2460Physics Investigatory Project

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    RYAN INTERNATIONALSCHOOL,

    GHAZIABAD

    INVESTIGATORY

    PROJECT ON:-

    Charging and disharging !"

    a#ai$!r in R-C ir%i$s

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    &

    INDE' S n!( TOPICS

    Pag)n!(

    *( AC+NOLEDGEENT

    .&( CERTI/ICATE

    0.( INVESTIGATORY PROJECT REPORT

    1i2 Ai3 41ii2 In$r!d%$i!n 4-51iii2 a$)ria6s r)7%ir)d 5-

    8

    1i92 Th)!r 8-*;192 Pr!)d%r)

    *;-*&19i2 O

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    .

    AC+NOLEDGEENTOn !3#6)$i!n !" 3 in9)s$iga$!r

    #r!>)$ I "))6 )?$r)3)6 d)6igh$)d )$ and h)6#ing 3)

    nania66 as @)66( Th)n I @!%6d 6i) $!

    $han 3 3)n$!r and $)ah)r r( A3i$

    ishra "!r $)ahing 3) $h)

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    0

    "!r s%##!r$ing 3) and gi9ing 3) $his

    !##!r$%ni$ $! 3a) $his #r!>)$( In

    $h) )nd I @!%6d 6i) $! $han $h)sh!#))#)r r( Ar%n +%3ar "!r

    #r!9iding 3) @i$h hard-$!-g)$

    3a$)ria6s a$ 9)r 6!@ #ri)(

    Shi9a3 Sh)har

    CERTI/ICATE

    This is h)r)

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    =

    $i$6)d FCharging and disharging !"a#ai$!rs in R-C Cir%i$(

    T)ah)rs Signa$%r)

    INVESTIGATO

    RY

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    4

    PROJECTON:-

    Charging and disharging!" a#ai$!rs in R-Cir%i$

    1. Aim:-

    T! 9)ri" $ha$ 4. harg) is s$!r)d in a a#ai$!r in a R-C ir%i$

    a$ i$s $i3) !ns$an$ and 4. harg) r)3ains @h)n a#ai$!r is

    disharg)d and h)n) #6!$ a gra#h

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    5

    An R-C ir%i$ is a ir%i$ !n$aining a r)sis$!r and a#ai$!r

    in s)ri)s $! a #!@)r s!%r)( S%h ir%i$s nd 9)r i3#!r$an$

    a##6ia$i!ns in 9ari!%s ar)as !" si)n) and in

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    8

    3)3http://en.wikipedia.org/wiki/Capacitancehttp://en.wikipedia.org/wiki/Potential_energy

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    .( * r)sis$!r

    0( 3%6$i3)$)r

    =( V

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    *;

    VQQ

    C

    P%$$ing a

    E -

    Q

    C - iRQ;

    Sin) iQdQ

    dt

    Th)r)"!r), E -Q

    C -dQ

    dt RQ;

    E -Q

    C QdQ

    dt R

    EC-Q

    dQ

    dt RCIn$)gra$ing

    0

    t1

    RC dt Q

    0

    Q1

    ECQdQ

    lnECQ

    EC Qt

    RC ( 1ii2

    *QEC Q e

    t

    RC

    H)n) @) g)$, QEC (1et

    RC)Sin) ECQ;"!r a a#ai$!r

    Th)r)"!r),

    Q; (1et

    RC) (( 1iii2H)r), harg) a$ $i3) $

    ! 3a? harg)

    A6s! QCV and !QCV!, @h)r) V and V!ar) 9!6$ag) a$ $i3) $

    and 3a? 9!6$ag) r)s#)$i9)6

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    **

    Th)r)"!r) "r!3 )7 1iii2,

    CVQCV! (1et

    RC)

    VQV! (1et

    RC) , $his is $h) r)7%ir)d )?#r)ssi!n(

    NOTE:- This is $h) harging )7%a$i!n !n6, "!r disharging

    )7%a$i!n #r!))d $h) sa3) @a

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    *&

    1ii2 N!@ $a) 3%6$i3)$)r 6)ads and #6a) $h)3 in $h) $@!

    $)r3ina6s sha#)d 6i) (1iii2 B)"!r) #r!))ding "%r$h)r @) 3%s$ ha9) a

    !3#!n)n$s( Th) !3#!n)n$s !%6d %s$ #%sh)d in$h) h!6)s and !nn)$i!ns !%6d

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    *.

    hanging r)adingsX B%$

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    *0

    0. 4(5& &(&* *0;

    . 5(;; *(=0 *8;

    . 8(*& ;(50 &=;

    1#. 8(0; ;(0. .;;

    raph:-P6!$ !" 9!6$ag) 9s $i3)

    Ti3) !n ?-a?is and 9!6$ag) !n -a?is1i2 /!r harging:-

    ; *;; &;; .;; 0;;

    ;

    *

    &

    .

    0

    =

    4

    5

    8

    charging of capacitor

    Y-Va6%)s

    1ii2 /!r disharging:-

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    *=

    ; =; *;; *=; &;; &=; .;; .=;

    ;

    *

    &

    .

    0

    =

    4

    58

    *;

    Discharging of capacitor

    Y-Va6%)s

    Th) !rigina6 gra#hs "!r disharging and harging r)s#)$i9)6 ar):-

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    *4

    Calculations:-

    N!@ sin) $h) gra#hs ar) 9)r 3%h si3i6ar $! $h) gra#hs !"

    harging and disharging !" a#ai$!r(

    A$ Q*;;s), d%ring harging !" a#ai$!r $h) 9!6$ag) !n

    a#ai$!r is =(4 9!6$ as i$ is !

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    *5

    VQ.(.&[.(.; @hih is ahi)9)d )?#)ri3)n$a66 as @)66

    0. Conclusion:-H)n) i$ is 9)ri)d )?#)ri3)n$a66 $ha$ 4. harg) is $h)r)

    !n a#ai$!r a"$)r $i3) !ns$an$ d%ring harging and 4.harg) is 6!s$ a$ $i3) !ns$an$ d%ring disharging(

    . References:- G!!g6)(!(in

    En(@ii#)dia(!rg

    C!n)#$s !" #hsis #ar$ & )$ is !3#6)$)6 r)a$)d @i$h $h) h)6# !" ir!s!"$

    @!rd &;;5 and $h) gra#hs, )7%a$i!ns and !