Download - U6 Phy L3 (1)
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B.Indah: No. 15A, 17A, 21A & 41A Jalan Indah 16/12, Taman Bukit Indah (Tel: 7!2"4#16$%
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utiaa a': "7A, Jalan utiaa a' 1/# (Tel: 16!712"$5/ 16!775$61#%Name : Teacher : Ms. Liow
Subject : Physics Second Term Class : U6 Physics
Chapter : ! Capacitance "# Lesson no: !
$ate: %%6
Time: .!&am '.!&pm
Topic (: Capacitance
(. Uses
. )s components in electronics and telecommunications.
(. *n radio and Tele+ision recei+ers and in transmitter circuits.
!. *n power supplies to smooth the recti,ication o, a.c. into d.c..
(.( Capacitors
. ) capacitor is a de+ice ,or storin- ener-y and electrical char-es. ut resultant char-e stored in a
parallel plate capacitor / &.
(. ) parallel plate capacitor consists o, two parallel metal plates separated by a thin dielectric
between the plates.
!. ) dielectric is an insulatin- material0 such as air0 oil0 mica0 paper or polystyrene.
$ielectric is used to increase the capacitance o, a capacitor.
1. Symbol :
(.! Capacitance0 C
. The capacitance0 C0 o, a body is de,ined as the ratio o, char-e stored to the potential o, the
body.
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QC
V=
0 2 / char-e stored on the body0 3 / potential o, body
(. The capacitance o, a parallel plate capacitor is:
QC
V=
where 2 / char-e stored on one plate0 3 / p.d between the plate.!. Unit o, capacitance is 4arad0 4
*n practice0 more common units are:6
&F F = 0(
&pF F= .1. $e,inition: ,arad "4# is the capacitance o, a parallel plate capacitor i, the char-e on either
plate is C when the potential di,,erence between the plates is 3.
5ample
"a# 7rite down an epression ,or the potential o, a metal sphere carryin- char-e 2.
"b# 8ence show that the capacitance C o, an isolated conductin- sphere is proportional to its radius
9.
"c# Calculate the capacitance o, the sphere i, its radius is (& m.
(.1 Parallel'plate Capacitor
. 5lectric ,ield stren-th inside the plates0
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VE
d=
where 3 / potential di,,erence between the plates
d / separation between plates
(. 4rom
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Problems
. 7hat is the capacitance o, two s>uare parallel plates 1.( cm on a side that are separated by
.? mm o, para,,in@
(. ) !&&p4 air-ap capacitor is connected to a !(3 battery. *, a piece o, mica ,ills the space
between the plates0 how much char-e will ,low ,rom the battery@
(.6 Capacitors in Series.
. Char-e on each capacitor is the same / 2
(. Since 2 / C30 the p.d. across each capacitor is:
QV
C=
(
(
QV
C=
!
!
QV
C=
!. Total potential di,,erence across the capacitors is:
( !
( !
Q Q QV V V V
C C C= + + = + +
( !
V
Q C C C = + +
The e>ui+alent or e,,ecti+e capacitance0 CT0 o, capacitors in series is:
T
V
C Q=
( !
TC C C C
= + +
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(.A Capacitors in Parallel
. Potential di,,erence across each capacitors is the same / 3
(. 4rom Q CV= 0 char-e on each capacitor are Q C V= ( (Q C V= ! !Q C V= .
!. Total char-e 2 supplied by the battery is:
( !Q Q Q Q= + +
( )
( !
( !
C V C V C V
C C C V
= + +
= + +
ut TQ C V=
The e>ui+alent or e,,ecti+e capacitance o, capacitors in parallel is:
( !TC C C C = + +5ample
4ind the combined capacitance o, each o, the ,ollowin- networBs0 assumin- each capacitor is ( F
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5ample (
4our capacitors each o, capacitance C are connected in such a way that their total capacitance is
also C. 7hich o, the ,ollowin- networBs -i+e this +alue@
5ample !
)n ?& F and a (& F capacitor are connected in series to a & 3 supply.
4ind: "a# the char-e on each capacitor "b# the p.d. across each capacitor.
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5ample 1
4ind the char-es 20 2(0 2!on the capacitors and the potential di,,erences 3and 3(across them.
(.6 5ner-y Stored *n a Char-ed Capacitor
. )t any instant durin- char-in-0 the char-e 2 on the capacitor increases as the potentialdi,,erence 3 o, the capacitor increase.
(. )s V Q 0 a -raph o, p.d. 3 a-ainst 2 is a strai-ht line passin- throu-h "&0.
!. 7orB done in char-in- the capacitor by dQ V dQ= / shaded area under -raph
1. The total worB done in increasin- the char-e ,rom Dero to 2 on the plates is:
0Q
o
QW V dQ V
C= =
. 8ence0 the ener-y stored in the capacitor
(
(
( ( (
QCV QV
C= = =
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5ample
) !& F capacitor is char-ed to !& 3 and a :& F capacitor is char-ed to 6 3. The batteries areremo+ed and the two capacitors are then connected with their plates o, liBe char-es to-ether.
"a# Calculate the new p.d. across each capacitor.
"b# Calculate the new char-e on each capacitor.
"c# 7hat is the loss o, electrical ener-y durin- this process@
7hat becomes o, this lost in potential ener-y@
(.A Char-in- ) Capacitor Throu-h a 9esistor "9'C char-in-#
. 7hen the contact o, the two'way switch E is at )0 the capacitor C will be char-ed by the
battery 3othrou-h the resistor 9.
(. 5lectrons are mo+ed ,rom plate a to plate b by the battery. Plate a becomes positi+ely char-ed0
with char-e F2 while plate b becomes ne-ati+ely with '2. ) current * ,lows throu-h the
capacitor.
!. The e>uations ,or current *0 char-e 2 and p.d. 3 durin- char-in- are:
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a# Char-in- current0
t
RCoI I e
=
b# Char-e on capacitor0
t
RCoQ Q e
=
c# P.d. across capacitor0
t
RCo
V V e
=
7here *o/ initial char-in- current0 9C / time constant0
2o/ maimum char-e0 3o/ supply +olta-e
(.? $ischar-in- a Capacitor throu-h a 9esistor
. 7hen the contact E is switched to 0 electrons are trans,erred ,rom plate b to plate a. )
dischar-e current * ,lows.
(. The e>uations ,or *0 2 and 3 durin- dischar-e are:
a# dischar-in- current is:
t
RCoI I e
=
b# char-e on the capacitor0
t
RCoQ Q e
=
c# p.d. across capacitor0
t
RCoV V e=
!. 4rom
t
RCoV V e
=
ln ln ot
V VRC
= +
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(.; Time'constant0 9C
. Time'constant0 9C0 is the time taBen durin- char-in- ,or the char-e on a capacitor to increase0
,rom Dero to 6!G o, its maimum char-e.
4rom:
t
RCoQ Q e
=
7hen t / time'constant / 9C
RC
RC
oQ Q e
=
( )
( )
&.!A &.6! 06!G
o o
o o o
Q e Qe
Q Q Q
= =
= =
5-: 4ind the time'constant in the ,ollowin- circuits@
a.
b.
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Problems
. The capacitance in the circuit is C/ &.!& p4 0the total resistance is (& Band the battery
em, is (3 $etermine "a# the time constant "b# the maimum char-e the capacitor could
ac>uire "c# the time it taBes ,or the char-e to reach ;;G o, this +alue "d# the current Iwhen
the char-e Qis hal, its maimum +alue "e# the maimum current and ",# the char-e Qwhenthe currentIis &.(& its maimum +alue.
(. *n the 9C circuit shown in ,i-ure0 the battery has ,ully char-ed the capacitor0 soQ
0=C E .Then at t/ & the switch is thrown ,rom position a to b .The battery em, is (&.&
30 and the capacitance C / .&( 4. The currentIis obser+ed to decrease to &.& o, its
initial +alue in 1& s. "a# 7hat is the +alue o, 20 the char-e on the capacitor0 at t = &@ "b#
7hat is the +alue o, 9@ "c# 7hat is 2 at t/ 6& s@
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