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CapacitorsSchool :- SMK Sultan Abdul Samad, Jalan 12/13, 462 !"talin# Ja$a, S"lan#or

Candidat" :- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

& / C 'o( :- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% )at" :- * +pt( )a$ (

+pt( 'o( :- 6 &nd" 'o( :- %%%%%%%%%%%%%%%%%%%%%%%%

.opic :- Capacitor

.itl" :- Capacitanc" and tim" constant

b0"cti" :- .o d"t"rmin" th" capacitanc" o a capacitor and th" tim" constant o an R C circuit(

.h"or$ :- .h" dia#ram shos an R C circuit(

5h"n th" sitch S is clos"d, char#in# o th" capacitor occurs(

.h" char#" Qo stor"d in a ull$ char#"d capacitor o capacitanc" C und"r a char#in# olta#" V is

#i"n b$

5h"n th" sitch S is op"n"d, th" capacitor ill dischar#" throu#h th" r"sistor o r"sistanc" R(

.h" pot"ntial di"r"nc"s across C and R , VC and VR r"sp"cti"l$, ar" no r"lat"d b$

V C R

S

(o

Q CV=

(C RV V- =

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& Q char#" on th" capacitor at tim" t.

I curr"nt loin# at tim" t,

th"n, , , ,

* I = positi", dQ n"#ati"

and no

or

&nt"#ration ollo"d b$ di"r"ntiation #i"s

h"r" Qo initial char#",

I o initial curr"nt,

Apparatus : - *i A 6 7 d(c( po"r suppl$ *i .o conn"ctin# ir"s "ach ith a crocodil"

*ii A sitch clip at on" "nd(

*iii A d(c( Milliamm"t"r *ii Som" conn"ctin# ir"s

*i A stopatch *iii A capacitor lab"ll"d C

* A r"sistor - pac8

Capacitors *2

,Q

IRC

- =

(dQ Q

Rdt C

- =

dQI

dt= -c

QV

C=

RV IR=

o

t

Q Q e -

=

o

t

I I e -

=

time constant .CR = =

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!roc"dur" : -

*a .h" apparatus as shon in th" dia#ram is s"t up, R b"in# th" ""cti" r"sistanc" across X and Y.

*b Startin# ith R 66 9 , sitch S is clos"d and R is d"cr"as"d in sta#"s b$ prop"r s"l"ction

o combination o r"sistors in th" r"sistor pac8 until th" r"adin# o curr"nt Io in th" milliamm"t"r is

about 1( mA( .h" alu"s o Io and th" corr"spondin# r"sistanc" Ro ar" r"cord"d and tabulat"d(

*c K""pin# th" alu" o Ro ith th" alu" o Io about 1 mA, switch S is opened and th" t"rminals

o th" capacitor ar" short"d ith a short conn"ctin# ir" to ull$ dischar#" it( *d Sitch S is clos"d a#ain to char#" th" capacitor until th" r"adin# o th" milliamm"t"r shos Io (

*" Sitch S is th"n op"n"d and simultan"ousl$ a stopatch is start"d and th" r"adin# o th"

milliamm"t"r is obs"r"d( .h" stopatch is stopp"d h"n th" curr"nt r"ach"s a c"rtain alu" o I (

.h" alu"s o I and th" corr"spondin# tim" t ar" r"cord"d(

* St"ps *d and *" ar" r"p"at"d until I (

*# 7alu"s o I , t , , and ar" also tabulat"d(

*h A #raph o "rsus t is plott"d and its #radi"nt , , is also d"t"rmin"d(

*i .h" tim" constant or th" R C circuit is calculat"d usin# th" "pr"ssion (

*0 .h" capacitanc" C o th" capacitor is d"t"rmin"d usin# th" "pr"ssion (

*8 rom th" #raph o "rsus t , an "pr"ssion or curr"nt I as a unction o tim" t is d"duc"d(

Capacitors *3

mA

6 7 d(c(

po"r

suppl$

S

C

+

-

.o r"sistor - pac8X

YR

oI

Iln o

I

I

ln oI

I

ln oII

kt

=

1

k =

o

CR

=

ln oI

I

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Capacitors *4

;"sults :- )"t"rmination o Io and th" corr"spondin# Ro

64

63

62

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Capacitors *> 7ariation o I ith t

*I= (1

mA

.im" *t= (1 s

* i * ii m"an

(?

(@ 1(2 1(2

( 3(4 4(4

(6 >(4 (

(> @(@ 1(

(4 13(2 14(4

(3 1?( 2(2

(2 2@( 2@(6

(1 41(@ 42(2

==

=

n

tt

==

=

n

I

I

I

I

o

o

ln

ln

I

Io

I

Ioln

* , ln - * B , B -Centroid oItI

= =

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Capacitors *6

raph :-

ln /Graph of versus soI

tI

0

ln oI

I

/t s

BBln =

I

Io

B B st = -

c"ntroid

* B , B

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Capacitors *Calculations:-

rom th" #raph o "rsus t / s,

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Capacitors *@

As th" #raph o "rsus t / s is a straight line through the origin ith slop" k,

" ha"

or

or

or

and or th" "p"rim"nt r"sults,

hich shos that curr"nt I is a d"cr"asin# "pon"ntial unction o tim" t or a dischar#in# capacitor(

I

Io

ln

ln

o

o

o

o

k t

k t

k t

I

k tI

Ie

I

Ie

I

I I e

-

-

= +

=

=

=

B ? mAtI e -=

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Capacitors *?)iscussion :-

*a !r"cautions

1( Sitch S must b" sitch"d o h"n th" po"r suppl$ is no lon#"r n""d"d so that th" "l"ctromoti"

orc" * "(m(( o th" po"r suppl$ do"s not d"t"riorat" as d"t"riorat"d "(m(( cannot proid" th"

sam" curr"nt Io

as r"Duir"d "ach tim" th" "p"rim"nt is r"p"at"d(

2( Also "nsur" that th" po"r suppl$ is not accid"ntall$ short circuit"d hil" dischar#in# th" capacitor, b$

"nsurin# sitch S b" op"n"d , as this can dama#" th" c"lls(

3( 5hil" ta8in# r"adin#s rom th" milliamm"t"r or stop-atch * analo#u" t$p" , ma8" sur" that th"

dir"ction o ision is p"rp"ndicular to th" scal" at th" point hos" r"adin# is r"Duir"d to aoid paralla

"rror(

4( +nsur" that all "l"ctrical conn"ctions ar" cl"an and ti#ht(

*b ;"liabilit$ o r"sults

1( .h" r"sults obtain"d or and C ar" accurat" to 2 or 3 si#niicant i#ur"s onl$(

2( &t is assum"d that th" capacitor and r"sistor ar" in #ood or8in# condition E an$ l"a8a#" or

malunction can a"ct th" accurac$ o th" r"sults(

*c Comm"nt

1( .h" po"r suppl$ rom a ull$ char#"d accumulator can proid" a st"adi"r curr"nt than a po"r pac8

o dr$ c"lls and is th"r"or" pr""rr"d(

2( &t is important to "nsur" that th" polar "l"ctrol$tic capacitor und"r t"st b" corr"ctl$ conn"ct"d to th"

circuit, i("( , ith its positi" and n"#ati" t"rminals b" conn"ct"d to th" positi" and th" n"#ati"

t"rminals o th" po"r suppl$ r"sp"cti"l$(

5ron# conn"ction can caus" th" capacitor to "plod" b"sid"s #iin# "rron"ous r"sults(

i *

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Capacitors *1

Conclusion :-

1( .im" constant, %%%%%%%%%%%%%% s(

2( Capacitanc", C %%%%%%%%%%%%%% (

3( Curr"nt I o a dischar#in# capacitor d"cr"as"s "pon"ntiall$ ith tim" t, i("( , or th" CR circuit,

or (

o

k tI I e -=

B ? mAtI e -=