Question

Temperature dependence of resistivity $\rho \left( T \right)$ of semiconductors, insulators and metals is significantly based on the following factors
(A) Number of charge carriers can change with temperature $T$
(B) Time interval between two successive collisions can depend on $T$
(C) Length of material can be a function of $T$
(D) Mass of carrier is a function of $T$

Answer 1

We are looking for the relation between resistivity, charge carrier and relaxation time. Also, the effect of resistivity on relaxation time. We use the resistivity formula:
$R = \rho \dfrac{l}{a}$
Here $R$ is the resistance
$\rho$ is the resistivity
$\dfrac{l}{a}$ is the ratio of length to cross sectional area.

Complete step by step answer
It is already known that resistivity depends on the mass of the charge carrier and relaxation time.
We know that resistivity $\left( \rho \right)$ depends on the mass of the charge-carrier $\left( m \right)$ , relaxation time $\left( \tau \right)$ . Length and mass cannot be a function of temperature as the mass of a body is constant everywhere. So discards answer (d) and length of body changes negligibly with temperature discards answer (c).
Also, on increasing temperature, relaxation time decreases due to rise in speed of change carriers. So, resistivity is a function of temperature.
So, we need to see from the above options, and select the correct value.
Thus, the correct answer is option A, B.

Additional Information
The resistivity of semiconductor decreases with increase in temperature as more electrons jump into conduction band increasing its conductivity. Resistivity depends on the temperature of the component. In metal conductors, when the temperature increases, the atoms in the metal vibrate more energetically. This hinders the flow of electrons, and resistivity increases.

Note
The resistivity of a material depends on its nature and the temperature of the conductor, but not on its shape and size. The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Resistance also depends on the material of the conductor. See resistivity. The resistance of a conductor, or circuit element, generally increases with increasing temperature. Resistivity is indirectly proportional to the temperature. In other words, as you increase the temperature of materials, their resistivity will decrease.