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Resistance and Resistivity is considered one the most difficult concept.
49 Questions around this concept.
An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the lengths and radii of the wires are in the ratio of 4/3 and 2/3, then the ratio of the currents passing through the wire will be
The thermistors are usually made of
Resistance
The resistance is known as the property of substance by virtue of which it opposes the flow of current through it.
Formula-
For a conductor of resistivity having a length of a conductor= l
and Area of a crosssection of conductor= A
Then the resistance of a conductor is given as
Where Resistivity
Its S.I unit is or ohm
Its Dimensions is
Reciprocal of resistance is known as conductance.
Resistance of a conductor depends on the following factors
Length -
As
So Resistance of a conductor is directly proportional to its length
i.e.
Area of cross-section-
As
Resistance of a conductor is inversely proportional to its area of cross-section
i.e.
Material of the conductor-
As
And For a conductor, if n = No. of free electrons per unit volume in the conductor, = relaxation time then the resistance of conductor
Then
for different conductors n is different
And depends on n
So R is also different.
Temperature-
As
And
So
And as temperature increases decrease
So as the temperature increases resistance increases
Temperature-dependent resistance is given by
Resistance at temperature
Resistance at temperature
temperature coefficient of resistance
Where the value of is different at different temperatures
From Ohm's law
Where Electric Resistance
Ohmic Substance: The substance which obeys Ohm's law are known as Ohmic substance. I-V graph is linear and the slope gives conductance which is reciprocal of resistance
2. Non-ohmic substances
Those substances which don't obey Ohm's law are known as Non-ohmic or non-linear conductors.
For example gases, crystal rectifiers, etc.
3. Superconductor: For certain materials resistivity suddenly becomes zero below a certain temperature (critical temperature). The material in this state is called a superconductor.
In Superconductor, resistivity is zero
Resistivity or Specific Resistance
As
If l=1 m and A= 1 m^2
Then R=
Resistivity is numerically equal to the resistance of a substance having a unit area of cross-section and unit length.
Where m is the mass, n is the number of electrons per unit volume, e is the charge of electron and is the relaxation time
Then
S.I Unit - Ohm.m
Dimensions-
And as reciprocal of Resistivity is known as conductivity.
So the dimension of conductivity is
Resistivity is independent of the shape and size of the body as it is an intrinsic property of the substance.
The resistivity of a conductor depends on the following factors
Nature of the body-
As
for different conductors n is different
And depends on n
So is also different.
Temperature-dependent Resistivity :
: Resistivity at temperature T
: Resistivity at the temperature
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