Calculate the drift speed developed in a metal wire when V potential difference is applied across length l of the wire. The number of free electrons per unit volume is n and conductivity of the material is `sigma`.

Explanation

To calculate the drift speed (v_d) developed in a metal wire when a potential difference (V) is applied across its length (l), we can use the relationship between current, charge, and drift speed. Here’s a step-by-step solution:

### Step 1: Understand the relationship between current, charge, and drift speed
The drift speed (v_d) of electrons in a conductor can be expressed in terms of the current (I), the number of charge carriers per unit volume (n), the charge of an electron (e), and the cross-sectional area (A) of the wire. The formula is given by:
\[ I = n \cdot e \cdot A \cdot v_d \]

### Step 2: Express current in terms of potential difference and resistance
According to Ohm's law, the current (I) flowing through a conductor is also related to the potential difference (V) and the resistance (R) of the wire:
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