Assertion: Resistivity of a metal conductor increases with the increase in temperature.
Reason: When the temperature of a conductor is increased then the number of free electrons per unit volumic increases.

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion
B. If both assertion and reason are correct but reason is not the correct explanation of the assertion
C. If assertion is correct but reason is incorrect
D. If assertion is incorrect but reason is correct

Answer

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

### Step 1: Understand the Assertion
The assertion states that the resistivity of a metal conductor increases with an increase in temperature. This is a well-established principle in physics. As temperature rises, the atoms in the metal vibrate more vigorously, which leads to more frequent collisions between the conduction electrons and the vibrating atoms.

**Hint:** Consider how temperature affects atomic vibrations and electron movement in a conductor.

### Step 2: Analyze the Reason
The reason given is that when the temperature of a conductor is increased, the number of free electrons per unit volume increases. This statement is not correct for most metals. In metals, the number of free electrons (n) remains relatively constant with temperature changes. Instead, what actually happens is that the kinetic energy of the existing free electrons increases, leading to more frequent collisions.

**Hint:** Think about the nature of free electrons in metals and how their density is affected by temperature.

### Step 3: Relate Assertion and Reason
Now, we relate the assertion and the reason. The assertion is correct because resistivity increases with temperature due to increased atomic vibrations and more frequent electron collisions. However, the reason is incorrect because the number of free electrons does not increase with temperature in metals.

**Hint:** Reflect on how the behavior of electrons changes with temperature and how this impacts resistivity.

### Step 4: Conclusion
Based on the analysis, we conclude that the assertion is correct while the reason is incorrect. Therefore, the correct answer to the question is that the assertion is true and the reason is false.

**Final Answer:** Assertion is correct, but the reason is incorrect (C part is the answer).