Assertion (A) : As temperature of wire increases, drift velocity of electrons decreases.
Reason (R ): As temperature increases, conductivity decreases.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not the correct explanation of A
C. A is true but R is false
D. A is false and R is also false

Explanation

To analyze the assertion and reason provided in the question, we will break down the concepts involved step by step.

### Step 1: Understand Drift Velocity
Drift velocity (\(v_d\)) is the average velocity that a charge carrier, such as an electron, attains due to an electric field. It is given by the formula:
\[ v_d = \frac{I}{n e A} \]
where:
- \(I\) = current,
- \(n\) = number density of charge carriers,
- \(e\) = charge of an electron,
- \(A\) = cross-sectional area of the wire.

### Step 2: Effect of Temperature on Drift Velocity
As the temperature of a wire increases, the thermal energy of the electrons also increases. This leads to more frequent collisions between the electrons and the lattice ions of the wire, which increases the resistance of the wire.

### Step 3: Relationship Between Temperature and Conductivity
The conductivity (\(\sigma\)) of a material is given by:
\[ \sigma = n e^2 \tau \]
where \(\tau\) is the relaxation time (the average time between collisions). As temperature increases, the relaxation time (\(\tau\)) decreases due to more frequent collisions, leading to a decrease in conductivity.

### Step 4: Conclusion on Assertion and Reason
From the above points, we can conclude:
- As temperature increases, the drift velocity (\(v_d\)) decreases because the increased collisions reduce the average velocity of the electrons.
- The conductivity decreases with an increase in temperature due to the decrease in relaxation time.

### Final Answer
Both the assertion (A) and reason (R) are correct:
- Assertion (A): As temperature of wire increases, drift velocity of electrons decreases. (True)
- Reason (R): As temperature increases, conductivity decreases. (True)

Thus, the correct option is that both the assertion and reason are correct.

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