COMEDK 2024 Shift 1 Paper

Let's analyze why the resistance of a conductor increases with the increase in temperature.
A conductor has free electrons that move through the material, and this movement constitutes electric current. The resistance of a conductor is determined by how easily these electrons can move through the material. The key factors influencing this movement are electron density, relaxation time, and the collision frequency of electrons with atoms.
Now, let's consider each of the options:
Option A: Electron density decreases
This is incorrect because the electron density in a conductor is not significantly affected by temperature. The number of free electrons available for conduction stays relatively constant.
Option B: Relaxation time increases
This is also incorrect. Relaxation time refers to the average time between collisions of electrons. Generally, with an increase in temperature, the atoms in the conductor vibrate more vigorously and electrons experience more frequent collisions, thereby decreasing the relaxation time.
Option C: Number of collisions between electrons decreases
This is incorrect. With an increase in temperature, the number of collisions between electrons actually increases because the thermal agitation of atoms in the conductor becomes more intense.
Option D: Relaxation time decreases
This is correct. The relaxation time (τ) is the average time interval between successive collisions of an electron. As the temperature increases, the thermal energy causes more vigorous vibrations of the atoms in the lattice structure of the conductor. This leads to an increase in the collision rate of electrons with these vibrating atoms, which results in a decrease in relaxation time.
The resistance R of a conductor is given by the formula:
R=‌

m

ne2τ

where:
m= mass of an electron
n= number of free electrons per unit volume
e= charge of an electron
τ= relaxation time
From the above equation, you can see that resistance R is inversely proportional to the relaxation time τ. Therefore, as the relaxation time decreases with an increase in temperature, the resistance increases. Hence, the correct answer is:
Option D: Relaxation time decreases