Assertion : If a current is flowing through a conducting wire of non-uniform cross-section, drift speed and resistance both will increase at a section where cross-sectional area is less.
Reason : Current density at such sections is more where cross-sectional area is less.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true and Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that if a current is flowing through a conducting wire of non-uniform cross-section, the drift speed and resistance both will increase at a section where the cross-sectional area is less.
- **Drift Speed**: The drift speed (v_d) is given by the formula:
\[ v_d = \frac{I}{n \cdot e \cdot A} \]
where \(I\) is the current, \(n\) is the charge carrier density, \(e\) is the charge of an electron, and \(A\) is the cross-sectional area.
- From this formula, we can see that drift speed is inversely proportional to the cross-sectional area (A). Therefore, as A decreases, \(v_d\) increases.

2. **Understanding Resistance**:
- The resistance (R) of a wire is given by the formula:
\[ R = \frac{\rho \cdot L}{A} \]
where \(\rho\) is the resistivity of the material, \(L\) is the length of the wire, and \(A\) is the cross-sectional area.
- Similar to drift speed, resistance is also inversely proportional to the cross-sectional area (A). Thus, as A decreases, R increases.

3. **Conclusion from the Assertion**:
- Since both the drift speed and resistance increase at sections where the cross-sectional area is less, the assertion is **True**.

4. **Understanding the Reason**:
- The reason states that current density (J) at such sections is more where the cross-sectional area is less.
- Current density is defined as:
\[ J = \frac{I}{A} \]
- Since the current (I) is constant throughout the wire, if the area (A) decreases, the current density (J) must increase. Thus, the reason is also **True**.

5. **Evaluating the Relationship**:
- Although both the assertion and reason are true, the reason does not correctly explain the assertion. The assertion focuses on the increase of drift speed and resistance, while the reason discusses current density, which is a different concept.

### Final Answer:
- Both the assertion and reason are true, but the reason is not a correct explanation for the assertion. Therefore, the correct answer is **B**.