Question

$\text{Statement-}1:$ Conductivity of a metallic conductor decreases with increase in temperature.
$\text{Statement-}2:$ On increasing temperature the number of free electrons in the metallic conductor decreases.

• A. $\text{Statement-}1$ is true, $\text{Statement-}2$ is true; $\text{Statement-}2$ is NOT a correct explanation for $\text{Statement-}1$
• B. $\text{Statement-}1$ is false, $\text{Statement-}2$ is true
• C. $\text{Statement-}1$ is true, $\text{Statement-}2$ is false
• D. $\text{Statement-}1$ is true, $\text{Statement-}2$ is true; $\text{Statement-}2$ is a correct explanation for $\text{Statement-}1$

Answer 1

The correct option is C $\text{Statement-}1$ is true, $\text{Statement-}2$ is false

For conductor, we know that resistivity $\left(\rho \right)$ increases with temperature

$\Rightarrow T\uparrow \rho \uparrow$

$\therefore \sigma =\frac{1}{\rho }\downarrow$

Resistance of the metallic wire increases with rise in temperature. If resistance increases conductivity decreases.
So, $\text{Statement-}1$ is true.

Number of free electrons in metals is not dependent on change in temperature.
Thus, $\text{Statement-}2$ is false.

Note : $\rho =\frac{2m}{n{e}^2\tau }=\frac{1}{\sigma }$ $\sigma$ is called conductivity and $\rho$ is conductivity. As temperature increases relaxation time $\tau$ decreases. Resistivity increases and conductivity decreases.