Electric Pofential &caratíconte?

21) 3)

72
XmY |mY

C-(unmmon)

(-a)

32) Ct centre,
P

Vp Va

Q (ov)
(6ov) hi9her tu Srt
lower

2)7 K-e)

600K1O =o(o-o4-v

W (Ve-va)a
Vp 0028
kaz
Vp= o-028

34) (VA- Ve)4mv

210xO2x

ose iF
Wo TE:lh'the above
then VaVB7

(Vg-vA ) to ,,. w=o.

33)-xo"m

3)

tet 'a' be charge

22

indueocl,
ehavge
3
3
charge iiner, Surtace of outer
shetl 'e?,
():
charge on Gutey Surtace ofc
224'
3
CAPACITANCe (c):

(vhen charge gven t0 the conductor is incveases t

Potenticl is lSo tnoreSeS,

C= U (scalar )’both àuanti rs Stalar.

Capåcitcnce of Conductor.
Here,c is known as Capacity(oY)
SI unit of 'c' is C (or) Farad

c-2TIJ
p:f of C: M2T2

()
conductor:
Capacity ot spherical
Consider'aisphercat conductor ot raclius y? corries the
v=l a
charge q. It's Potentil

JS Capaeity.
C depends .on size shape o} the conductong surroun
ding mecdium
contuctór &
’ i s inde pe hdent of chargè on the
Potential.
r'is decined aJ!
it"S i
The charge reuired by the concluceor to rise
Cgiven)
Potentia by lvi
Capocity of thearth

(m)

(Farad (3 the
bi99eS unt of
Cpocity)
 opacitor! isis used
ujed to Store tarqe
plectricl device
’T is the tuwer
Potential
of charge t
ot capacitori
Principal and cuorking
prircipe; f'te,

is increases by plocir.
The apaity ot the onductor Conductor,
an ídenticcu earth connected Parollel
- B

:(v)

the above arrarnge mert s knouwn ay patllel plate

caractoY
NUTE: The charge on inner Surface
f
as change on' the cagacitor: psitive Plate i ake
Expression for Cupaciy of Parcltl pate (6)
-’1t consists ot two caraci toy :
a distante of 'd
Parcle plotej, each of
area,
(dcca)
(t) A

(aa
A

’1he (() A

eleetric field blw

unitorm Platey ot the cafacitor is aloys
t the e
this is djes of the Plate, lines
Knaun as. of force are curvSd,

heglect ec Fringing
4 cOn be e frect
as d i fay les
than '
 lectiing ffeld blw Plates,

Plates of capacitor,

(o-)
2)
V 4 dd
A Eo

Wow cafacits o chargeel

flate, air y Eo A

two Plates s completely filed

> Sf sepevation blu
slab, withconstat teloive
diclectic
withe dietctric
fesmitiviy-E )
Cwth'dielettric y Cete EA Eo ErA
d

kto A

Cdie

9Due to the diel ectric slab, Ca pacity incveas es by

k times.

capacity of the gracitor derendts on )Avec of the plate

)seperation blw the, plates .(CrA)

Ii) Medi vrn blw +he plates,

) Blw the ptatcs dietecti,
diet 'constond ' thicknes t! is Plaed.
with
xt
) Blw the Plotes Pd : (d t) AVEo

v lat+)
Now the

d-t-l)

z. (here, capacity inire ases,

td dee ve aes )
to get ovlginal cayacity origig1al pd; the seron.
mus be inreaged b x blw the plates.

Ameal slab (Ko) of thickneys

Plotes of the copacitor
ts ttacèd beo

Now the
cayocity with metal glab,
CoA
tnevcal
dt
td 1hen
9 Co A
9d-d

capoity bc comey do vb)ecty

 copocit ars:
Seíes Combincttion of (2
+4 -

I n Series Cormbincation
i3 sarne (2=coit)
each capacity
) charge
2)v' undevgoes spitting
V3
V= V) t V2t
combnation,
effective aapacity of the
3) Let be the
V and vz
V,=Y V2 C3 Cs
vClues ?n the above cqn,
By Placeng these

Cs

Ca
Cs

es than least capaeiky ein

s
of cCs is
the vaue of
-
the com blnation.

’TEiCom bination having only2'capatits

Cs

3x6
=2uF

Cs is ley then lcast Value

’Ratio ol the chavge

KettU ct the pd's

Vg--L:
V,?Vy C C3
h' icentical Copacitors ecch of Caacity care ine
ot the Com bincot ion
then e FFective Cayacity

Cs
pavallel combination:
plcd ej ot all caitoY S aie ccnnected fo |point

P-d acCYOS ecch cpacitor is Sane.

Cv)
9) charge wi be divided.

2) (edCp be the effective.

capacity ot the .com binchon

By placing theie veuues in the aove edation,

the is 9reatey than highes

cagatiy
fn ahe combination.
Ratio o the charge
 )Ratio cB p c(?s
Cidnticel)

CepecitoYs ecch ot, ca poacity c' are

bidenticl

pavaluel, the eFrect ca pacity is Jiven by,

Conne(teel st
are
each of e of.their
ca pa citUrs
identicl
Serlesr now
the ratio
’n
v lel and th er in
fn pa
effective coapatitles.

Cs

Cpns

Znergy stored in a capacitor: Thurscly

cons ider Uncha rqed capcc itor, havine Capacity'c is cone
ctec to the cett han'ng Prd 6 v bor chargirg.
The mà xìmym Charqe oni Capa cto fs Q'.

At a in Stat of time, durin ing' troC eSs det

chavej inqi
Srnall lq be the char9e on Capacitoyo
Here, V- Cp-d bluw the plet es)
tor giving the charge de to
the
The work one
Capa citoY a gaingt tield (aqainst the re pul sive Fovee)

The wd t0 ingrease the charge fromo Q , n

to inhease
the capacitur 7s given bys
 -(cv)?
2C

2
(cv: a)
) This amount of the work dOne is Store d
ay elecr
Potential energy in the electric Field b
Plates.

Thergy Store d in the cagocitor,

2
2C 2

lor)
QV

NOTE work . done by the celto charqe the

CapacitoY,
Weeu va
Wcel =Va 2r
Here, Hal & o 4he wort done by the ceu is Conversed'
fnto energy stored in a ca focitor,
the wd by the remaining 2
by cell co nverted int Het energ,
(onnecting wire :
énengy Stored per vnit
volume/Electyc olensitys
Ue U CV2
Ad
Ad

Eo 6 2
 NATE enevq1 Storec Pens unit voturme,
Co ¬2 hay dimers iong of presSure
(0-f)

)In series combinction of Capacitor,

Qi Constant

In parcllel combination of capacitor,

(aV,eU)

arameters ot Capari
-ffect of delectric on ifferent
tance:
Unchargeo ccpactor with air ay a medium, with
-
dhoyed by'thece,
CeL Pacity Co
o - ] it bulty

cOse ci):
k!
nt k!
d dielectric sab with conStant is plecced blw
PIates at the capacitor, dfter disco hnecting the boetery.
-Here charge o the Plcutey Qo is Conjtant
Isolete d
(O Heve cbe comes ktimes of Co

A%ter
Placing slab, Pavemeters ((a,v,u,C, 6J
D a o, lContyant)
 Vo
C K Co

Case tii);A dielectric Slab with tonstantk is placed

blw Plctes of the capacitor witheut disconnect.
the battey

Here, VVo Constant

Extra chare transferredd

to the Capacitor,
Da kao- Qo(k-)a.

’forte bleo plates ofok the

ceyacitoxs
Copcitor
-

1
 of fhe rac or S trccie,
blu Plates
The forcecharged Plate tes in electic fielcl ot another
one chavged

Pla te. capacitor (er

7solcted
case o}
oleL'h: In th
ted afte charging) /a ani]

F 26oA
cbpoeitor, ft
chavqeol
CeLse o iso toteolbtw the plale.
*)In the
indegendent of distance tor.
cted to the capac
Conne
remainy

when cell is
Couse (iil:
(vecorstont )
d
F= (cv)2
2 EoA
2Eo A

the
blw
on, clis tance
’S this cose p' depencls
Plates
of the capacitoy s f.
EX foYce on a charqe blw plctes
Now the force of the same charge Fter vemoving
one of the p lcue

2¬0

) hrt
2l0
diffese nt
If two charq ed boclies are Copacitors having
then they hare comm
rorenhay are connected together, high, potential
GePotential Here charge fows f rom
body to ow potential bocly.
 fz-0 Capatance
48)
lohave cornnch
v' tteus
42
C C2
Co Co A
Common Potenticl,

X lo-2

(a1t22tag us )
Com mon C, C,°C3(3 =12 3
Si) qiven, to A
d

sínce v'is consta nt, thickness ():2nd

- 2d

:16 24)

1t2+3
d-2d
6
cEo A
|6
(
6

SA
36
24 e

so) A I00x (04m2

A LO2 m
S3)x= 3-9 mm 60xs

K?

Crommon factor'e')

Cs
t(r)
t
6t3t2

Eot
Cs6
su)
c' to A
d
Ci ven thet,

(doubiey )

s5)
! capacitors are

K ff, 2 f e 3

K:3

K9-5

$) iven, coJY"
d
-d
yr!
Re -dlistri butíon f charge:
Case-ci Co ngider sphericoul cohducto rs, hoing the tk.
cwith radii ig2 are conneLed

tuire:

C22TEr2

VI 7 Y2

From St sphere to 2na spheres then

charge flows
potentiad
the Cornmon
Haire
t
C tC2
(trang fer charge)!
Amount of charge kuws

atz
Cait2)
rtre

charge remains, on
on t spheey

(onnet:
energy 1 l o s t , i n
Tn this Cale Some amount of

wires.
Ameunt, of loss ot energy Storecly
2

2CL t2Ca

LCte
 coapacit y S ,Potental v, le
.i0TE : A Charg cd SPhere with
Connected to unchargedt conduetor with capae'ty

Here V2 0

ergy stored,
l0ss of en
DU
Gtl2

ol. ot cne ryy

C2 Xl0a
-Xl0o

identical fee)
cese,
if spheres are
above
’ T n the Lost hy half)
C,= C2cCithen (ener4

". uf energy is tost,-lo0

Cu ¢ (2 are
(ase Cii): I w0 Cepacitorf having capacity C o n n e e t e din
re
Yespcctivelys
paxael
-LV1)

Ct2

Co mnon

doss of enexgy storedt Du

2
e y t t Covy (to)
 cho¥ged qpackox ís conn eCtet pavctlel t
voTe:
Unchavged ca pacitor.

Citl2

(Cit C2)v2

caue tiii) ? Two chavgecd capacitors with

chaurgel to v& V2 respectively COnnected

wn in the figure
8hown

"/a df en ergy lost

CtC2 (v,tva)
,
 83) woYr don e by the
V20V
cel tor full Charg ing,
Ve'ci0

(V-co nst ant, Paalled)

84) Y, l2cm

t6tC2 4=U2 constan

81) A-200 Cm2 (custe)

Qconshan'

d=silom
UQ2
2C

V, c200 v

6 Cpi h'Cs
02 2-67K\o
2025

electric dirote (2s)

with dipole momnent
ot hmag ntuole
neet>

in the direction of fielel

pole is
Yotatedl to cngle Coo° ) The c hange pE od the
olipole9
0°)60

Pécoso
Initiad Pe, U=-

U fincl= -Pe
--PE

2Pt - PE Pe

CAre Seperated
plate copacitoy
parallel
The ptates of
2025
didet rlc cong tan$ k, fkz
cuith
by d!. Two slabs inserte d in
3d sd respectively are
with thictnss become
2+ìrmes to
this capacity
Capacitor. Due
the voue of K, is
the initial capacitor If k, l·2S k2)

cl2c

c'=
tz
d-(tttt
Eo A
2C=

8ki 2X}k,

)
kË
 wo i dentical chavqed conducting spheres 4 R
Placed at Certai n distance, chaye on each sphere
'a. The force of vepuls ion blw them s A
hind iderticel uhch qvoed ondseting sphere t..
ught in ontact with Sphere A, first+& then
B. dnd fnaly remöved fom the both: No
fovce ot Yre pulsion blw A B is
()() | )
(a)
A

)
3f

Capacity of the capocitoy.with alr as a medivm

Blw the plote two Slabs with dielectric Constns ki

Place as shown in the fig.

Case 1

d,
 C

SEective capaeitylo)

faralle {
caprcity in
Combitio n, 2C
CitC2

dietectri
SFfective
(et Fp be thedielectiC Constcant ,(ks)
Hfective
constant (kp) of

kitk
KpC:

k,)

K2 K dl2

2k

In the cbove wg CoL4esg.

Cs
 thyee dielect ric slabs are placed blw the
y shown in h Fig. platey
Al2
di2 (o,) K, k2 (o)
(3) k3

let e be the effective dielectric

constant ot 3slabs.

Czt(3

kztk3

kitk3 ketk3
2.36

2r

KT 2 K
3r
K3 -3K
(9)
Cerfeckive tc
 k1tks Ka tK3

-kGoA

20 d

pication-9-9

Small drof
Biqdree
Y
ne

na

UJtn13,2

2l3V

1 u'-le'=n'en
Cons; der '3' identical meto Plates kep
ctt Same distance d' Area ot e ach
in Pares
shown 1n the figures. (nedir ir boi oi)

(multirie capacitor)

C blw AB;
CAA = c 3Eo A

If combination having 'n' Prates

then Ceffective,
Eo A
eff

there ig a gla bs bleo

the Plctes
(n-)kto A
:d

|+

(-)
3 B
A

A
(tve)

(- ve)