Electricity

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Electricity


There are two types of phenomenon related to charges
i.
Static electricity or electrostatics and
ii.
Current electricity.
Electrostatics:











Static electricity is the study of the charges which are at rest and their effects and
current electricity is the study of charges which are in motion.
Charge is the fundamental property of matter that exhibits electrostatic repulsion or
attraction.
Matter is generally made up of atoms, in atom there exist electrons which revolves
around the nucleus, and inside the nucleus there are protons and neutrons. Protons
and electrons are elementary charged particles.
Unit for charge is Coulombs. We represent it with letter C.
Protons has a mass of 1.6 x 10-27 kg and a charge of + 1.6 x 10-19 C
Electron has a mass of 9.1 x10-31kg and a charge of - 1.6 x 10-19 C
Usually when a body gains electrons, it becomes negatively charged. When it loses
electrons it becomes positively charged.
Whenever two bodies are charged by rubbing, one gets positively charged and the
other, negatively charged. The net charge on the two bodies, however, remains zerothe same as that before rubbing. In other words charge is conserved. It can neither
be created nor destroyed.

Charging a body:
Charging means gaining or losing of electrons. We can charge a body in different ways in
such a way that it will host a positive charge or a negative charge. The nature of charge and
polarity will depend on the process of charging.


Charging by friction: When you rub one material to another, they are charged by
friction. Material losing electron is positively charged and material gaining electron
is negatively charged. Amount of gained and lost electron is equal to each other.
Eg: Rubbing a glass rod with a silk cloth.



Charging by Contact: There are equal numbers of electrons and protons in a
neutral matter. If something changes this balance we can say it is charged.
Eg: Charging of a sphere by ebonite rod.



Charging by induction:Induction charging is a method used to charge an object
without actually touching the object to any other charged object.



Charging by conduction Charging by conduction involves the contact of a charged
object to a neutral object. The difference between charging by conduction and
contact is that, in the first case, the material must be a conductor whereas the later
need not be.
Eg: The charging of a neutral sphere by another charged sphere by conduction
of charge.

Properties of charge:
If the sizes of charged bodies are very small as compared to the distances between them,
we treat them as point charges. All the charge content of the body is assumed to be
concentrated at one point in space.
Additivity of charges:
If a system contains two point charges q1 and q2 , the total charge of the system is obtained
simply by adding algebraically q1

and q2 . i.e., charges add up like real numbers or they are

scalars like the mass of a body. But the difference is mass always exists in positive scale
whereas charge can be negative too.
If a system contains ‘n’ charges q1 , q2 , q3 ...qn then the total charge of the system is

Q  q1  q2  q3  .....  qn
Charge is conserved:
Within an isolated system consisting of many charged bodies, due to interactions among
the bodies, charges may get redistributed but it is found that the total charge of the isolated
system is always conserved. Conservation of charge has been established experimentally.
It is not possible to create or destroy net charge carried by any isolated system
although the charge carrying particles may be created or destroyed in a process.Sometimes
nature creates charged particles: a neutron turns into a proton and an electron. The proton

and electron thus created have equal and opposite charges and the total charge is zero
before and after the creation.
Quantization of charge:
All free charges are integral multiples of a basic unit of charge denoted by e.Thus charge
qon a body is always given by
Q = ne
where nis any integer, positive or negative.
This basic unit of charge is the charge that an electron or proton carries. By convention, the
charge on an electron is taken to be negative; therefore charge on an electron is written as
–e and that on a proton as +e. The value of this basic unit is 1.6 x 10-19 C
Solved Problems:
Q1. Find how many electrons are present in ONE coulomb of charge.
Solution: One electron contains - 1.6 x 10-19 C charge. Let ‘n’ electrons carries one coulomb
of charge.

 ne  1C
n

1C
1C

e 1.6  10 19

 n  6.6  1018 electrons

Coulomb’s law
The force of attraction or repulsion between two charges is given by Coulomb’s law.

Coulomb’s law state that the force of attraction or repulsion between two charges is
-

Directly proportional to the product of magnitudes of the charges,

F  Q1  Q2
-

Inversely proportional to the square of the distance between the two charges.

F

1
R2

By summing the above two conditions F 

Q1  Q2
R2

By applying a constant ‘K’

F

K1Q1Q2
Newtons
R2

Where Q1 ,Q2 are the charges; ‘K’ is proportionality constant;
‘R’ is the distance between the charges.
The constant ‘K’ is given by

1
= 9 x 109 Nm2C-2
4 0

where  0 is called as the permittivity of free space . The value of

0

0

in SI units is

= 8.854 × 10–12 C2N–1m–2

Solved Problems:
Q2. Two charges 10 C and 5 C are separated by a distance 2 m. Calculate the electrostatic
force between them.
Solution:

Given Q1 = 10 C and Q2 =5 C
Distance R = 2 m.
From the formula: F 

F

KQ1Q2
R2

K (10  5)
22

 F  12.5K

Q3. If the distance is doubled between two charges, find the new electrostatic force
between them.
Solution: Let the force of attraction between the two charges is F1.
Let the new distance is R2 = 2R1

 F2 

KQ1Q2
R22

 F2 

KQ1Q2
4 R12

 F2 

F1
4

Forces Between Multiple Charges:
Force on any charge due to a number of other charges is the vector sum of all the forces on
that charge due to the other charges, taken one at a time. The individual forces are
unaffected due to the presence of other charges. This is termed as the principle of
superposition.

Conductors and Insulators:
Current electricity is the study of charges in motion. Based on the motion of charge, the
materials are said to be Conductors and Insulators.
Conductors
 The substances which conduct electricity easily are called electric conductors.
 Conductors have large number of free electrons
 All metal are generally good conductors.
Insulators
 The substances which do not conduct electricity
 Wood, rubber, mica insulators do not have free electrons.

Electric field:
This is the area in which the force of influence of an electric charge is present.
Consider a charge ‘Q’ due to which a test charge ‘q’ (test charge is always assumed to be
positive in nature and unity magnitude) is experiencing a force ‘F’ when placed at a
distance ‘r’ in the vacuum
Then electric field due to charge ‘Q’ is defined as

E

F
q

From Coulomb’s law of electrostatics, the force is expressed as F 

E

E 

KQq
r2

kQ
r2

1 Q

4 0 r 2

Where rˆ is a unit vector

Electric field is a vector quantity. The SI unit of electric field is N/C*
*Volt/meter also used as unit of electric field

Physical Significance of Electric Field:





Electric field is an elegant way of characterizing the electrical environment of a
system of charges.
Electric field at a point in the space around a system of charges tells the force on a
unit positive test charge experienceif placed at that point.
Electric field is a characteristic of the system of charges and is independent of the
test charge that is placed at a point to determine the field.
The term fieldin physics generally refers to a quantity that is defined at every point
in space and may vary from point to point. Electric field is a vector field, since force
is a vector quantity.

Lines Of Force Of Charge:
These are the imaginary lines, which show the path of a unit positive test charge placed in
an electric field.


When electric field is caused by a positive charge, the test charge will be repelled
and moves out of the field. If we draw a line along the path of the test charge, it will
be outward from the charge as shown below.



When electric field is caused by a negative charge, the test charge will be attracted
and moves towards the center. If we draw a line along the path of the test charge, it
will be towards the center as shown below.



Hence, we can conclude that
i) Field lines start from positive charges and end at negative charges. If there is a
single charge, they may start or end at infinity.
ii) Two field lines can never cross each other. (If they did, the field at the point of
intersection will not have a unique direction, which is absurd.)
iii) In a charge-free region, electric field lines can be taken to be continuous curves
without any breaks.
iv)Electric lines of force do not form any closed loops. This follows from the
conservative nature of electric field.

Electric Dipole:
An electric dipole is a pair of equal and opposite point charges q and –q, separated by a
distance 2l.By convention, the direction from –q to q is said to be the direction of the dipole.
The total charge of the electric dipole is obviously zero.This does not mean that the field of
the electric dipole is zero.Since the charge q and –q are separated by some distance, the
electric fields due to them, when added, do not exactly cancel out.

Dipole moment:
The dipole moment of an electric dipole is defined as the product of magnitude of charge ‘q’
and the distance of separation ‘2l’. This is a vector quantity.

p  (q  2l ) pˆ

Electric Current

The rate of flow of charges is defined as electric current.It is denoted by ‘I’.If “Q” is the net
charge passing through any cross section of a conductor in a time “t”, then

I

Q
t

If the net charge is made up of say ‘n’ electrons, then I 

ne
t

Current is a scalar quantity. S.I. unit of current is ampere (A).
One ampere:
The current passing through a conductor is said to be one ampere if the net flow of charge
is one coulomb in second through its cross section.
I

Q ne

t
t

n- Number of charge carriers,
e = magnitude of charge of an electron.
Standard definition of ampere:
If two infinite long parallel conductors are separated by onemeter distance in vacuum, then
if the force of attraction or repulsion due to flow of current is 2 x 10-7 N then the current
flowing through the conductors is said to be 1 ampere.
Electric current is measured by Ammeter. This instrument is always used in series with in a
circuit. Internal resistance of an ideal ammeter is zero.
Solved Problems:
Q4. A current of 10 A flows through a conductor for two minutes. Calculate the amount of
charge.
Solution: Given Current (I) = 10 A;
Time (t) =2 minutes = 120 seconds.

From the formula: I 

Q
t

 Q  It

= 10 x 120
 Q  1200C

Electric Potential:
Imagine a situation, where a unit charge to be moved from infinity to a point inside an
electric field. To perform this action, some work supposed to be done against the force of
attraction/repulsion by the field.
The amount work done to bring unit positive test charge from infinity to a point in the
electric field is defined as the electric potential at that point.



Usually, we don’t define the absolute potential at a point but potential difference
between two points in an electric field.
It is denoted by V

V 


W
q

If VoA and VOB are the potentials at points A and B in an electric field, then
Potential difference between A and B is given by
VAB  VOB  VOA




Units: The units of electric potential are Volts.
1 volt = 1 Joule/1coulomb
Electric potential is measured by Voltmeter. This is always used in shunt.(parallel)
The resistance of an ideal voltmeter is infinity.

Solved Problems
Q5. A and B are two points in a circuit. When a charge of 3 C passes from A to B, the work
done is 18 J. Calculate the potential difference between A and B.
Solution: Given W = 18 J and Q = 3 C.
From the formula: V 

V 

18
 6V
3

W
Q

Potential Energy Due To Single Charge:
Consider a point charge ‘Q’ at the origin. For definiteness, take ‘Q’ to be positive.Let the
potential at any point ‘P’ with position vector ‘r’ from the origin is to be determined. For
that we must calculate the work done in bringing a unit positive test charge from infinity to
the point P.

For Q > 0, the work done against the repulsive force on the test charge is positive.Since
work done is independent of the path, we choose a convenient path along the radial
direction from infinity to the point P.
The work done is defined as  w = F. r '
Here the force can be calculated from the Coulomb’s law.
The total work done is obtained by integrating the above equation between the limits

r   to r  r '
By solving the expression for work done and substituting it in V 

W
, we have the
Q

following expression for electric potential.

V (r ) 

1 Q
4 0 r

Electric Circuit:
An electric circuit can be defined as the path of charge (usually electrons) from a voltage
source or current source. This path is always a closed loop. The different electronic
components are represented by various symbols in the electric circuit. Some of them are
shown below.

Ohm’s law:
According to this law, at constant temperature the current passing through a conductor (i)
is proportional to the voltage (V) applied to it.
Mathematically

V i
V  iR

where R is a constant of the conductor, called as Resistance.
Resistance is the property of a material which opposes the flow of electric current. Its S.I
units are Ohms.

Mathematically R 


V
and
i

1 Ohm =

1Volt
1amp

The reciprocal of resistance is called conductance.The units of conductance are Mho.

Factors affecting the resistance of a material:


Resistance is proportional to length of the wire.



Resistance is inversely proportional to cross-sectional-area of the wire.
Resistance depends on the material the wire is made of.
Resistance increases with the temperature of the wire.




Relation between Resistance, Length & Area of cross section:





Usually the resistance of a material depends on its geometrical parameters like its
length, area of cross section etc. So for an element, resistance is variable. Hence
another parameter called as “resistivity” is defined.
Resistance of a material is directly proportional to its length and inversely
proportional to its area of cross section.
l
R
Hence
a

R 

l
a

where  is the resistivity of the material

For a given material, the resistivity is constant and the resistance will vary based on its
geometry. The units of resistivity are Ohm-meter
Some of the materials with their resistivity values are given below



The reciprocal of resistivity gives the conductivity of a material.
1
 

Conductivity has the units Mho/meter

Limitations of Ohm’s Law:


Ohm’s law is valid at constant temperature.However, even at constant temperature,
some materials do not obey Ohm’s law, these materials are called as Non-ohmic
materials. The other materials which obeys the law are called Ohmic materials.



At the variable temperature, this law doesn’t obeyed by the materials.

Resistance of a system of Resistors:


In an electric circuit, the electronic components can be connected in two ways
mainly.
i) Series.
ii) Parallel.

A circuit composed solely of components connected in series is known as a series.
i.e., the components are connected in a single path or end to end. In parallel circuits,
the components are connected parallel.

An example of series and parallel circuits is shown below using resistors.

System of Resistors:
The resistors can be used in either series or parallel combination.
Resistors in Series:
When resistors are connected in series, the current in the circuit is constant and the
potential across the resistors will vary, based on the resistance value.
Let three resistors are connected in series as shown below.

If a source of voltage ‘V’ is connected to the circuit, then
V  V1  V2  V3
From Ohm’s law
IR  IR1  IR2  IR3
 IR  I ( R1  R2  R3 )
 R  ( R1  R2  R3 )
Hence when resistors are connected in series, the resultant resistance is the sum of the
individual resistance.
Resistors in Parallel:
Let three resistors are connected in parallel as shown in figure.

From Kirchoff’s current law:
I  I1  I 2  I 3
From Ohm’s law

V V V V
  
R R1 R2 R3


1
1 1
1
  
R R1 R2 R3

(Potential is constant in parallel circuit.)

The same can be extended for ‘n’ resistors either in series or parallel.

Electric Power:
The power of a device is defined as the product of its rated voltage and current.
i.e.,

P=VxI

Units: Watt, horse power,Watt hour, KWH
From Ohm’s law: V = IR
 P  I 2R

Also, I = V/R  P 

V2
R

Solved Problems
Q6. A conductor has a resistance of 10 Ohms resistance. If the applied voltage is 50 Volts,
find the current passing through it.
Solution: Given R = 10 Ohms; V = 50 V
From Ohms law:

I

V
50
=
= 5A
R 10

Q7. An electric heater rated as 240 V and 6 A. Find its power consumption.
Solution: Given P = 240 V and I = 6 A.
Power P = V x I = 240 x 6 = 1440 Watt.

Heating effects of Current:
When current is passing through a conductor, it generates heat. The amount of heat
generated due a current “I” is given by
Q  I 2 Rt
where R is the resistance of the material measured in Ohms.
t is the time measured in seconds.
It is said that, 1 J heat is generated, provided the current passed is 1A through a conductor
of resistance 1Ohm for 1 second time.

Practical Applications of Heating Effect of Electric Current
The heating effect occurs in the circuits because the electrons collide with atoms as they
pass through a conductor. The electrons lose energy. The atoms gain energy and vibrate
faster. Faster vibrations mean a higher temperature. Heating effect of electric current has
many useful applications.
 The electric laundry iron, electric toaster, electric oven, electric kettle and electric
heater
 The electric heating is used to produce light from an electrical lamp. The filament
retains as much of the heat generated, so that it gets very hot and emits light
 Fuse is used in electric circuits to protect the appliances by stopping the flow of high
electric current.

Temperature Dependence Of Resistivity:
The resistance of a material depends on many factors, one of the most important being the
temperature. For many materials, such as conductors, the relationship between T and R is
fairly linear over a wide range of temperatures. It can be written:

R = Ro [1+α (T − To)]
where α is the temperature coefficient of resistivity of the material.
To is the reference temperature (i.e. room temperature)
Ro is the resistance at To
Usually, for conductors, the resistance decreases with decrease in temperature and for
semiconductors, resistance decreases with increase in temperature.
Hence conductors have the positive temperature coefficient of resistance and semiconductors have negative temperature coefficient of resistance.

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