Assertion : Current is passed through a metallic wire, heating it red. Half of its portion is cooled by cold water jacket, then rest of the half portion become more hot.
Reason: Resistances decreases due to decrease in temperature and so current through wire increases.

Options

A. If both assertion and reason are true and reason is the correct explantion of assertion.
B. If both assertion and reason are true and reason is not the correct explantion of assertion.
C. If assertion is false but reason is true
D. If assertion is true but reason is false.

Explanation

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

### Step 1: Understand the Assertion
The assertion states that when a current passes through a metallic wire, it heats up and turns red. If half of the wire is cooled by a cold water jacket, the other half becomes hotter.

**Explanation:**
When current flows through a metallic wire, it encounters resistance, which generates heat due to the Joule heating effect. If half of the wire is cooled, the temperature of that portion decreases, which affects the overall resistance of the wire.

### Step 2: Analyze the Effect of Cooling
When the cold water jacket cools half of the wire, the resistance of that cooled portion decreases.

**Formula:**
The resistance \( R \) of a wire is given by:
\[ R = R_0 (1 + \alpha \Delta T) \]
where:
- \( R_0 \) is the original resistance,
- \( \alpha \) is the temperature coefficient of resistance,
- \( \Delta T \) is the change in temperature.

Since the cooled portion has a lower temperature, its resistance decreases.

### Step 3: Current Distribution
With the decrease in resistance in the cooled portion, the total resistance of the wire changes.

**Current Relation:**
Ohm's law states that \( I = \frac{V}{R} \). If the resistance decreases, the current through that portion of the wire increases.

### Step 4: Heating of the Other Half
As the cooled portion's resistance decreases, more current flows through the remaining heated portion of the wire.

**Conclusion:**
This increased current in the heated portion leads to more heat generation in that part, causing it to become even hotter.

### Step 5: Analyze the Reason
The reason states that resistance decreases due to a decrease in temperature, which leads to an increase in current through the wire.

**Explanation:**
This is consistent with the assertion. As the temperature of the cooled portion decreases, its resistance decreases, leading to an increase in current.

### Final Conclusion
Both the assertion and the reason are correct. The assertion correctly describes the physical situation, and the reason correctly explains why the assertion occurs.