INSTITUTO POLITÉCNICO NACIONAL UNIDAD PROFESIONAL INTERDISCIPLINARIA DE INGENIERIA CIENCIAS SOCIALES Y ADMINISTRATIVAS.
ELECTROMAGNETISMO (LABORATORIO) PRACTICA 7
CARGA Y DESCARGA DE UN CAPACITOR CAPACITOR PROFESORA: SALAS JUAREZ IRMA S. SECUENCIA: 2IM34 INTEGRANTES: • • •
LOPEZ ERNANDEZ ERNANDEZ BRAYAN BRAYAN MAR!UEZ ARELLANO MARCO ANTONIO MU"OZ VARELA CRISTIAN
FECA DE REALIZACI#N: REALIZACI#N: 24 $% &'* $% 2+,7 FECA DE ENTREGA: 3, $% &'* $% 2+,7
OBJETIVOS •
•
•
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INTRODUCCIÓN TEÓRICA A) CARGA DEL CAPACITOR:
C8'$* % *%' 8 '6'1* $%'<'$* ' $* 68* =8% % %8%' ' 6*%1'0% $11*> %0 '6'1* * % '<' 1'9%'&%% 1* =8% '$=81%% 1%' '<' 6* 81$'$ $% 1%&6*> =8% $%6%$% $% 8 '6'1$'$ ? $% 0' %1%1' $%0 181*.
L' F1<8' , %6%%' 8 '6'1* ? 8' %1%1' *%'$* % %1% ' $* 68* %% 0* 8'0% % &'1%% 8' $15%%1' $% 6*%1'0. S1 q % 0' '<' $%0 *$%'$* % 1%* 1'% 6*%1* '0 1%% $%0 1%86* % i % 0' 1%1$'$ $% 0' *1%% % %0 181* % %0 &1&* 1'%> % 1%%: − t RC
q =Q F ( 1− e i= I o e
)
−t RC
D*$% Qf % %0 /'0* 51'0 @'1' %0 8'0 1%$% '11'&%% 0' '<' $%0 '6'1*> I0 % 0' *1%% 111'0 ? % 2>7, % 0' -'% $% 0* 0*<'1&* '8'0%.
E 0' F1<8' 2 % %6%%' 0' <951' $% '&-' %8'1*%> % $*$% % *-%/' =8% 0' '<' 111'0 $%0 '6'1* % %* ? =8% 0' *1%% 1%$% '11'&%% ' %*. A0 '-* $% 8 1%&6* 1<8'0 ' RC> 0' *1%% % %0 181* @' $1&181$* ' ,% ≅ +>3 $% 8 /'0* 111'0. E %% &*&%* 0' '<' $%0 '6'1* @' '0''$* 8' 5'1 (, ,%) ≅ +>32 $% 8 /'0* 51'0. E0 6*$8* RC %> % *%8%1'> 8' &%$1$' $% 0' /%0*1$'$ $% '<' $%0 '6'1* ? 6* %00* % 00'&' *'% $% 1%&6*. C8'$* RC % 6%=8%H'> %0 '6'1* % '<' 961$'&%% 8'$* % &9 <'$%> %0 6*%* $% '<' *&' &9 1%&6*.
B) DESCARGA DEL CAPACITOR: S86*<'&* '@*'> % 0' F1<8' ,> =8% %0 '6'1* ?' @' '$=811$* 8' '<' Q0 ? =8% '$%&9 @%&* =81'$* 0' 58%% $%0 181* ? 81$* 0* 68* '-1%*. S1 '@*' %'&* %0 1%86*> %$%&* =8%: −t RC
q =Q 0 ( 1− e i= I o e
)
−t RC
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EQUIPO Y MATERIAL
• • • • • • • •
2 C'6'1'% %0%*01* $% K5 ' 3++ V (* , $% ,K5) , F8%% $% +3++ /*0 $% C.D. ('<%%0@) , V*0&%* $1<1'0 (MD,++ P*&';) , C*&%* &'8'0 , I%86* 8 6*0* 8 1* 4 C'-0% '1&9'1&9 2 C'-0% B''''1&9
PROCEDIMIENTO EXPERIMENTAL ,. C*%'&* 0* '6'1*% % 6''0%0*> %1%$* 81$'$* $% *%' 0* -*% 6*11/* * 6*11/* * 6*11/* ? %<'1/* * %<'1/*. 2. C*%'&* %0 /*0&%* $1<1'0 ' 0* -*% *%6*$1%% $%0 '6'1* C4> $%0 '%<0* $% '6'1*%> 81$'$* $% *%' *%'&%% 0* -*% *%6*$1%%. 3. D%0 -*% () $% 0' 58%% *%'&* ' 8* $% 0* -*% $%0 1%86* S ($%9$*0* '-1%*) ? %0 ** -*% $% S *%% * %0 '6'1* C> % 8 -*% 6*11/*. 4. D%0 -*% () $% 0' 58%% *%% %0 -*% %<'1/* $% C. . C*0*'&* 0' 6%100' $% 0' 58%% % %* ? % %<81$' %1$'0'. . E0 /*0&%* $1<1'0 $%-% %' % 0' %'0' 6'' &%$1 ,+++ V $% C.D. 7. C%'&* %0 1%86* S> ? /'% 0' 6%100' $% 0' 58%% @'' =8% 8 /*0&%* $1<1'0 &'=8% 3++ V. . D%'&* %'$* %0 1%86* S 6* 8 1%/'0* $% 3+ %<8$*. Q. A-' %0 1%86* S '0 &1&* 1%&6* =8% % 6*% % &'@' %0 *&%* &'8'0 ? '0 1%&6* %<8$*> 0%% 0' $15%%1' $% 6*%1'0 =8% 1$1' %0 /*0&%* $1<1'0. '<' 8 '*'1 % 0' '-0' $% /'0*% =8% % $' ' *18'1. ,+. C1%% %0 1%86* S ? $%% 6* 3+ %<8$* % $1@' 6*11. ,,. E '* $% =8% 8 /*0&%* $1<1'0 * 0% $ 0' 0%8' $% 3++ V '%0' ' $1@' L%8' * 0' 58%%. ,2. R%61' %0 11* Q '@*' 6'' ,+ %<8$*> '*'$* %0 /'0* $% 0' $15%%1' $% 6*%1'0 0%$' % 0' '-0' *%6*$1%%. ,3. R%61' %0 6*%$1&1%* $% Q ' Q 6'' 1%&6* $% ,> ' 2+ %<8$*> @'' *&60%' 0' '-0' $% /'0*%
DATOS
DATOS DE CARGA DEL CAPACITADOR
t (s) 0 5 10 15 20 25 30 35 40
dV (V) 0 1.186 1.576 1.739 1.784 1.799 1.804 1.805 1.806
Vf =1.81 TABLA DE CAMBIO DE VARIABLE
t (s) 0 5 10 15 20 25 30 35 40
y=Ln[1ΔV /Vf ] 0 1.064931756 2.045761009 3.238402247 4.242985586 5.103186851 5.709322655 5.891644212 6.114787763
DATOS DE DESCARGA DEL CAPACITADOR
t (s) 0 10 20 30 40 50 60 0 80 !0 100 110 120 130 140 150 160 10 180 1!0 200 210 220 230 240 250 260 20 280 2!0 300 310 320 330 340 350
GRAFICAS
Voltaje # %$& (V) Ln V 1.2 (V) 10 0.00995 1.01 20 -0.1935 0.824 30 -0.3681 0.692 40 -0.5464 0.579 50 -0.7215 0.486 0.402 60 -0.9113 0 0.3392 -1.0811 80 0.2872 -1.247 !0 0.2453 -1.405 0.2073 100 -1.573 0.173 110 -1.7544 0.1426 120 -1.9064 0.1265 130 -2.0675 0.1061 140 -2.2358 0.0906 150 -2.4013 0.0727 160 -2.5549 0.0647 10 -2.7379 0.0546 180 -2.9077 0.0463 1!0 -3.0726 0.0392 200 -3.239 0.0337 210 -3.3902 0.0283 220 -3.5648 0.0241 230 -3.7255 0.0203 240 -3.8971 0.0172 250 -4.0628 0.0146 0.0123 260 -4.2267 0.0105 20 -4.3981 0.0089 280 -4.5563 0.0075 2!0 -4.7217 0.0064 300 -4.8928 0.0054 310 -5.0514 0.0045 320 -5.2213 0.0039 330 -5.4036 0.0033 340 -5.5467 350 -5.7138
GRAFICAS PARA CARGA DE CAPACITOR "#a$%a de t &s ΔV
"#af'%a de t &s ΔV
"#a$%a de t &s Ln [1-ΔV /Vf ]
GRAFICAS PARA DESCARGA
CALCULOS A) CARGA DEL CAPACITOR D%68 $% %'01' %0 '&-1* $% /'1'-0%> '601'&* %<%1 01%'0> *-%1%$* 0* 1<81%% $'*: '( -0.1957 )( -0.80 *( -0.9695
Ley *e#'+ental L +1-
ΔV 1 0.1957 t −0.80 V f , ( s
,*l'%ando la fn%'n e*onen%'al Δ V e V f
1−
0.1957 t
−
=
Δ V V f
1−
s
−
∙e
0.5035
0.20 t
−
0.45 e
=
0.20 t
−
0.45 e
−
s
s
Δ V V f
=
Ley s'%a Δ V =1.81
V [ −
1 0.45 e
−0.20 t s
]
CALCULO DE CAPACITANCIA m=
−1 RC
−1 C = Rm R , M%<'*@&1* M , +++ +++ O@&1* & +.,Q7
1
s
Sustitu!"#$ C
=
−
( 1 000 000 Ω )
1
(
0.1957
−
1
s
)
6
−
5.109862 x 10
=
B) DESCARGA DEL CAPACITOR D%68 $% %'01' %0 '&-1* $% /'1'-0%> '601'&* %<%1 01%'0> *-%1%$* 0* 1<81%% $'*: & +.+,3+Q
V S
- +.,+Q4,+2+, +.QQQQ4 L! F%si&' v =e m=
R=
R=
0.1094 v
0.0166
−
e
v s
−1 RC
−1 mc
−1
(−
0.016685
)
v (1 x 10−6 F ) s
=208.3333 x 106 Ω
ERROR EXPERIMENTAL
|
E=
|
Valor Teórico −Valor exp . ∗100 Valor Teórico
−6
4.7 X 10
−5.109862 x 10−6
4.7 X 10
−6
¿
E =¿
|
∗100 =¿
CONCLUSIONES E %0 $%'*00* $% 0' 691' % 68$* /% =8% 8 '6'1* % $1% '<'$* 8'$* %;1% $15%%1' $% 6*%1'0 % 0 ? =8% 58% %0 '* % 6'180' =8% % %8$1. A0 %' %0 '6'1* '<'$*> % %' 8' '<' *'0 ? 8' $15%%1' $% 6*%1'0> '0 '&-1' %0 1%86* % *-%/ 1&%$1''&%% 8' $1&181 % 0' $15%%1' $% 6*%1'0 %% 0' %&1'0% $%0 '6'1* ' 58% *&* % 6%% %0 5%&%* $% $%'<' $%0 '6'1*. T'&-1 % *' $% 5*&' /11-0% ? %1' 6* &%$1* $% 9080* 0' %;1%1' $% 0' %1%1' =8% 1%' %0 181* %' 58% $%%&1'$' 6* %0 1%&6* =8% '$' % $%'<'% 6* *&60%* %0 '6'1*.
BIBLIOGRAF(A •
FSICA. T*&* II. R?&*$ A. S%'?. MG'100I%'&1%1'' E$1*%> SA $% CV.> M;1* DF.,QQ7.
