A constant potential difference is applied across a metal wire. Let the average thermal velocity of electrons in the wire be `v_t` and let the drift velocity be `v_d` . As the temperature of the wire rises:

Options

A. Both `v_t` and `v_d` increase
B. Both `v_t` and `v_d` deccrease
C. `v_t` increases and `v_d` decreases
D. `v_t` increases and `v_d` decreases

Explanation

To solve the problem, we need to analyze the effects of increasing temperature on the average thermal velocity of electrons (`v_t`) and the drift velocity (`v_d`) in a metal wire under a constant potential difference.

### Step-by-Step Solution:

1. **Understanding Drift Velocity (`v_d`)**:
- The drift velocity of electrons in a conductor is given by the formula:
\[
v_d = \frac{I}{nqA}
...