To solve the question, we need to analyze the assertion (A) and the reason (R) provided in the question.
### Step-by-Step Solution:
1. **Understanding the Assertion (A)**:
- The assertion states that when a steady current flows through a conductor of non-uniform cross-section, the current density (J), electric field (E), and drift velocity (Vd) do not remain constant.
- This is true because, in a conductor with varying cross-sectional area, the current must adjust to maintain a constant flow. As the area changes, the parameters J, E, and Vd will also change.
**Hint**: Consider how current behaves in different cross-sectional areas.
2. **Understanding the Reason (R)**:
- The reason states that for a constant current, the current density (J), electric field (E), and drift velocity (Vd) are inversely proportional to the cross-sectional area (A).
- This can be derived from the equation for current (I = J * A) and the relationship between drift velocity and electric field (Vd = E * τ / m, where τ is the mean time between collisions and m is the mass of the charge carriers).
- From the equation J = I/A, we see that if I is constant, then J is inversely proportional to A. Similarly, since Vd = I/(n * e * A), Vd is also inversely proportional to A.
**Hint**: Recall the equations relating current, current density, and drift velocity.
3. **Conclusion**:
- Since both the assertion and reason are correct, and the reason provides a valid explanation for the assertion, we conclude that:
- Assertion (A) is correct.
- Reason (R) is correct and explains assertion (A).
4. **Final Answer**:
- Therefore, the correct option is that both A and R are correct, and R is the correct explanation of A.
### Summary of the Solution:
- The assertion is true because current density, electric field, and drift velocity change with varying cross-section.
- The reason is also true as it explains the relationship between these quantities and the cross-sectional area when current is constant.
