Electricity
In this Chapter...
!
Ohm’s Law
!
Resistance
!
Combination of Resistors
!
Heating Effect of Electric Current
! Electric Power
Electricity is one of the most convenient and widely used
V-I Graph
forms of energy in today’s world. It is a controllable and
The graph between the potential difference V and the
convenient form of energy.
corresponding current I is found to be a straight line passing
through the origin for ohmic (metallic) conductors.
Ohm’s Law
Y
It gives a relationship between current I, flowing in a
metallic wire and potential difference V, across its terminals.
A
According to this law, the electric current flowing through a
conductor is directly proportional to the potential difference
applied across its ends, providing the physical conditions
(such as temperature) remain unchanged.
θ
If V is the potential difference applied across the ends of a
X
O Current, I
conductor through which current I flows, then according to
Ohm’s law,
V-I graph for metallic conductor
V∝I
[at constant temperature]
Resistance
or
V = IR
It is that property of a conductor by virtue of which it
or
I= V
opposes/resists the flow of charges/current through it. Its SI
R
unit is ohm and it is represented by Ω.
where, R is the constant of proportionality called resistance of
V
Resistance of a conductor is given by, R
=
the conductor at a given temperature.
I
The conductors which obey Ohm’s law are called ohmic
It is said to be 1 ohm, if a potential difference of 1 volt across
conductors while the conductors which do not obey Ohm’s
the ends of the conductor makes a current of 1 ampere to flow
law are called non-ohmic conductors.
through it.
1 volt
i.e.
1 ohm =
Combination of Resistors
1 ampere
There are two methods of joining the resistors together which
1V
⇒
1Ω=
=
1 VA-1
are as given below.
1A
1. Series Combination
Factors on which the Resistance of a
When two or more resistors are connected end to end to each
Conductor Depends
other, then they are said to be connected in series.
V1
V2
V3
The electrical resistance of a conductor depends on the
R1
R2
R3
following factors
(i) Length of the Conductor The resistance of a conductor
I
V
+
R is directly proportional to its length l.
+
–
I
A
i.e.
R∝l
…(i)
–
(ii) Area of Cross-section of the Conductor The resistance
+ -
of a conductor R is inversely proportional to its area of
K
V
cross-section A .
The equivalent resistance is equal to the sum of the all
1
i.e.
R∝
…(ii)
individual resistances.
A
i.e.,
R=R
1
+R
2
+R
3
(iii) Nature of the Material of the Conductor The resistance
The equivalent resistance is thus greater than the resistances
of a conductor depends on the nature of the material of
of either resistor. This is also known as maximum effective
which it is made. Some materials have low resistance,
resistance.
whereas others have high resistance.
The current through each resistor is same. The potential
Therefore, from Eqs. (i) and (ii), we can write
difference across each resistor is different.
l
R∝ l
or R
=ρ
A
A
2. Parallel Combination
where, ρ is the constant of proportionality and is called
When two or more resistors are connected simultaneously
electric resistivity or specific resistance of the material
between two points to each other, then they are said to be
of the conductor.
connected in parallel combination.
R1
Resistivity
I1
R2
It is defined as the resistance of a conductor of unit length and
I2
R3
unit area of cross-section. Its SI unit is ohm-metre (Ω-m).
I3
I
● The resistivity of a material does not depend on its length
+
I
V
or thickness but depends on the nature of the substance
+
-
A
-
and temperature. It is a characteristic property of the
material of the conductor and varies only, if its
+
-
temperature changes.
K
V
● Insulators such as glass, rubber, ebonite, etc., have a very
The reciprocal of equivalent resistance is equal to the sum of
12
17
high resistivity (10
to10
Ω -m), while conductors have a
the reciprocal of individual resistances.
−8
−6
very low resistivity (10
to10
Ω-m).
1
1
1
1
i.e.
=
+
+
● Alloys have higher resistivity than that of their constituent
R R
R
R
1
2
3
metals. They do not oxidise easily at high temperatures,
The equivalent resistance is less than the resistance of
this is why they are used to make heating elements of
either resistor. This is also known as minimum effective
devices such as electric iron, heaters, etc.
resistance.
● Tungsten is almost used exclusively for filaments of
The current from the source is greater than the current
electric bulbs, whereas copper and aluminium are
through either resistor. The potential difference across each
generally used for electrical transmission lines.
resistor is same.
The filament is thermally isolated and the bulb is filled with
Heating Effect of Electric Current
chemically inactive nitrogen and argon gas to prolong the life
When an electric current is passed through a high resistance
of filament.
wire like nichrome wire, then the wire becomes very hot and
produces heat.
2. Electric Fuse
In purely resistive circuits, the source of energy continuously
It is used as a safety device in household circuits. It protects
gets dissipated entirely in the form of heat. This is called the
the circuits, by stopping the flow of any unduly high electric
heating effect of current.
current. It is connected in series with the mains supply. It
This is obtained by the transformation of electrical energy
consists of an alloy of lead and tin which has appropriate
into heat energy. e.g. electric heater, electric iron, etc.
melting point.
2
Heat produced is expressed as, H = I
×R×t
When the current flowing through the circuit exceeds the safe
It is known as Joule’s law of heating.
limit, then the fuse wire melts and breaks the circuit. This
This law implies that heat produced in a resistor is
helps to protect the other circuit elements from heavy current.
Fuses are always rated for different current values such as 1 A,
(i) directly proportional to the square of current for a given
2 A, 5 A, 10 A, 15 A, etc.
resistance.
(ii) directly proportional to the resistance for a given current.
Electric Power
(iii) directly proportional to the time for which the current
It is defined as the amount of electric energy consumed in a
flows through the resistor.
circuit per unit time.
Practical Applications of Heating Effect of
Electric power is expressed as, P = VI
2
Electric Current
or
P= V
R
There are two applications of heating effect of electric
current which are given below
The SI unit of electric power is watt (W).
It is said to be 1 watt, if 1 ampere current flows through a
1. Electric Bulb
circuit having 1 volt potential difference.
It has a filament made of tungsten. So, most of the power
i.e.
1 watt = 1 volt × 1 ampere = 1 VA
consumed by this, is dissipated in the form of heat and some
part is converted into light because it has high resistivity and
Commercial unit of electrical energy is kilowatt-hour.
high melting point.
1 kWh = 3.6 × 106 J
