Question

Specific resistance of a conductor increases with –
A) Increase in temperature.
B) Increase in cross section area.
C) Increase in cross section area and decrease in length.
D) Decrease in cross section area.

Answer 1

Hint: We need to understand the quantity which is defined as specific resistance in order to understand its relation between the other physical parameters such as the length of the wire and the cross-sectional area of the wire, the temperature and so on.

Complete answer:
We know that resistance is the property of a material which resists the flow of current through it. The resistance which plays the constant of proportionality in the Ohmic relation for resistors is proportional to the length of the wire and inversely proportional to the area of cross section of the wire as –
\[R=\rho \dfrac{l}{A}\]
Where, the constant of proportionality, \[\rho \]is the resistivity or the specific resistance of the material.
The specific resistivity is defined as the resistance of a material per unit length of the material. The resistivity is a characteristic property of a material and is independent of the physical dimensions such as length and cross section area of a wire or piece of resistor.
From the detailed study on the mobility of electrons in an ohmic resistance, we know that the resistivity is given by the relation –
\[\rho =\dfrac{m}{n{{e}^{2}}\tau }\]
Where m is the mass of an electron, \[\tau \] is the relaxation time, n is the number of electrons and e is the electronic charge.
The relaxation time is directly proportional to the temperature of the system. So, the resistivity is also temperature dependent.
We understand that the temperature and material are the only factors on which the specific resistivity is dependent.

The correct answer is option A.

Note:
The relaxation time is defined as the time interval between two successive collisions of an electron with an atom in the resistor. As the temperature increases, the electrons move faster, the collision frequency increases and therefore lesser relaxation time.