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TOPPER GUIDANCE ACADEMY

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Physics By – Er. A . kumar
Class 12th Unit – 2 (Capacitor)
Capacitor or condenser :-

• It is a device on which electric charge may be stored so that it possesses

electric energy .
• It is arrangement of two identical plates .
• which is used for different purpose (1) for storing the energy
(2) for creating the electric field (3) for filtration of vibrating components

Types of capacitor
1. Parallel plate capacitor
2. Incline plate capacitor
3. Spherical capacitor
4. Cylindrical capacitor
5. Air capacitor
6. Paper capacitor
7. Mica capacitor
8. Wood capacitor

Capacity :-

It is defined as the ability of any capacitor to store energy.

• Denoted by C .
• Represented by −∥ −
𝑪𝒉𝒂𝒓𝒈𝒆 𝑸
• C= =
𝒑𝒐𝒕𝒂𝒏𝒕𝒊𝒂𝒍 𝑽
• It is scalar quantity
• SI unit farad (F) . ( 1𝝁F =𝟏𝟎−𝟔 𝑭 , 1𝑷F =𝟏𝟎−𝟏𝟐 𝑭 )
• Dimension [𝑴−𝟏 𝑳−𝟐 𝑻𝟒 𝑨𝟐 ]
• It is independent of charge & potential (v) of capacitor .
• It is depends only on the shape , size , area & separation of capacitor plate .
• It is also depend upon nature of dielectric between the plates .
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Capacity of capacitor :-

1. Parallel plate capacitor :-

Case -1 :- when no any dielectric are filled in parallel plate capacitor .
𝑪𝒉𝒂𝒓𝒈𝒆 𝑸 𝑸 𝑸 𝝈𝑨 𝜺𝒐𝑨
C= = = =𝝈 =𝝈 =
𝒑𝒐𝒕𝒂𝒏𝒕𝒊𝒂𝒍 𝑽 𝑬𝒅 ⁄𝜺𝒐 𝒅 ⁄𝜺𝒐 𝒅 𝒅

Case – 2 :- When the dielectric are filled in parallel plate capacitor .

𝜺𝒐 𝑨
C = k𝑪𝒐 = 𝒌
𝒅

2. Cylindrical capacitor (outer surface earth ) :-

𝑪𝒉𝒂𝒓𝒈𝒆 𝑸 𝟐𝝅𝜺𝒐 𝒍
C= = =
𝒑𝒐𝒕𝒂𝒏𝒕𝒊𝒂𝒍 𝑽 𝟐.𝟑𝟎𝟑𝐥𝒐𝒈(𝒃⁄𝒂)

Where l = length of cylinder , a = inner radius , b = outer radius

3. spherical capacitor (outer surface earth ) :-
𝑪𝒉𝒂𝒓𝒈𝒆 𝑸 𝒂𝒃
C= = = 4𝝅𝜺𝒐 ( )
𝒑𝒐𝒕𝒂𝒏𝒕𝒊𝒂𝒍 𝑽 𝒃 −𝒂

Where - a = inner radius , b = outer radius

Grouping of capacitor :-

1. Series grouping :-
The capacitors are said to be connected in series between two points when we can proceed
form one point to other only through one path .
• The value of charge through each of the capacitors same.
• The potential difference across each of the capacitors will be different .
𝑸
𝑽𝒂 -𝑽𝒃 = ⁄𝑪 -------(1)
𝟏
𝑸
𝑽𝒃 -𝑽𝒄 = ⁄𝑪 --------(2)
𝟐
𝟏 𝟏 𝑸 𝟏 𝟏
Eqn (1) & (2) 𝑽𝒂 -𝑽𝒄 = Q ( + ) =Q( + )
𝑪𝟏 𝑪𝟐 𝑪𝒆𝒒 𝑪𝟏 𝑪𝟐

𝟏 𝟏 𝟏
= +
𝑪𝒆𝒒 𝑪𝟏 𝑪𝟐

2. Parallel grouping :-
The capacitors are said to be connected in parallel between two points when we can proceed
form one point to other through different path .
• The value of charge through each of the capacitors will be different .
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• The potential difference across each of the capacitors will be same.

Q = 𝑸𝟏 + 𝑸𝟐
𝑪𝒑 (𝑽𝒂 -𝑽𝒃 ) = 𝑪𝟏 (𝑽𝒂 -𝑽𝒃 ) +𝑪𝟐 (𝑽𝒂 -𝑽𝒃 )
𝑪𝒆𝒒 = 𝑪𝟏 + 𝑪𝟐
Dielectrics :-
It is insulating material which transmit electric effect without actually conducting
electricity . Eg – water , glass , mica , polyvinyl chloride .
Types of dielectric :-
(1) Non polar dielectrics :- (2) Polar dielectrics :-
Non polar dielectrics :-
In such molecules the center of positive charge coincides with the center of
negative charge in the molecule is called non-polar dielectric .
• The dipole moment of nonpolar dielectric molecule is zero .
• Eg -𝑯𝟐 , 𝑶𝟐 , 𝑵𝟐 .
Polar dielectrics :-

In such molecules the center of positive charge not coincides with the center of
negative charge in the molecule is called non-polar dielectric .
• The dipole moment of nonpolar dielectric molecule is not zero .
• Eg -𝑯𝟐 O , 𝑵𝑯𝟑 , 𝑵𝟐 𝑶 , 𝑪𝑶𝟐
Electric polarization :-
The dipole moment per unit volume is called polarization .
• Denoted by 𝝈𝒑 .

𝝈𝒑 = 𝑷⁄𝑽
• SI unit – coulomb - 𝒎−𝟐
Dielectric constant :-
The ratio of external electric field applied to the reduced value of electric field is
constant for the material.
• Denoted buy K .
• The dielectric constant of polar dielectrics is inversely proportion of
temperature .
𝑬 𝑪 𝜺
K= = =
𝑬𝒐 𝑪𝒐 𝜺𝒐
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Dielectric strength :-
The maximum electric field that a dielectric medium can withstand without
breaking down of its insulating property is called its dielectric strength .
𝑽 𝑸 𝑸 𝑸
E= = = 𝑨
=
𝒅 𝑪𝒅 𝒌𝜺𝟎 𝒅 .𝒅 𝒌𝜺𝒐 𝑨

Electric susceptibility :-
It is found that the electric polarization P is directly proportional to the reduced
value of electric field .
• Denoted by 𝝒
• P = 𝝒𝜺𝑬
• K=1+𝝒
Energy stored in capacitor :-
• When a cell in connected across a capacitor it starts sending the charge to
the capacitor . Let q amount of charge remains on the plates of the capacitor
and the further charge dq is send by the cell which is opposed by the charge
already present on the capacitor due to higher potential of the cell it does
some work to send this charge and this amount of work done remains stored
in this charge and this amount of work done remains stored in the form of
potential energy in capacitor.
𝑸 𝒅𝑸
V= → dV =
𝒄 𝒄
𝒅𝑸 𝟏 𝑸 𝑸𝟐
∆𝑾𝒄𝒆𝒍𝒍 = ∫ 𝒒𝒅𝒗 = ∫ 𝒒 = ∫𝟎 𝒒𝒅𝒒 =
𝒄 𝒄 𝟐𝒄

This amount of work done by the cell remains stored in the capacitor in the form
of potential energy .
𝑸𝟐 𝑪𝑽𝟐 𝑸𝑽
U= = =
𝟐𝒄 𝟐 𝟐
• Total energy of series and parallel grouping of capacitor :-
• U = 𝑼𝟏 + 𝑼𝟐 + 𝑼𝟑 + 𝑼𝟒 ---------
Energy density :-
• It is defined as the total energy stored per unit volume of the conductor .
• Denoted by u .
𝐭𝐨𝐭𝐚𝐥 𝐞𝐧𝐞𝐫𝐠𝐲 𝟏
U= = 𝜺𝒐 𝑬𝟐
𝐯𝐨𝐥𝐮𝐦𝐞 𝟐
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VAN - DE - GRAAFF Generator:-

• Van de graaff generator is used to generate high voltages of the order of a
few million volts. This results in generation of large electric fields for
experimental purposes.

Principle
• The inner sphere has a higher potential than outer if the charge q is
positive.
• If the two spheres are connected through a wire, the charge will
flow from high to low potential.
• Thus, providing smaller potentials at the inner sphere will keep
building large amount of charge at the outer sphere, till the
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breakdown field of air (3 x 10 V/m) is reached.
• This accumulates close to millions of volts.
Construction :-

• A large spherical conducting shell (of few meter radius) is supported at a

height several meters above the ground on an insulating column.
• A long narrow endless belt insulating material, like rubber or silk, is wound
around two pulleys – one at ground level, one at the center of the shell.
• This belt is kept continuously moving by a motor driving the lower pulley.
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• It continuously carries positive charge, sprayed on to it by a brush at ground

level, to the top.
• There it transfers its positive charge to another conducting brush connected
to the large shell.
• Thus positive charge is transferred to the shell, where it spreads out
uniformly on the outer surface and a voltage difference of as much as 6 or 8
million volts (with respect to ground) can be built up .
Electrostatic circuit :-
When the capacitors , cells and resistance are connected by the conductors the
network obtained is known as the electric circuit .
Types of circuit :-
(1)Open circuit (2) closed circuit
Open circuit :-
In open circuit the resistance of the circuit is supposed to be infinity and hence
the value of current or charge flowing through it is zero .
Closed circuit :-
In closed circuit the resistance of the circuit is supposed to be finite and hence
the value of current or charge flowing through it .
Conservation of charge :-
Kirchhoff 1st law :-
The any junction the value of incoming charges should be equal to the value of
outgoing charges .
𝒒𝒕𝒐𝒕𝒂𝒍 = 𝒒𝟏 + 𝒒𝟐 + 𝒒𝟑 + -----
Kirchhoff 2nd law :-
The algebraic sum of charges in potential around any closed loop involving
resistance & cells in the closed loop is zero .
𝒒 𝒒
𝜺+ + =0
𝑪𝟏 𝑪𝟐
Wheat stone bridge :-
𝑪𝟏 𝑪𝟒
If any circuit the condition = is satisfied in this case the potential of points p
𝑪𝟐 𝑪𝟑
and q becomes equal and as a result there will be no charge flowing through the
capacitor hence it is neglected .
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