Question

The relaxation time in conductors
A. Increase with the increase of temperature
B. Decrease with the increase of temperature
C. It does not depend on temperature
D. All of sudden change at 400 K

Answer 1

Hint: First start with finding the relation between the temperature and relaxation time in case of conductors. Then try to find what changes occur in conductors when the temperature increases or decreases. Whether the relaxation time in case of conductors depends on the temperature or not.

Formula used:
1. Resistance, $R = \rho \dfrac{l}{A}$
Where, $\rho $ is resistivity, A is the area of the given conductor and l is the length of the wire.
2. Relaxation time, $\tau \propto \dfrac{1}{\rho }$

Complete step by step solution:
In the case of a conductor we know that; conductor contains free electrons that help in conduction of electricity. When the temperature of the conductor rises, atoms start vibrating more frequently which causes an increase in the number of collisions of atoms.

Therefore, this increases resistance to the movement of electrons present in the atoms which are colliding. Now, from the formula of resistance we know that;
$R = \rho \dfrac{l}{A}$
Which implies,
$R \propto \rho $
So, both the quantities are directly proportional to each other. It means when temperature increases, resistance increases and hence the resistivity will also increase.

Now we know that, relaxation time is given by:
$\tau \propto \dfrac{1}{\rho }$
As relaxation time and resistivity are inversely proportional to each other as we can see from the formula. Therefore, when resistivity increases then the relaxation time will decrease for conductors for increase in temperature.

Hence, the correct answer is option B.

Note: Here the case of conductors was given so we know that electron density increases in conductors on increase in temperature which causes resistivity increase but it is not the case when semi-conductors or insulators are used in place of the conductors. Relaxation time here depended on temperature.