OHM'S LAW
The relationship between voltage across conductor and current through a conductor was first
discovered by German scientist George Simon Ohm . This relationship is called
Ohm's law and may be stated as under :
At constant temperature and same physical condition,
The current ( I ) flowing through a conductor is directly proportional to the
potential difference ( V ) across its ends .
i.e , I ∝ V or
V ∝ I
V / I = R
Where R is a constant of proportionality and is called
resistance of the conductor .
* If I-V graph is drawn between current ( I ) and applied
potential difference ( V ) of the
conductor , it will be a straight line passing through the origin.
* Slope of the graph gives the resistance of the conductor.
i.e. R =
tan θ (
θ is angle between I- axis and
straight line )
* Those conductors ( e.g. , metals ) which obey Ohm's law are
called Ohmic conductors .
* If the material is not ohmic , relation between V and I will
not be linear and R is not constant .
RESISTANCE OF A CONDUCTOR
* Resistance of a conductor is defined as the ratio of p.d.
applied across its ends to the resulting current through the conductor.
I.e. , V / I
= R
* S.I Unit of
Resistance is V/ A or
Ohm ( Ω ) .
* Resistance is opposition offered by the substance to the
flow of electric current .
This opposition occurs because atoms and molecules of
the substance obstruct the flow of charge carriers.
* Resistance is also called electric friction.
Question- Define 1 Ohm.
Ans- A conductor is said
to have a resistance of 1 Ohm if a p.d. of 1 V across its ends causes a current
of 1 A to flow through it .
Question- What is
International ohm ?
Ans- It is defined as the
resistance of 106.3 cm long mercury column of 1 mm² cross - sectional area and
mass 14.4521 g at 0 ° C .
Type of substance:
* Those substances which
offer very little opposition to the flow of electric current are called conductors . e.g. , metals such as silver , copper .
aluminium , etc.
* Those substances which offer very high opposition to the
flow of electric current are called insulators , e.g. , glass , rubber , mica ,
etc.
FACTORS UPON WHICH RESISTANCE DEPENDS
The resistance R of a conductor depends on following
factors-
( i ) is directly proportional to its length , i.e. , R ∝ L
( ii ) is inversely proportional to its area of cross section
, i.e. , R ∝ 1 / A
( iii ) depends upon the nature of the material
( iv ) changes with temperature .
Derive Resistance Formula
At constant temp-
R ∝ L / A
Or,
R = p L /A ( Resistance formula )
* Where p ( Greek letter ' Rho ' ) is a constant of
proportionality and is known as resistivity or specific resistance of the
conductor .
* Its value depends upon the nature of the material and
temperature .
Resistivity or Specific
Resistance
We know that ,
R = ρ L / A
If L = 1 m ; A
= 1 m² , then R = ρ
* Hence specific resistance ( or resistivity ) of a material
is the resistance offered by 1 m length of wire of the material having area of
cross section of 1 m² .
* Resistivity may be defined as the resistance between the
opposite faces of a metre cube of the material .
Types of Substance according to resistivity
* Resistivity of metals and alloys is very small . Therefore ,
these materials are good conductors of electric current .
* Resistivity of insulators is extremely large . As a result ,
these materials hardly conduct any current .
* Resistivity of semiconductors lies between conductors and insulators .
CONDUCTANCE
The reciprocal of resistance of a conductor is called
its conductance ( G ) .
If a conductor has resistance R. then its conductance
G is given by ;
G = 1 / R
* The SI unit of conductance is mho or
Siemen ( S )
Electrical conductivity
The reciprocal of resistivity of a conductor is called
its electrical conductivity .
* It is denoted by the symbol σ ( sigma ) .
* If a conductor has resistivity p . then its conductivity is
given by ;
σ = 1
/ ρ
Conductance , G = σ A/ L
* SI unit of electrical conductivity is Siemen /metre ( S/m )
.
CLASSIFICATION OF MATERIALS ON ELECTRICAL
CONDUCTIVITY
On the basis of electrical conductivity , the
materials are classified as
( i ) insulators , ( ii ) conductors and ( iii ) semiconductors
.
( i ) Insulators
Those materials whose electrical conductivity is
negligible are called insulators e.g. mica , glass , wood , rubber etc.
* There are practically no free electrons in an insulator .
For this reason , they are poor conductors of electric current as well as heat
.
( ii ) Conductors
Those materials whose electrical conductivity is very
high are called conductors e.g. copper , silver , aluminium etc.
* Metals are generally good conductors .
* There are a large number of free electrons in a conductor .
For this reason , they are good conductors of electric current as well as heat
.
( iii ) Semiconductors
Those materials whose electrical conductivity lies between
conductors and insulators are called semiconductors e.g. germanium , silicon
etc.
* When a small potential difference is applied across a
semiconductor , a very weak current flows through it .
* The conductivity of a semiconductor can be increased by
adding controlled amount of suitable impurities .
* Semiconductors are being widely used in the manufacture of a
variety of electronic devices .
VARIATION OF RESISTIVITY
Resistivity of a material , p = m / ne² t
Where, m = mass
of electron
n
= number of electron per unit volume
e= charge on electron
t
= Relaxation time
Since m and e are constants for a material , then p ∝ 1 / n t
Therefore , resistivity of the material depends upon
the following factors :
( i ) It is inversely proportional to the number of free electrons
per unit volume ( n ) of the material . Since the value of n depends upon the
nature of the material , the resistivity of a material depends upon the nature
of material and not on its dimensions .
( ii ) It is inversely proportional to the average relaxation time
( t ) . The value of t decreases with the increase in temperature and vice -
versa .
Resistivity Of material
1. Conductor - In case of Conductor , the
resistivity increases with the increase
in temperature and vice - versa .
Reason-
In most of the metals , the value of n does not change
with temperature. But On increasing temperature
, the amplitude of vibrations of the positive ions also increases .
Consequently , the relaxation time decreases . This in turn increases the value
of p .
2. Semiconductors - The resistivity of a
semiconductor decreases with the increase in temperature and vice - versa .
Reason-
* In case of semiconductors , the value of n ( i.e. , free
electron density ) is very small as compared to metals . When the temperature
of a semiconductor increases, the value of ‘ n’ increases and that of ‘ t ‘ decreases .
* But the increase in the value of n is greater than the
decrease in the value of t . The net result is that the resistivity of a
semiconductor decreases with the increase in temperature.
3. Insulators - The resistivity of an insulator decreases exponentially with
the rise in temperature .
Reason-
A temperature rise in insulators creates many more
free electrons than existed in the cooler state . Often this increase in the
number of free electrons more than offsets the interference to the drift
movement caused by the increased molecular activity . Hence the resistivity of
an insulator decreases with the increase in temperature and vice – versa.
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