Assertion: Drift velocity of electrons is independent of time.
Reason: Electrons are accelerated in the presence of electric field.

Options

A. If both assertion and reason are true and reason is the correct explantion of assertion.
B. If both assertion and reason are true and reason is not the correct explantion of assertion.
C. If assertion is false but reason is true.
D. If assertion is true but reason is false.

Explanation

To analyze the given assertion and reason, we will break down the concepts of drift velocity, electric field, and the relationship between them.

### Step-by-Step Solution:

1. **Understanding Drift Velocity**:
- Drift velocity (\(v_d\)) is the average velocity that a charge carrier, such as an electron, attains due to an electric field in a conductor. It is given by the formula:
\[ v_d = \frac{I}{nqA} \]
where \(I\) is the current, \(n\) is the number density of charge carriers, \(q\) is the charge of the carrier, and \(A\) is the cross-sectional area of the conductor.

2. **Dependence on Time**:
- Drift velocity is influenced by the relaxation time (\(\tau\)), which is the average time between collisions of the electrons with the lattice ions in the conductor. The relationship can be expressed as:
\[ v_d = a \cdot \tau \]
where \(a\) is the acceleration of the electrons due to the electric field.

3. **Acceleration in Electric Field**:
- When an electric field (\(E\)) is applied, electrons experience a force given by:
\[ F = qE \]
This results in an acceleration (\(a\)) of the electrons:
\[ a = \frac{qE}{m} \]
where \(m\) is the mass of the electron.

4. **Conclusion on Assertion**:
- The assertion states that "drift velocity of electrons is independent of time." This is incorrect because drift velocity is directly proportional to the relaxation time (\(\tau\)), which is a measure of time. Therefore, the assertion is false.

5. **Conclusion on Reason**:
- The reason states that "electrons are accelerated in the presence of an electric field." This is true, as the electric field exerts a force on the electrons, causing them to accelerate. Thus, the reason is correct.

6. **Final Evaluation**:
- Since the assertion is incorrect and the reason is correct, we conclude that the assertion and reason are not related. Therefore, the correct answer is:
- Assertion (A) is incorrect.
- Reason (R) is correct.