Which of the following is constant when a steady current flows through a metallic conductor of non-uniform cross-section:

Options

A. drift speed
B. current
C. current density
D. Resistivity

Explanation

To determine which quantity remains constant when a steady current flows through a metallic conductor of non-uniform cross-section, we can analyze the relevant equations and concepts in electrical circuits.

### Step-by-Step Solution:

1. **Understanding Current (I)**:
- The electric current (I) is defined as the rate of flow of charge. It is constant in a steady state, meaning that the total current entering a section of the conductor is equal to the total current leaving that section.
- **Hint**: Recall that in a closed circuit, charge conservation implies that the current remains constant.

2. **Analyzing Cross-Sectional Area (A)**:
- In a non-uniform conductor, the cross-sectional area (A) can vary along the length of the conductor. As the area changes, the current density (J) will also change.
- **Hint**: Remember that current density is defined as J = I/A, which indicates that if A changes, J must also change to maintain the constant current.

3. **Drift Speed (V_d)**:
- The drift speed (V_d) of charge carriers is related to the current (I) and the number density of charge carriers (n) as well as the charge of the carriers (e). The formula is given by:
\[ I = n \cdot e \cdot A \cdot V_d \]
- Since A varies, V_d must also vary to keep I constant.
- **Hint**: Consider how the drift speed is affected by changes in area and current density.

4. **Current Density (J)**:
- The current density (J) is defined as:
\[ J = \frac{I}{A} \]
- Since A changes in a non-uniform conductor, J will also change, meaning it is not constant.
- **Hint**: Think about how J is dependent on both I and A.

5. **Conclusion**:
- The only quantity that remains constant in a steady current through a metallic conductor of non-uniform cross-section is the current (I).
- Therefore, the answer to the question is that the current (I) is constant.

### Final Answer:
The quantity that remains constant when a steady current flows through a metallic conductor of non-uniform cross-section is the **current (I)**.