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8/9/2019 CHARGING AND DISCHARGING OF CAPACITOR.docx
1/22
PHYSICS PROJECT | PRATYUSH KUMAR, CLASS XII A
KENDRI
YAVIDYALA
YANO.
1
CHARGINGANDDISCHARGINGOFCAPACITORINR-CCIRCUIT
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CONTENT
1. ACKNOWLEDGEMENT
2. CERTIFICATE
3. INTRODUCTION TO R-C CIRCUIT
4. AIM
5. MATERIALS REQUIRED
6. THEORY
7. PROCEDURE
. O!SER"ATION AND CALCULATION
#. CONCLUSION
1$. REFRENCE
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ACKNOWLEDGEMENT
I would like to express my special thanks of
gratitude to my teacher Mr. G. D. SHARMA sir as
well as our principal who gae me the golden
opportunity to do this wonderful pro!ect on the
topic "harging and discharging of capacitor in R#"
circuit$ which also helped me in doing a lot ofResearch and I came to know a%out so many new
things I am really thankful to them.
Secondly I would also like to thank my parents and friends who
helped me a lot in finalizing this project within the limited time
frame. I also thank the authors of various articles that I referred
to. And I also thank our physics lab attendant to allow me doing
my practical work there.
At last I thank all the people who helped me.
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INTRODUCTION
An R-C cic!i" i# $ cic!i" c%n"$inin& $ '#i#"% $n(
c$)$ci"% in #'i'# "% $ )%*' #%!c'. S!c+ cic!i"#
n( ' i/)%"$n" $))0ic$"i%n# in $i%!# $'$# %
#ci'nc' $n( in 2$#ic cic!i"# *+ic+ $c" $# 2!i0(in&
20%c3# % /%('n "'c+n%0%&ic$0 ('ic'#.I" #+%!0( 2' '$00 +'0)!0 i *' &'" c%/%"$20'
*i"+ "+' "'/in%0%&i'# c+$&in& $n(
(i#c+$&in& % c$)$ci"%#.4i5 C%&'()*( +, &&)/+' 6-
A &&)/+' i# $ )$##i' "*%-"'/in$0
'0'c"ic$0 c%/)%n'n" !#'( "% #"%'
'n'&in $n '0'c"ic '0(.In "+' +($!0ic $n$0%&, c+$&' c$i'#
7%*in& "+%!&+ $ *i' $' $n$0%&%!# "%
*$"' 7%*in& "+%!&+ $ )i)'. A c$)$ci"%
i# 0i3' $ !22' /'/2$n' #'$0'( in#i('
$ )i)'. 8$"' /%0'c!0'# c$nn%" )$##
"+%!&+ "+' /'/2$n', 2!" #%/' *$"'c$n /%' 2 #"'"c+in& "+' /'/2$n'.
T+' $n$0%& c0$i'# $ '* $#)'c"# %
c$)$ci"%#6
http://en.wikipedia.org/wiki/Passivity_(engineering)http://en.wikipedia.org/wiki/Terminal_(electronics)http://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Hydraulic_analogyhttp://en.wikipedia.org/wiki/Terminal_(electronics)http://en.wikipedia.org/wiki/Energyhttp://en.wikipedia.org/wiki/Hydraulic_analogyhttp://en.wikipedia.org/wiki/Passivity_(engineering)8/9/2019 CHARGING AND DISCHARGING OF CAPACITOR.docx
7/22
&he 'ow of current alters the charge on a
capacitor, 9!#" $# "+' 7%* % *$"' c+$n&'# "+')%#i"i%n % "+' /'/2$n'. M%' #)'cic$00,
"+' ':'c" % $n '0'c"ic c!'n" i# "% inc'$#'"+' c+$&' % %n' )0$"' % "+' c$)$ci"%, $n(('c'$#' "+' c+$&' % "+' %"+' )0$"' 2 $n';!$0 $/%!n". T+i# i# 9!#" 0i3' +%*, *+'n *$"'7%* /%'# "+' !22' /'/2$n', i" inc'$#'#"+' $/%!n" % *$"' %n %n' #i(' % "+'/'/2$n', $n( ('c'$#'# "+' $/%!n" % *$"'%n "+' %"+' #i('.
&he more a capacitor is charged$ the larger itsoltage drop< i.'., "+' /%' i" =)!#+'# 2$c3=$&$in#" "+' c+$&in& c!'n". T+i# i# $n$0%&%!#"% "+' $c" "+$" "+' /%' $ /'/2$n' i##"'"c+'(, "+' /%' i" )!#+'# 2$c3 %n "+'*$"'.
"urrent can 'ow (through( a capacitor eenthough no indiidual electron can get from oneside to the other.T+i# i# $n$0%&%!# "% "+' $c""+$" *$"' c$n 7%* "+%!&+ "+' )i)' ''n"+%!&+ n% *$"' /%0'c!0' c$n )$## "+%!&+"+' !22' /'/2$n'. O c%!#', "+' 7%*c$nn%" c%n"in!' "+' #$/' (i'c"i%n %''"
T+' cic!i" (i$&$/ % "+i# '>)'i/'n" i#
&i'n 2'0%*6-
A))0in& Kic++%:# 0$* in "+' $2%' cic!i"
(!in& c+$&in&, i.'. c$)$ci"% i# c%nn'c"'( "%
"+' 2$""'
EVc iRB.. 4i5
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VcQ
C
P!""in& $2%' $0!' in ';. 4i5E
Q
CiR=0
Sinc' idQ
dt
T+''%', E -Q
C -dQ
dt RB
E -
Q
C
dQ
dt R
EC-dQ
dt RC
In"'&$"in& 2%"+ #i('#
0
t1
RC dt 0
Q1
ECQdQ
lnEC
Q
EC tRC . 4ii5
1Q
EC et
RC
H'nc' *' &'", EC (1et
RC)
Sinc' ECB% $ c$)$ci"%T+''%',
B (1et
RC) .. 4iii5H'', c+$&' $" "i/' "
8/9/2019 CHARGING AND DISCHARGING OF CAPACITOR.docx
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% /$> c+$&'
A0#% CV $n( %CV%, *+'' V $n( V%$' %0"$&'
$" "i/' " $n( /$> %0"$&' '#)'c"i'0
T+''%' %/ '; 4iii5,
CVCV% (1et
RC)
VV% (1et
RC) , "+i# i# "+' ';!i'( '>)'##i%n.
NOTE6- T+i# i# "+' c+$&in& ';!$"i%n %n0, %(i#c+$&in& ';!$"i%n )%c''( "+' #$/' *$ 2!"
%n0 '/%' E %/ Kic++%: 0$*# ';!$"i%n.
T+!# ';!$"i%n % (i#c+$&in&,
VVB (et
RC)
8+'n RC", "+'n ';!$"i%n 2'c%/'#,
VV% (1e1 )
8+ic+ %n #%0in& &i'#
VB.V%, i.'. "+' %0"$&' %n c$)$ci"% $" "i/'
"RC 2'c%/'# % "+' /$> %0"$&', *+ic+
/'$n# % "%"$0 c+$&' +$# 2''n #"%'( in "+'
c$)$ci"%.
8/9/2019 CHARGING AND DISCHARGING OF CAPACITOR.docx
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T+i# )%(!c" % R $n( C +$# 2''n &i'n $ n'* n$/', i.'. /)
+*0/&*/$n( i# ('n%"'( 2 , *+ic+ /'$n# % $n c$)$ci"% in
RC cic!i" % "%"$0 c+$&' i# #"%'( $" "i/' c%n#"$n".
In / '>)'i/'n" I +$' !#'( $ 1BBF c$)$ci"% $n( $ 1M'#i#"% "+!# "i/' c%n#"$n" 1BBQ1B -Q1B1$$ 0.
PROCEDURE
i. C%nn'c" $00 "+' c%/)%n'n"# in "+'
2'$(2%$( $# #+%*n in "+' %00%*in&
)ic"!'
ii. N%* "$3' /!0"i/'"' 0'$(# $n( )0$c' "+'/
in "+' "*% "'/in$0# .iii. @'%' )%c''(in& !"+' *' /!#" +$' $
2i" % 3n%*0'(&' $2%!" 2'$(2%$(. A
2'$(2%$( i# $ #i/)0' cic!i" 2!i0(in&
('ic' !#'( "% 2!i0( "'/)%$ cic!i"# 9!#"
"% "'#" "+'i *%3in&. I" i# ' #i/)0' "%
*%3 *i"+ $# i" (%'# n%" ';!i' $n
#%0('in& % $""$c+/'n" % c%/)%n'n"#.
T+' c%/)%n'n"# c%!0( 2' 9!#" )!#+'( in
"+' +%0'# $n( c%nn'c"i%n# c%!0( 2' /$('
'$#i0. A #"$i&+" 0in' )$""'n % +%0'#
8/9/2019 CHARGING AND DISCHARGING OF CAPACITOR.docx
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'#'/20'# $ *i' $n( "+' $$n&'/'n" %
"+'#' +%0'# $' #+%*n 2'0%*6-
8/9/2019 CHARGING AND DISCHARGING OF CAPACITOR.docx
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i. N%* "$3' "+' 2$""' $n( c%nn'c" i"#
"'/in$0# $c%## "+' "'/in$0# % "+'
c$)$ci"% $n( #"$" "+' #"%) *$"c+. N%"'
"+' '$(in $" B#'c in"'$0# $n( *i"'"+'/ (%*n. NOTE6- R'$(in& "+' )'i%!# #"$"'/'n" c%!0( 2'
$#"%ni#+in& $# i" #$# "+$" /'$#!' %0"$&' $" B#'c
in"'$0 2!" %n' c%!0( ;!'#"i%n "+$" c!'n" /%' $"
' +i&+ #)''( #% +%* c%!0( %n' /'$#!' "+'
c+$n&in& '$(in @!" 2'0i'' /' i" *$#n" $n '$#
"$#3 2!" #inc' "+' %0"$&' (')'n(# %n 'ci)%c$0 %
'>)%n'n"i$0 !nc"i%n $n( $# "i/' )$##'# 2 "+'c+$n&in& '$(in *i00 &'" #0%*'( (%*n $n( ''n $"'
inni"' "i/' "+' c$)$ci"% c%!0( n%" 2' c+$&'( !) "%
/$> %0"$&'. A0#% #inc' i"# "i/' c%n#"$n" i# 1BB #'c
*+ic+ i# ;!i"' )$c"ic$0 "% /'$#!' $" $n( +'nc' "+i#
'>)'i/'n" i# ' /!c+ 9!#"i'(
. T$3' 1B '$(in $n( i ';!i'( "+' B#'c
&$) c%!0( 2' inc'$#'( 2'c$!#' $# "+'
"i/' )$##'# 2 "+' c+$n&' in %0"$&'
2'c%/'# #/$00' $n( #/$00'.i. N%* 0'" "+' c$)$ci"% 2' c+$&'( !) "%
B #'c 2'c$!#' "+'n i" *i00 2'c%/'
. c+$&'( #inc' *' +$' $ 0i/i"'(
"i/' $n( *' c$n" *$i" % inni"' "i/' %
i" "% c+$&' c%/)0'"'0. N%* '/%' "+'2$""' $n( n%* $""$c+ $ *i' in )0$c' %
"+' 2$""' "'/in$0# $n( $&$in n%"' "+'
/!0"i/'"' '$(in c+$n&in& $n( 'c%(
"+'/.
8/9/2019 CHARGING AND DISCHARGING OF CAPACITOR.docx
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Vii. P0%" $ &$)+ 2'"*''n %0"$&' $n( "i/' %
c+$&in&
$# *'00 $# (i#c+$&in&.
1. O0'&/)+*0 &*
&&/)+*08-
S.*
+.
M/)/'
'&)*( 9%)
%&'()*(: )* +/;
M/)/'
'&)*( 9%)
)0%&'()*(:)*
+/;
T) : )*
0+*0;
1. B . B
2. 1. . B
3. .B .BB B
4. .11 .1 B
5. .B .B B
6. 5.6# 3.3$ 1$$ :i#
). F% c+$&in&
8/9/2019 CHARGING AND DISCHARGING OF CAPACITOR.docx
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B 1BB BB BB BB
B
1
%&'()*( +, &&)/+'
Y-V$0!'#
4ii5B B 1BB 1B BB B BB B
B
1
1B
D)0%&'()*( +, &&)/+'
Y-V$0!'#
F% (i#c+$&in&6-
8/9/2019 CHARGING AND DISCHARGING OF CAPACITOR.docx
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T+' %i&in$0 &$)+# % (i#c+$&in& $n( c+$&in&
'#)'c"i'0 $'6-
8/9/2019 CHARGING AND DISCHARGING OF CAPACITOR.docx
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CALCLATIONS:
N%* #inc' "+' &$)+# $' ' /!c+ #i/i0$ "% "+' &$)+# %
c+$&in& $n( (i#c+$&in& % c$)$ci"%.
A" 1BB#'c, (!in& c+$&in& % c$)$ci"% "+' %0"$&' %n
c$)$ci"% i# . %0" $# i" i# %2#''( in "+' '>)'i/'n". N%*
!#in& "+' c+$&in& %/!0$6-
V41- et
t 5
V41-1
e 5
V. 5.69 *+ic+ i# $c+i''( '>)'i/'n"$00 $# *'00.
Si/i0$0 (!in& (i#c+$&in&,
V e1
V..B *+ic+ i# $c+i''( '>)'i/'n"$00 $# *'00.
8/9/2019 CHARGING AND DISCHARGING OF CAPACITOR.docx
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CONCLUSION:
H'nc' i" i# 'i'( '>)'i/'n"$00 "+$" c+$&'i# "+'' %n c$)$ci"% $"' "i/' c%n#"$n" (!in&
c+$&in& $n( c+$&' i# 0%#" $" "i/' c%n#"$n"
(!in& (i#c+$&in&.
RERENCE:
G%%&0'.c%.in
En.*i3i)'(i$.%&
C%nc')"# % )+#ic# )$" 2 H.C. V'/$
T+i# )%9'c" i# c%/)0'"'0 c'$"'( *i"+ "+' +'0) % Mic%#%"*%( BB $n( "+' &$)+#, ';!$"i%n# $n( %2#'$"i%n "$20'#
$' $0#% c'$"'( *i"+ "+' +'0) % "+' #$/'.
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