Across a metaalic conductor of non-uniform cross-section a constant potential difference is applied. The quantity which remains constant along the conductor is :

Options

A. current
B. drift velocity
C. electric field
D. current density

Explanation

To solve the problem, we need to analyze the behavior of a metallic conductor with a non-uniform cross-section when a constant potential difference is applied across it.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a metallic conductor with a non-uniform cross-section. This means that the area of the conductor changes along its length.

2. **Applying a Constant Potential Difference**:
- A constant potential difference (V) is applied across the conductor. This means that the voltage difference between the two ends of the conductor remains the same.

3. **Current in the Conductor**:
- The current (I) flowing through the conductor is defined as the charge (Q) flowing per unit time (t), i.e., \( I = \frac{Q}{t} \).
- According to the principle of conservation of charge, the amount of charge entering any section of the conductor must equal the amount of charge leaving that section in a given time interval.

4. **Current Continuity**:
- Since the charge is conserved, the current must remain constant throughout the conductor. This means that regardless of the changes in the cross-sectional area, the current flowing through any cross-section of the conductor is the same.

5. **Effect of Non-Uniform Cross-Section**:
- Although the cross-sectional area (A) changes, the current (I) remains constant. This is because if the area decreases, the drift velocity (V_d) must increase to maintain the same current, and vice versa.

6. **Conclusion**:
- The quantity that remains constant along the conductor is the **current (I)**.

### Final Answer:
The quantity which remains constant along the conductor is **current (I)**.