On increasing the temperature of a conductor, its resistance increases because

Options

A. relaxation time increases
B. electron density decreases
C. relaxation time decreases
D. relaxation time remains constant

Answer

To solve the question regarding why the resistance of a conductor increases with temperature, we can follow these steps:

### Step 1: Understand the relationship between resistance and temperature
The resistance \( R \) of a conductor can be expressed using the formula:
\[ R = \frac{m}{n e^2 \tau} \cdot \frac{L}{A} \]
where:
- \( m \) is the mass of the electron,
- \( n \) is the number of free electrons (electron density),
- \( e \) is the charge of an electron,
- \( \tau \) is the relaxation time,
- \( L \) is the length of the conductor,
- \( A \) is the cross-sectional area of the conductor.

### Step 2: Analyze the effect of temperature on relaxation time
As the temperature of the conductor increases, the atoms in the conductor vibrate more vigorously. This increased vibration leads to more frequent collisions between the conduction electrons and the vibrating atoms, which effectively reduces the relaxation time \( \tau \).

### Step 3: Relate relaxation time to resistance
Since \( R \) is inversely proportional to \( \tau \) (i.e., \( R \propto \frac{1}{\tau} \)), if \( \tau \) decreases due to an increase in temperature, the resistance \( R \) will increase.

### Step 4: Conclusion
Thus, the correct reason for the increase in resistance with temperature is that the relaxation time decreases as the temperature increases.

### Final Answer
The resistance of a conductor increases with temperature because the relaxation time decreases.

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