Question

The temperature of a conductor is increased. The product of resistivity and conductivity:

• A. increases
• B. decreases
• C. remains constant
• D. may increase or decrease

Answer 1

The correct option is C remains constant

The resistivity of a conductor is given by
$\rho =\frac{m}{n{e}^2\tau }$
where, m is mass of an electron, e is charge on electron, n is number of free electrons per unit volume in conductor and $\tau$ is relaxation time.
$\Rightarrow \rho \propto \frac{1}{\tau }$ .............(1)
Also, the conductivity is reciprocal of resistivity i.e.
$\sigma =\frac{1}{\rho }$ .................(2)
$\Rightarrow \sigma \propto \tau$ .............(3)............from (1) and (2)
When temperature increases relaxation time will decrease and hence, resistivity will increase and conductivity will decrease.
Hence, the product of resistivity and conductivity remains constant and it is unity.
$\rho \sigma =1$ ...............from (2) which is always a constant value. Hence correct option is C