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
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → v
The drift velocity is set by the electric field \( E \) inside the wire. With \( \tau \) the relaxation time,
\( \displaystyle v_{d} = \frac{eE\tau}{m} = \frac{e\tau}{m}\,\frac{V}{L} \)
For copper \( e \), \( \tau \) and \( m \) are fixed. The potential difference \( V \) and the length \( L \) are the same for both wires, so the field \( E = V/L \) is the same. The diameter does not appear, so the drift velocity is still \( v \).
A thicker wire carries a larger current (its resistance is smaller), but the extra current comes from the larger area, not from faster electrons.