When a potential difference is applied across a copper wire, the drift velocity of the electrons is v. If the same potential difference is applied across another copper wire of the same length but twice the diameter, the drift velocity of electrons will be

v

The correct answer is Option (3) → v

Drift velocity in a wire: $v_d = \frac{I}{n e A}$

Current in the wire: $I = \frac{V}{R}$, and resistance $R = \rho \frac{L}{A}$

So, $v_d = \frac{I}{n e A} = \frac{V}{R n e A} = \frac{V}{(\rho L / A) n e A} = \frac{V}{\rho L n e}$

Observation: $v_d$ is independent of cross-sectional area $A$ if same material, same length, and same applied voltage.

∴ For a copper wire of same length and same potential difference, but twice the diameter, the drift velocity remains v