2. C O N T E N T S
Origin of electricity
Types of electricity
Forces of attraction &
Electric field intensity
Electric line of forces
Relation between electric
field and potential
Potential Energy of a
Combination of capacitors
Series & Parallel
combination of capacitors
4. Electricity is a kind of energy that can only be valued by the effects it gives. It
is a fundamental part of nature and it is one of the commonly used forms of
energy. This word comes from the Greek word elektron which means amber.
The term 'electricity' is derived from a term used by William Gilbert in 1600 to
describe static electricity. The discovery that lightning is electrical was made
by Benjamin Franklin in 1759
Electricity cancan be converted to other form of energy and other form of
energy can be converted to electricity and work can be done my electricity.
Origin Of Electricity
5. The study of electricity is divided into 3 different branches as:
Electrostatics: Static electricity is the result of an imbalance between negative
and positive charges in an object.It is the study of the force that acts
between point charges.
Current Electricity : An electric current is the rate of flow of electric charge past a point or region. An electric
current is said to exist when there is a net flow of electric charge through a region. There are two kinds of
current electricity: direct current (DC) and alternating current (AC). With direct current, electrons move in one
Types Of Electricity
6. Conductor : A conductor facilitates the easy flow of an electron from
one atom to another atom when the proper application of voltage.
This is because there are no band gaps between the valence and
Example - metals, aqueous solutions of salts, graphite, and the
Semiconductor: The substance though which electricity or charge
can flow partially . The resistance of a semiconductor falls as its
Example: silicon, germanium & gallium arsenide.
Insulator: An insulator is a material that has very high electrical resistance & it does not allow the flow of
current. There are no free electrons in insulators thus they do not conduct electricity.
Example: Wool, dry air, plastics, and polystyrene foam.
7. Coulomb's law states that: The magnitude of the electrostatic force of
attraction or repulsion between two point charges is directly
proportional to the product of the magnitudes of charges and inversely
proportional to the square of the distance between them. The SI derived
units for the electric field are volts per meter (V/m) and newtons per
k is proportionality constant and equals to 1/4 π ε0. Here, ε0 is the
epsilon naught and it signifies permittivity of a vacuum. The value of k
comes 9 × 109 Nm2/ C2 when we take the S.I unit of value of ε0 is 8.854 ×
10-12 C2 N-1 m-2.
8. One coulomb is equal to the amount of charge from a current of one ampere flowing
for one second
Force of attraction : The force of attraction or repulsion between the two charges depends on
the three factors.
•The amount of two charges
•Distance between the two charges
•Medium between two charges
Point Charge : A point charge is a hypothetical charge located at a single point in space. While
an electron can for many purposes be considered a point charge, its size can be characterized
by length scale known as the electron radius.
Force Of Attraction & Point Charge
9. Test Charge: A test charge is a charge with a
magnitude so small that placing it at a point has a
negligible affect on the field around the point.
The region around the electric charge in which the
stress or electric force act is called an electric field
or electrostatic field. If the magnitude of charge is
large, then it may create a huge stress around the
region. The electric field is represented by the
symbol E. The SI unit of the electric field is newton
per coulomb which is equal to volts per meter.
10. Electric Field Intensity
The space around an electric charge in which its influence
can be felt is known as the electric field. The electric field
Intensity at a point is the force experienced by a unit
positive charge placed at that point.
•Electric Field Intensity is a vector quantity.
•It is denoted by ‘E’.
•Formula: Electric Field = F/q.
•Unit of E is NC-1 or Vm-1.
The electric field intensity due to a positive charge is
always directed away from the charge and the intensity due
to a negative charge is always directed towards the charge.
Electric Field Intensity
11. The properties of electric lines of force are:
i) Lines of force start from positive charge and terminate at negative charge.
ii) Lines of force never intersect.
iii) The tangent to a line of force at any point gives the direction of the electric field at that point.
iv) The number of lines per unit area, through a plane at right angles to the lines is proportional
to the magnitude of E. That is, when the lines of force are close together, E is large and where
they are far apart, E is small.
v) Each unit positive charge gives rise to ε01 lines of force in free space. Hence, number of lines
of force originating from a point charge q is N=ε0q in free space.
Electric Line Of forces
12. Electric potential: The electric potential, or voltage, is the
difference in potential energy per unit charge between two
locations in an electric field.
Electric potential energy : It is the energy that is needed to
move a charge against an electric field.
There are two key elements on which the electric potential
energy of an object depends.
It’s own electric charge.
It’s relative position with other electrically charged objects.
13. Electric potential due to a point charge
k is a constant equal to 9.0×109 N⋅m2/C2.
The electric potential at a point is equal to the electric potential energy (measured in joules) of
any charged particle at that location divided by the charge (measured in coulombs) of the particle.
Potential difference: The difference in potential between two points that represents the work
involved or the energy released in the transfer of a unit quantity of electricity from one point to the
Electric Potential Due To A Point Charge
14. Potential Of A Charged Sphere
The use of Gauss' law to examine the electric field of a charged sphere shows
that the electric field environment outside the sphere is identical to that of
a point charge. Therefore the potential is the same as that of a point charge:
The electric field inside a conducting sphere is zero, so the potential
remains constant at the value it reaches at the surface:
Potential Of A Charged Sphere
15. The electric field exists if and only if there is a electric potential difference. If the charge is uniform at all
points, however high the electric potential is, there will not be any electric field. Thus, the relation
between electric field and electric potential can be generally expressed as – “Electric field is the negative
space derivative of electric potential.”
The relation between Electric field and electric potential is mathematically given by-
Direction of Electric Field
•If the field is directed from lower potential to higher then the direction is taken to be positive.
•If the field is directed from higher potential to lower potential then the direction is taken as negative.
Relation Between Electric field & Electric Potential
17. Electrical Capacitance
Electrical conductance of a conductor is defined as the capacity to store charge in it. Whenever charge
is applied to an insulator its potential is raised to some certain level. Charge on a conductor and its
electric potential are both directly proportional to each other. So, as we increase the charge electric
potential also increases.
Where, the variable C is the proportionality constant. It is also called capacitance. Capacitance of a
conductor is affected by the shape and size of the conductor. Medium also affects the capacitance in
which the conductor is placed. Capacitance is never affected by the material used to make the
If V=1 then
Q=C X 1
Refined definition of Capacitance is:
“It is the amount of charge required to increase its electric potential by unity”.
It is a unit of electrical capacitance (ability to hold an electric charge), in the metre–kilogram–second system
of physical units, named in honor of the English scientist Michael Faraday. The capacitance of a capacitor
is one farad when one coulomb of electricity changes the potential between the plates by one volt. The unit
of capacitance is the Farad (F), which is equal to a Coulomb per Volt (1 F = 1 C/V), though most electronic
circuits use much smaller capacitors.
Capacitance Of a Spherical Conductor:
An isolated charged conducting sphere has capacitance. Applications
for such a capacitor may not be immediately evident, but it does
illustrate that a charged sphere has stored some energy as a result of
being charged. Taking the concentric sphere capacitance expression:
Capacitance Of a Spherical Conductor
19. We know that, C=V/Q and hence Q=CV
Here, C is the capacitance of the capacitor, Q is the charge stored in it and V is the potential
difference between the two plates of the capacitor. An intermediate stage in which a charge of
magnitude q is present on the capacitor and V be its potential difference. Whenever some extra
charge gets stored, the P.D. goes on increasing. Since it's very small, the change in P.D. can be
ignored and can be considered as constant as V.
Work needs to be done in charging it. Let the small work done in depositing the charge dq be dW.
This work done gets stored in the form of potential energy P.E. in the capacitor.
Hence the small gain in P.E. is dW.
Potential Energy Of A capacitor
20. We know that work done is w=qV
substituting from the very 1st equation, we get,
Hence the total work done in the complete charging is given by the intergral.
Since the min and max values of q are 0 and Q, we take them as limits.
Potential Energy Of A Capacitor
21. Energy Stored in a Capacitor
Work has to be done to transfer charges onto a conductor, against the force of repulsion
from the already existing charges on it. This work is stored as a potential energy of the
electric field of the conductor.
The Capacitor’s Potential Energy. A capacitor C charged to a voltage V has charge
Potential Energy Of A Capacitor In A Electric Field
22. At an intermediate stage of charging let the voltage be v
During the charging process both v and q increase. Both start at zero. When the capacitor voltage v
reaches the applied voltage v= V, the charge reaches q=Q
At the intermediate stage, it takes effort (work) to “lift” an additional infinitesimal element of charge dq
from the negative plate to the positive plate, because the charge is being lifted through the potential v .
The work dw required to lift dq is:
The total work required to charge the capacitor from q=0 to q=Q is the infinite sum.
This is the potential energy stored in the capacitor.
Potential Energy Of A capacitor In A Electric Field
23. How Capacitors are connected?
Capacitors combination can be made in many ways. The combination is connected to a battery
to apply a potential difference (V) and charge the plates (Q). We can define the equivalent
capacitance of the combination between two points to be: C=V/Q
Two frequently used methods of combination are:
Combination Of Capacitors
24. Parallel Combination of Capacitors
When capacitors are connected in parallel, the potential difference V across each is the same and the charge
on C1, C2 is different i.e., Q1 and Q2.
The total charge is Q given as:
Equivalent capacitance between a and b is:
C = C1 + C2
Parallel Combination of Capacitors
25. The charges on capacitors is given as:
In case of more than two capacitors, C = C1 + C2 + C3 + C4 + C5 + …………
Parallel Combination of Capacitors
26. Series Combination of Capacitors
When capacitors are connected in series, the magnitude of charge Q on each capacitor is same. The
potential difference across C1 and C2 is different i.e., V1 and V2
Q = C1 V1 = C2 V2
The total potential difference across combination is:
V = V1 + V2
Series Combination of Capacitors
27. The ratio Q/V is called as the equivalent capacitance C between point a and b.
The equivalent capacitance C is given by:
The potential difference across C1 and C2 is V1 and V2 respectively, given as follows:
In case of more than two capacitors, the relation is:
Series Combination of Capacitors
28. Important Points:
If N identical capacitors of capacitance C are connected in series, then effective capacitance = C/N
If N identical capacitors of capacitance C are connected in parallel, then effective capacitance = CN
The most common use for capacitors is energy storage. Additional uses include power
conditioning, signal coupling or decoupling, electronic noise filtering, and remote sensing. Because of its
varied applications, capacitors are used in a wide range of industries and have become a vital part of
Uses Of Capacitors