Question

Temperature dependence of resistivity $\rho \left(T\right)$ of semiconductors, insulators and metals is significantly based on the following factors:

• A. (a) and (b) above.
• B. length of material can be a function of $T$.
  
• C. mass of carriers is a function of $T$..
  
• D. time interval between two successive collisions can depend on $T$.
  
• E. number of charge carriers can change with temperatur.e $T$.
  

Answer 1

The correct option is A (a) and (b) above.

Formula used: $\rho =\frac{m}{n{e}^2\tau }$

Given,

Resistivity is the intrinsic property of the substance and for metal is given by

$\rho =\frac{m}{n{e}^2\tau }$

As we increase temperature, average speed of the electrons (which act as the carriers of current) increases resulting in more frequent collisions. The average time of collisions 𝜏, thus decreases with temperature $\left(T\right)$.

In a metal, $n$ is not dependent on temperature to any appreciable extent and thus the decrease in the value of $\tau$ with rise in temperature causes $\rho$ to increase.

For insulators and semiconductors, however, $n$ increases with temperature. This increase more than compensates any decrease in $\tau$ in so that for such materials, $\rho$ decreases with temperature

Mass is constant at all temperatures and for short temperature changes, thermal expansion of solids is ignored.

Final Answer: (𝑎), (𝑏)