UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
CONTENIDO
Pág.
I.
Resumen
2
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INDICE GRÁFICAS Y TABLAS TABLAS ,. TABLA , 2. TABLA 2
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UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
I.
LEY DE OHM
Resumen
En '( )*(+"#+( se $e*##+% e1)e*#men"('men"e '( 'e3 &e O:m 3 '( #n'uen+#( &e '(s *es#s"en+#(s #n"e*n(s &e '%s #ns"*umen"%s &e me&(; en e' +á'+u'% &e '%s $('%*es &e '(s *es#s"en+#(s. P*#me*(men"e se *e('# un +#*+u#"% en e' +u(' e' $%'"-me"*% es"(( en )(*('e'% +%n '( *es#s"en+#( 3 e' (m)e*-me"*% ue*( &e '( +%ne1#/n; en e' +u(' se %"u$#e*%n $('%*es +%n '%s +u('es se *e('#<% '( g*(#+( V $s. I %"en#=n&%se '( e+u(+#/n e1)e*#men"(' &e '( 'e3 &e O:m. T(m#=n se *e+%'e+"(*%n '%s &("%s &e' $%'"(!e 3 '( #n"ens#&(& &e +%**#en"e &e %"*% +#*+u#"% en >ue e' (m)e*-me"*% es"(( en se*#e +%n '( *es#s"en+#( )(*( *e('#<(* e' +á'+u'% &e '(s *es#s"en+#(s. II.
Objetivos de la práctica II.1
Objetivo general
- Ve*##+(* e1)e*#men"('men"e II.2
III.
'( 'e3 &e O:m
Objetivos específicos
-
An('#<(* '( #n'uen+#( &e '(s *es#s"en+#(s #n"e*n(s &e '%s #ns"*umen"%s en '( me&( &e *es#s"en+#(s.
-
C('+u'(* e' $('%* &e '( *es#s"en+#( e1)e*#men"('; ( "*($=s &e '%s +#*+u#"%s e1)'#+(&%s.
-
C%m)(*(* e' $('%* e1)e*#men"(' &e '( *es#s"en+#( +%n su $('%* "e/*#+%.
Marco Terico !e" de O#m1
S# se ()'#+( un( e*en+#( de )%"en+#(' ?&.&.).@ ( '%s e1"*em%s &e un +%n&u+"%* el$ctrico% )(*( +(&( &.&.). ()'#+(&% +#*+u'(*á un( #n"ens#&(& &e +%**#en"e I .
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929
UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
&igura 1- diferencia de potencial
V d.d.p. aplicado (v) I Intensidad de corriente (A) R = Resistencia eléctrica ( ς )
S# se +%ns"*u3e un( g*á#+( &e' $%'"(!e ?&.&.).@ ()'#+(&% en un&/n &e '( #n"ens#&(& &e +%men"e; se %"#ene un( '-ne( *e+"( >ue n%s #n+( >ue e' $%'"(!e ()'#+(&% es *e+"(men"e )*%)%*+#%n(' ( '( #n"ens#&(& &e +%**#en"e; =s"( (se$e*(+#/n es $á'#&( s# su)%nem%s >ue '( "em)e*("u*( &e' +%n&u+"%* se m(n"#ene +%ns"(n"e. V α R '1( V RI
A '( +%ns"(n"e &e )*%)%*+#%n('#&(& se '( &en%m#n( Res#s"en+#( e'=+"*#+( >ue "#ene +%m% un#&(& &e me&( e' %:m#% ?ς@. '2( R =
V I
Es"e #m)%*"(n"e *esu'"(&% es $á'#&% )(*( +%n&u+"%*es me"á'#+%s 3 se +%n%+e +%m% '( 'e3 &e O:m. T%&% +%n&u+"%* ?e1+e)"% un su)e*+%n&u+"%*@ "#ene un( *es#s"en+#( >ue es '( %)%s#+#/n >ue =s"e )*esen"( ( '( +#*+u'(+#/n &e +%**#en"e e'=+"*#+(. E1#s"en *es#s"en+#(s >ue se +%ns"*u3en +%n un $('%* #!% 3 >ue %+u)(n )%+% $%'umen; e' $('%* &e es"(s *es#s"en+#(s es mu3 g*(n&e +%m)(*(&% +%n e' &e '%s +('es >ue se u"#'#<(n en '( +%ne1#/n &e un +#*+u#"%. L(s )(*"es &e un +#*+u#"% +u3( *es#s"en+#( es &es)*e+#('e es *e)*esen"(&% )%* un( '-ne( *e+"( ?+('es &e +%ne1#/n@. O"*% "#)% +%mn es '( *es#s"en+#( $(*#('e ''(m(&( *e/s"("%; >ue +%ns#s"e en un( *es#s"en+#( +%n +%n"(+"% &es'#<(n"e ( '% '(*g% &e "%&( su e1"ens#/n $(*#(n&% &e =s"( m(ne*( su $('%*. L( *es#s"en+#( &e un +%n&u+"%* $(*#( +%n '( "em)e*("u*(; en '%s 949
UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
+%n&u+"%*es me"á'#+%s '( *es#s"en+#( +*e+e +u(n&% '( "em)e*("u*( (umen"(; en e' %ns"(n"án '( *es#s"en+#( es #n&e)enen"e &e '( "em)e*("u*( 3 en e' C(*/n ?g*(#"%@ '( *es#s"en+#( &e+*e+e ( me&( >ue (umen"( '( "em)e*("u*(. ?F#g. 2@ Cu(n&% '( *es#s"en+#( $(*#( +%n '( "em)e*("u*( +%n '( "em)e*("u*(; su $('%* se &e"e*m#n( )%* ')( R
= Ro ?, + α ∆T @
R= Resistencia eléctrica a la temperatura T Ro=Resistencia eléctrica a la temperatura T o Q
Coeficiente de variación térmica (depende del material) ∆T = T − T o
( es ?@ +u(n&% '( *es#s"en+#( +*e+e +%n e' (umen"% &e '( "em)e*("u*(. ( es ?9@ +u(n&% '( *es#s"en+#( &e+*e+e +%n e' (umen"% &e '( "em)e*("u*(.
&igura 2 * +rafica R vs. T de algunos materiales ,otencia disipada
A'gun(s *es#s"en+#(s "*(en +%m% &("% '( má1#m( )%"en+#( >ue )ue&en s#)(* % '( #n"ens#&(& % '( "ens#/n má1#m( >ue )ue&en s%)%*"(*. Es"(s m(gn#"u&es es"án *e'(+#%n(&(s )%* P
m
= I
2
R = V I
m
m
m
Pm = Potencia m!ima disipada Im Intensidad de corriente m!ima Vm = Volta"e o Tensión m!ima 979
UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
P(*( *e('#<(* e' e1)e*#men"% es ne+es(*#% +%ne+"(* #ns"*umen"%s &e me&( >ue +uen"(n +%n un( *es#s"en+#( #n"e*n(; =s"( *es#s"en+#( )%&*-( #n'u#* 3 ('"e*(* '(s 'e+"u*(s ee+"u(&(s. P%* es"( *(
&igura ) mperímetro antes de la conein del voltímetro
# $uer%a electromotri% (f.e.m.) Volta"e &ue entre'a la fuente (v) R' Resistencia interna del ampermetro R = Resistencia interna del voltmetro I' Intensidad de corriente &ue detecta el ampermetro l = Intensidad de corriente &ue circula a travos de la resistencia l ( Intensidad do corriente &ue circula por el voltmetro.
P(*( =s"e "#)% &e +%ne1#/n; '( #n"ens#&(& &e +%**#en"e >ue #n+( e' (m)e*-me"*% es"á &(&( )%* '/( I a
959
= I r +
I v
UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
A&emás
'0( I v
=
V Rv
En"%n+es
'( I v
= I a −
V Rv
V &.&.). >ue m(*+( e' $%'"-me"*% en"*e '%s )un"%s A 3 B P%* '% "(n"%; e' $('%* &e '( *es#s"en+#( se*á
R =
'(
V I r
V
=
I a
−
V Rv
S# se ()'#+(*( *e+"(men"e '( 'e3 &e O:m
I '3( R
=
V I a
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∆ I r = I a − I r =
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∆ I r
I r
=
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9J9
I v I r
=
R Rv
UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
Segn '( e+. ?,4@ )%&*-( ()'#+(*se *e+"(men"e '( 'e3 &e O:m; s#n ee+"u(* n#ngun( +%**e++#/n )(*( I( se e' +%+#en"e R K R $ es mu+:% men%* (' e**%* &e' '-m#"e &e '%s #ns"*umen"%s u"#'#<(&%s. En"%n+es se &ee +um)'#* '15( Rv
>>> R
En +(s% +%n"*(*#% se &ee +%**eg#* u"#'#<(n&% '( e+. ?0@. P(*( >ue se( &es)*e+#('e '( )%"en+#( >ue se s#)( en e' $%'"-me"*%; "(m#=n &ee +um)'#*se '( +%n+#/n '15(. b( mperímetro entre las coneiones del voltímetro
&igura 5 mperímetro entre las coneiones del voltímetro
En es"e +(s% e' (m)e*-me"*% &e"e+"( e' $('%* I( I* ; )%* es"(* +%ne+"(&% en se*#e ( '( *es#s"en+#(. E' $%'"-me"*% m#&e '( &.&.). en"*e '%s )un"%s A 3 B V = I r R + I r Ra
R =
V − I r Ra
'10( R =
I r V I r
−
Ra
E' e**%* en '( me+#/n es n% :(e* +%ns#&e*(&% '( *es#s"en+#( #n"e*n( &e' (m)e*-me"*% I '1( ∆ R = R − R = Ra
989
UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
E' e**%* *e'("#$%
'1(
∆ R
R
=
Ra R
Se )%&*-( ()'#+(* *e+"(men"e '( 'e3 &e O:m; s#em)*e >ue '( *e'(+#/n R ( K R se( mu+:% men%* >ue e' e**%* (' e**%* '-m#"e &e '%( #ns"*umen"%s &e me&(. Se &ee +um)'#* en"%n+es '13( R >>> Ra
P(*( >ue se( +%ns#&e*(&( &es)*e+#('e '( )%"en+#( s#)(&( en e' (m)e*-me"*% "(m#=n &ee*á +um)'#*se '( +%n+#/n '13(. I6.
Marco 7onceptual. Resistencia2.- Se
&en%m#n( *es#s"en+#( &e' +%n&u+"%* ( '( *(
&e' )%"en+#(' % "ens#/n ()'#+(&( ( '%s e1"*em%s &e un +%n&u+"%*; VB9 VA; 3 ( '( #n"ens#&(& I >ue +#*+u'( )%* =' se *e)*esen"( )%* R. Es"( &e#n#+#/n es $á'#&( )(*( +u('>u#e* +%n&u+"%*; se( un e'e+"*%'#"%; un g(s #%n#<(&% % un +%n&u+"%* me"á'#+%. Resistor.- Es e' e'emen"% >ue *e('#<( -s#+(men"e un( *es#s"en+#( . Resistencia el$ctrica !e" de O#m.- E'
+%n+e)"% &e *es#s"en+#( e'=+"*#+( n(+e &e '(
e1#s"en+#( &e (#s'(n"es 3 &e +%n&u+"%*es; 3 &e' :e+:% &e >ue; en"*e '%s +%n&u+"%*es; un%s %*e+en más (+#'#&(& >ue %"*%s (' )(s% &e '( +%**#en"e e'=+"*#+(. Cu(n&% en"*e '%s e1"*em%s &e un +%n&u+"%* se es"('e+e un( e*en+#( &e )%"en+#('; ( "*($=s &e' m#sm% +#*+u'( un( +%**#en"e +u3( #n"ens#&(& I &e)en&e &e' m("e*#(' &e >ue es"á :e+:% e' +%n&u+"%* 3 &e sus mens#%nes. S# se m%#+( '( e*en+#( &e )%"en+#('; '( #n"ens#&(& "(m#=n $(*-(; )e*% &e %*m( >ue e' +%+#en"e &e '( e*en+#( &e )%"en+#(' )%* '( #n"ens#&(& se m(n"#ene +%ns"(n"e. L( 'e3 &e )*%)%*+#%n('#&(& en"*e '( e*en+#( &e )%"en+#(' ()'#+(&( 3 '( #n"ens#&(& >ue +#*+u'( )%* e' +%n&u+"%* +%ns"#"u3e '( 'e3 &e O:m R
2
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D%*(&%; A'%ns% D#++#%n(*#% en+#+'%)=+% un#$e*s('; Págs. 07 9 072
909
UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
A' se* '( *es#s"en+#( e' +%+#en"e en"*e un( "ens#/n 3 un( #n"ens#&(&; su /*mu'( mens#%n(' es [ R] = [ , ] M [ +] 2 M [ T ]
−4
M [ I ]
−2
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sens#'emen"e '(s
+(*(+"e*-s"#+(s &e *es#s"en+#( )u*( &e' *es#s"%*. L(s *es#s"en+#(s )ue&en se* #!(s ? $('%* #n$(*#('e@; (!us"('es? $('%* (!us"('e +%n e' +#*+u#"% 3( m%n"(&%@ 3 $(*#('es? +u3% $('%* )ue&e +(m#(*se s#em)*e >ue se &esee@. En e' +(s% &e'(s *es#s"en+#(s #!(s; '(s más +%munes &e '(s +u('es sue'en se* &e +(*/n +%n +u#e*"( &e +e*ám#+(; su $('%* n%m#n(' 3 su "%'e*(n+#( ?e*en+#( má1#m( (&m#"#&( en"*e e' $('%* *e(' 3 e' n%m#n(' &e '( *es#s"en+#(@ se sue'en #n+(* me(n"e (n&(s &e +%'%*es. C%ns#&e*(n&% '( )*#me*( (n&( +%m% '( más )*/1#m( (' e1"*em% &e' *es#s"%*; s# =s"e ''e$( #m)*es(s +u("*% (n&(s; '(s &%s )*#me*(s #n+(n +#*(s s#gn##+("#$(s &e' $('%* &e '( *es#s"en+#(; '( "e*+e*(; e' (+"%* )%* e' >ue es(s +#*(s &een mu'"#)'#+(*se; 3 '( +u(*"(; '( "%'e*(n+#(. En e' +(s% &e '%s *es#s"%*es &e +#n+% (n&(s; '(s "*es )*#me*(s #n+(n +#*(s s#gn##+("#$(s; 3 '( +u(*"( 3 '( >u#n"( e' (+"%* mu'"#)'#+(&%* 3 '( "%'e*(n+#(. Resistividad.-
L( *es#s"en+#( &e un +%n&u+"%*es m(3%* +u(n"% más '(*g% es e'
*e+%**#&%; es &e+#*; >ue (umen"( +%n '( '%ng#"u& ' &e' +%n&u+"%*; 3 es men%* +u(n"% m(3%* es '( se++#/n S; 3( >ue ( m(3%* se++#/n más (m)'#( es '( ($en#&( )%* '( >ue se )ue&en +#*+u'(* '%s e'e+"*%nes. P%* su)ues"%; "(m#=n &e)en&e &e' m("e*#(' &e >ue es"á :e+:% e' +%n&u+"%*. E1)e*#men"('men"e se +%m)*ue( >ue 99
UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
R
=
p
l -
&%n&e ) es '( *es#s"#$#&(& &e' +%n&u+"%*; +(*(+"e*-s"#+( >ue &e)en&e &e' m("e*#(' ' es '( '%ng#"u& &e' +%n&u+"%* 3 S; su se++#/n . &e (+ue*&% +%n es"( /*mu'(; '( *es#s"#$#&(&es m#&e en %:m#%s )%* me"*% ?m@. En %+(s#%nes; en 'ug(* &e '( *es#s"en+#( )ue&e #n"e*es(* +%ns#&e*(* su $('%* #n$e*s%; >ue se &en%m#n( +%n&u+"(n+#( 3 se m#&e en s#emens?S@; s#en&% ,S,9,; &e (:- >ue :(s"( :(+e un%s (%s se &en%m#n(( %:m ( es"( un#&(&. Aná'%g(men"e. E' $('%* #n$e*s% &e '( *es#s"#$#&(& se &en%m#n( +%n&u+"#$#&(& 3 se m#&e en s#emensKm. En '%s +%n&u+"%*es; '( *es#s"#$#&(& $(*#( &e %*m( )*á+"#+(men"e '#ne(' +%n '( "em)e*("u*(; (umen"(n&% +%n =s"(; 3( >ue +u(n"% más ('"( se( '( "em)e*("u*( m(3%* se*á '( (g#"(+#/n "=*m#+( 3; )%* '% "(n"%; m(3%* se*á e' nme*% &e +:%>ues &e '%s e'e+"*%nes +%n '%s #%nes me"á'#+%s #!%s; s#en&% es"%s +:%>ues '%s +(us(n"es &e '( *es#s"en+#( ( '( +%n&u++#/n . P%&*em%s )ues es+*##* p
= p
(, + ) M t )
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P(*( es"( )*á+"#+(; se us(*%n '%s s#gu#en"es m("e*#('es • • • • • •
T('e*% &e *es#s"en+#(s Am)e*-me"*% V%'"-me"*% Fuen"e &e $%'"(!e C('es &e +%ne1#/n Tes"e*
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UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
En es"( )*á+"#+(; us(m%s &%s +%ne1#%nes s"#n"(s; )(*( '( )*#me*(; +%ne+"(m%s en )(*('e'% e' $%'"-me"*%; 3 ue*( &e es"( +%ne1#/n +%ne+"(m%s un (m)e*-me"*%; en"%n+es )(*( me* e' $%'"(!e &e '( *es#s"en+#(; 3 'e u#m%s &(n&% e*en"e $%'"(!e; )(*( me* e' (m)e*(!e >ue n%s &(( ( e*en"e $%'"(!e. P(*( e' segun&% +(s%; +%ne+"(m%s (' (m)e*-me"*% en se*#e +%n '( *es#s"en+#(; es &e+#*; ( (' +%ne1#/n (n"e*#%*; )us#m%s e' (m)e*-me"*% en se*#e. En"%n+es mem%s e*en"es $%'"(!es 3 s(+(m%s '(s #n"ens#&(&es &e +(&( $%'"(!e >ue (**%!(( e' (m)e*-me"*% 6I.
nálisis " tratamiento de datos -
C%ns"*u#* '( g*á#+( V en un+#/n &e I +%n '%s $('%*es %"en#&%s )(*( (m%s +#*+u#"%s. 7ircuito 1
9:
Tabla 1 8atos obtenidos en laboratorio 6 '6oltios(
I 'amp(
, 2 4 7 5 J
2.82 7.28 J.,7 0., ,. ,,.
.7 .8 ., .,4 .,8 .2
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9 ,, 9
UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
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7ircuito 2
9:
Tabla 2 8atos obtenidos en laboratorio 6 'voltios(
, 2 4
2.2 7., J., 9 ,2 9
I 'amperios(
.7 .8 .,
UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
7 5 J 8
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UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
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UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
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UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
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UNIVERSIDAD MAYOR DE SAN ANDRES FACULTAD DE INGENIERÍA FÍSICA BASICA II
LEY DE OHM
9 ,8 9