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

Options

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

Explanation

To solve the question, 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 that has a non-uniform cross-section (meaning the area of the conductor changes along its length).
- A constant potential difference (V) is applied across the conductor.

2. **Ohm's Law**:
- According to Ohm's Law, the relationship between voltage (V), current (I), and resistance (R) is given by:
\[ V = I \cdot R \]
- Rearranging this gives us:
\[ I = \frac{V}{R} \]

3. **Resistance Calculation**:
- The resistance (R) of a conductor is given by the formula:
\[ R = \frac{\rho L}{A} \]
where \(\rho\) is the resistivity of the material, \(L\) is the length of the conductor, and \(A\) is the cross-sectional area.
- Since the cross-section is non-uniform, the area \(A\) will vary along the length of the conductor.

4. **Current Density**:
- The current density (J) is defined as:
\[ J = \frac{I}{A} \]
- Since the area \(A\) is not constant, the current density will also vary along the conductor.

5. **Current Flow**:
- Even though the cross-sectional area is changing, the total current (I) flowing through the conductor must remain constant. This is because the charge carriers (like electrons) that flow through the conductor do so at a constant rate when a constant potential difference is applied.
- Therefore, while the current density changes due to the varying cross-section, the total current remains the same throughout the conductor.

6. **Conclusion**:
- The quantity that remains constant along the conductor, despite the non-uniform cross-section, is the **current (I)**.

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

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