if E denotes electric field in a uniform conductor and `v_(d)` the corresponding drift velocity of free electrons in the conductor, then which of the following graph is correct

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the relationship between the electric field (E) in a uniform conductor and the drift velocity (v_d) of free electrons, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The drift velocity (v_d) of free electrons in a conductor is directly proportional to the electric field (E) applied across the conductor. This relationship can be expressed mathematically as:
\[ v_d \propto E \]

2. **Expressing the Proportionality**:
We can write the proportionality in a more formal way:
\[ v_d = kE \]
where \(k\) is a constant of proportionality that depends on the material and the number density of free electrons.

3. **Graphical Representation**:
Since \(v_d\) is directly proportional to \(E\), the graph of \(v_d\) versus \(E\) will be a straight line that passes through the origin. This indicates that when there is no electric field (E = 0), the drift velocity (v_d) is also zero.

4. **Identifying the Correct Graph**:
From the options provided, we need to identify the graph that shows a straight line passing through the origin. This will be the graph that correctly represents the relationship between drift velocity and electric field.

5. **Conclusion**:
Based on the analysis, the correct graph that represents the relationship between \(v_d\) and \(E\) is the one that is a straight line starting from the origin. Therefore, the correct answer is option A.