With increse in temperature, the conductivity of a conductor

Options

A. remains same
B. decreases
C. increases
D. may increase or decrease

Answer

To solve the question regarding the effect of temperature on the conductivity of a conductor, we can follow these steps:

### Step 1: Understand the Concept of Conductivity
Conductivity (\( \sigma \)) is a measure of a material's ability to conduct electric current. It is influenced by the number of charge carriers (like free electrons in metals) and their mobility.

**Hint:** Remember that conductivity is related to how easily charge carriers can move through a material.

### Step 2: Analyze the Effect of Temperature on Metals
In metals, conductivity is primarily due to the movement of free electrons. As the temperature increases, the metal ions vibrate more vigorously.

**Hint:** Consider how increased thermal energy affects the motion of particles in a conductor.

### Step 3: Determine the Impact on Resistance
As the temperature rises, the increased vibration of metal ions leads to more frequent collisions with the free electrons. This results in an increase in resistance (\( R \)) of the conductor.

**Hint:** Think about how collisions affect the flow of electrons and thus the overall resistance.

### Step 4: Relate Resistance to Resistivity
Resistance is directly proportional to resistivity (\( \rho \)). Therefore, if the resistance increases with temperature, the resistivity also increases.

**Hint:** Recall the relationship: \( R \propto \rho \).

### Step 5: Connect Resistivity to Conductivity
Conductivity is the reciprocal of resistivity, given by the formula:
\[ \sigma = \frac{1}{\rho} \]
If resistivity increases, then conductivity must decrease.

**Hint:** Remember the mathematical relationship between conductivity and resistivity.

### Step 6: Conclusion
With an increase in temperature, the conductivity of a conductor (specifically metals) decreases. Therefore, the correct answer to the question is that the conductivity of a conductor decreases with an increase in temperature.

**Final Answer:** The conductivity of a conductor decreases with an increase in temperature.