-

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Carga y descarga de un condensador en un circuito RC

c 1− R

2

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Carga y descarga de un condensador en un circuito RC

I S /

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Carga y descarga de un condensador en un circuito RC

, . /

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Carga y descarga de un condensador en un circuito RC

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Carga y descarga de un condensador en un circuito RC

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Carga y descarga de un condensador en un circuito RC nominal ( nF )

C1 = 9.82 C2  =2 = 28.85

C1 = 10.79 C2 = 30.74

8.98% 6.15%

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Carga y descarga de un condensador en un circuito RC iminima=0.36 μA

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