Informe-Final-RLC.doc

UNIVERSIDAD NACIONAL DE INGENIERÍA FACULTAD DE INGENIERÍA ELÉCTRICA Y ELECTRÓNICA

  REGIMEN TRANSITORIO DE CIRCUITOS R-L-C

CURSO : LABORATORIO LABORATORIO CIRCUITOS ELÉCTRICOS I

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

ALUMNO

: LOPEZ SOTO JHON ALEX

SECCIÓN

:

N

201!II

DESARROLLO DESARROLLO DEL CUESTIONARIO 1"

D#$#%& D#$#%&'(# '(# )'(* )'(*'+ '+,(* ,(*- *#$,.. *#$,..,*,& ,*,&#($ #($# # .-/ ,/,/-/ / ., #+, #+,+'3 +'3( ( *'4#% *'4#%#(+ #(+',. ',. *#. *#. +'%+ +'%+'$ '$*# ., #5#%'#(+',"

i1

 i2 i1- i2

(1)

 L = 2,7 2, 7 H  C = 156,5 nF   R1 = 11,.7 k W  R = 27,1 k W �  R2 = �  R = 49.5 k W � Sea E(t) la tensión tensión de entrada En la malla (1)

(2)

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

En la malla (2)

0=

1 C 

� i1(t )

(i �

2 (t )

- i1(t ) )dt + R2i2(t ) di2( t )

= i2 ( ) + CR2 t 

……. (b)

dt 

Luego reemplazando (b) en (a) se obene: 2

 E (t )

=

 E (t )  LCR2

LCR2

=

d i2 ( t ) dt

d 2i2( t ) dt 2

2

+

+

( L + CR2 R1 )

di2( t )

( L + CR2 R1 ) di2( t ) LCR2

dt

dt

+

+

 

( R1 + R2 )i2 ( t )

( R1 + R2 ) LCR2

i2( t )

Haemos:

2a = w0 =

CR2 R1 + L  LCR2  R2 + R1

, a  : Coeficiente de amortiguamiento , w 0 : Frecuencia natural de resonancia del sistema

 LCR2

!or lo tanto:  E (t )  LCR2

2"

2

=

d i2 ( t ) dt

2

+

2a

di2( t ) dt 

+

w 02i2 ( t )

C,.+. C,.+.# # ,(,.6 ,(,.67+, 7+,&#( &#($# $# 89 89; 8T < 8= 8=-; -; +-&, +-&,%# %# #/$ #/$-/ -/ >,.>,.-%# %#// +-( .-/ ?,..,* ?,..,*-/ -/ #5#%'&#($,.&#($#; #5#%'&#($,.&#($#; @/7+,(*- .,/ *'>#%#(+',/" a=

CR2 R1 + L 2 LCR2

, w0 =

R2 + R1 LCR2

, w = w02 -a 2

,   T  =

2p  w 

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

"eemplazando los alores se obene los alores teórios:

a=

CR2 R1 + L 2 LCR2  R2 + R1

w0 =

 LCR2

2p

T=

w0 - a  2

=

(156, 156, 5.10 5.10 -9 )(27,1. )(27,1.10 10 3)(9.31 )(9.31.1 .10 0 3) + 2,7 2.( 2, 7) 7)(156, 5. 5.10 -9 )( 27,1.10 3) 27,1 27,1.1 .10 0 3 + 9,31.10 ,31.103

=

(2,7)(15 (2,7)(156,5.10 6,5.10-9 )(27,1. )(27,1.10 10 3 )

=

2

� w 0 = 3112,797

2p 

� T = 3,164 ms

(3112 (3112,, 797) - (2646 (2646,11 ,1102) 02) 2

� a  = 2646,1102

2

Caso 2

!ara: "1#%++'(poteniómetro) "1#%++'(poteniómetro) % "2#/$%+' % *#1+,%+ *#1+,%+ n % L# 2%H

a=

CR2 R1 + L 2 LCR2  R2 + R1

w0 =

 LCR2 2p

T=

w0 - a  2

=

(156,5. 156,5.10 10-9 )(49,5. )(49,5.10 103 )(7,55. )(7,55.10 10 3) + 2,7 2.( 2, 7) 7)(156, 5. 5.10 -9 )( 49, 5. 5.10 3) 49,5.1 49,5.10 03 + 7,55.1 7,55.10 03

=

(2,7)(15 (2,7)(156,5.10 6,5.10-9 )(49, )(49, 5.10 5.10 3 )

=

2

� w 0 = 3088,867

2p  (3088 (3088,867) ,867) - (2380, (2380,141 1417) 7) 2

� a  = 2380,141

2

� T = 3,191 ms

Caso 3

!ara: "1#0%'(poteniómetro) "1#0%'(poteniómetro) % *#1+,%+ n % L# 2%H

a =

w0 =

T

=

 R1   8,07.10 3

=

2 L

2.2, 7

1

2,7.156,5.10

2p w0

2

1

=

 LC 

-

�a  = 1494,44

2

a 

=

-9

� w 0 = 2420.42

2p  (2420 (2420,, 42) 42)

2

-

�T (1494 1494,94) ,94)

2

=

3,3 ms

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

poteniómetro3 adem4s debemos tener presente 5ue mientras aemos dereer el alor del poten potenióm iómetr etro% o% e6is e6iste te una resis resiste tenia nia 5ue perma permane nee e asi asi onst onstant ante e 7dem4s 7dem4s debemo debemoss menionar 5ue mientras ariamos el alor del poteniómetro% no solo las amplitudes disminu8e si no 5ue tambi9n se en aetados la reuenia natural de resistenia % as; omo el oe =">%% es de dism dismin inui uirr las las ampl amplit itud udes es m46i m46ima mass de una una onda onda subamorgu subamorguada% ada% 5ue es an4logo an4logo o pareido pareido al de la resiste resistenia nia el potenióme poteniómetro. tro. !ero !ero a dierenia de los ambios 5ue produe al ambiar "3 este produe un ambio notorio 8a sea inrementando la amplitud (puede dupliarse) o disminuirla al punto de no isualizarla. En otras palabras es el 5ue ae ariar el alor del deremento .

"

  *'4#% *'4#%#(+ #(+',/ ',/ -K/# -K/#%>, %>, ,. +,&K +,&K',% ',% #. #. >,.>,.-%% *# ., %#/' %#/'/$ /$#(+ #(+', ', R+ R+ < , # /# *#K# *#K#( ( #/$,/ *'4#%#(+',/ *'4#%#(+',/

En ada paso obtenemos una onda amorguada% la dierenia 5ue e6isten es debido a los par4metros w 8

a%

por 5ue si

w a

% es el aso de una onda sub-amorgua sub-amorguada da %esta lases de

amorguamiento se obene en el paso tres uando ariamos el alor del poteniómetro asta obtener dio amorguamiento. En el paso / ariamos el alor del poteniómetro asta obtener una onda r;amente amorguada % esto se da uando

w # a .

En el paso + uando eliminamos

" obtenemos una onda sub-amorguada de menor amplitud m46ima en omparaión on la onda obtenida en el paso tres esto se debe a la ariaión de los par4metros par4metros

w 8 a debido

est4n en unión de "1% *% L 8 ".

"

A ,%7% ,%7% *# ., /-.+' /-.+'3( 3( -% #+,+' #+,+'-(# -(#// *'4#% *'4#%#(+ #(+',. ',.#/ #/ >#%' >#%' # # ., 43%&. 43%&.,, *#. *#. *#+%#&#($- .-,%6$&'+.-,%6$&'+El deremento logar;tmio lo alulamos de la siguiente manera:

 e   T     D =   =  Ln  n  = a   2  en +1  Para el caso 1:

 = 2380,141.

3,191.10 -3 2

Para el caso 2:

3,191.10 -3

�   = 0, 3218

a 5ue

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

 = 1494, 44.

"

3,3.10-3

�   = 2, 465

2

S-. S-.+' +'-( -(# # ., %#* %#* +-( +-( ., ., , es mas sur sure e un amb ambio io desp desprreia eiabl ble% e% est esto sign signi< i dism dismin inu8 u8e e onsiderablemente.

"

E5.' E5.'# # < *'K *'K@# @# .,/ .,/ *#&/ *#&/ >,%' >,%',K. ,K.#/ #/ *#. *#. +'%+ +'%+'$ '$- +-&+-&- -% -% #@#& #@#&..- ., $#(/' $#(/'3( 3( )VL )VL #( ., +,%, < ., +-%%'#($# *#. /'/$#&, )I" S-K%#,&-%7,*-"Q A nalizando en un periodo periodo =I> en este gr4