When current passes through a conductor then its temperature increases due to heating effect. Which of the following quantities do change due to heating?

Options

A. Number density of free electrons
B. Conductivity
C. Drift speed
D. Resistance

Explanation

To solve the question regarding which quantities change due to heating when current passes through a conductor, we can analyze the effects of heating on various physical quantities involved in the conduction process.

### Step-by-Step Solution:

1. **Understanding the Heating Effect**:
When current flows through a conductor, it generates heat due to the resistance of the conductor. This heat causes the temperature of the conductor to rise.

**Hint**: Remember that the heat generated in a conductor due to current can be described by the formula \( Q = I^2 R t \).

2. **Effect on Temperature**:
As the temperature increases, the kinetic energy of the charge carriers (electrons) in the conductor also increases. This leads to more frequent collisions between the electrons and the lattice ions of the conductor.

**Hint**: Think about how temperature relates to the motion of particles in a conductor.

3. **Relaxation Time**:
The increased frequency of collisions means that the relaxation time (\( \tau \)), which is the average time between collisions, decreases. A decrease in relaxation time indicates that electrons are colliding more often.

**Hint**: Recall that relaxation time is inversely related to the frequency of collisions.

4. **Resistivity and Resistance**:
The resistivity (\( \rho \)) of the conductor is given by the equation \( \rho = m / (n e^2 \tau) \). Since \( \tau \) decreases with increasing temperature, the resistivity \( \rho \) must increase. Consequently, the resistance \( R \) of the conductor, which is given by \( R = \rho \frac{L}{A} \), also increases.

**Hint**: Consider how changes in resistivity affect the overall resistance of the conductor.

5. **Conductivity**:
Conductivity (\( \sigma \)) is the inverse of resistivity (\( \sigma = 1/\rho \)). Since resistivity increases, conductivity must decrease.

**Hint**: Remember that conductivity is a measure of how easily current can flow through a material.

6. **Drift Velocity**:
The drift velocity (\( v_d \)) of the electrons is given by the equation \( v_d = -\frac{eE\tau}{m} \). Since \( \tau \) decreases with increased temperature, the drift velocity will also change (specifically, it will increase).

**Hint**: Consider how the drift velocity is affected by both the electric field and the relaxation time.

7. **Number Density of Free Electrons**:
The number density of free electrons (\( n \)) in the conductor does not change with temperature. The number of free electrons remains constant; only their motion becomes more vigorous.

**Hint**: Think about the physical meaning of number density and how it relates to the material properties of the conductor.

### Conclusion:
From the analysis, we conclude that:
- The quantities that **change** due to heating are:
- Resistance (\( R \))
- Resistivity (\( \rho \))
- Conductivity (\( \sigma \))
- Drift Velocity (\( v_d \))

- The quantity that **does not change** due to heating is:
- Number Density of Free Electrons (\( n \))

### Final Answer:
The quantity that does not change due to heating is the **number density of free electrons**.