The drift velocity of electrons for a conductor connected in an electrical circuit is $$V_d$$. The conductor is now replaced by another conductor with same material and same length but double the area of cross-section. The applied voltage remains same. The new drift velocity of electrons will be

The drift velocity is given by:

$$ V_d = \frac{eE\tau}{m} $$

where $$E = \frac{V}{L}$$ is the electric field, $$\tau$$ is the relaxation time, and $$m$$ is the electron mass.

When the conductor is replaced by one with the same material and same length but double the cross-section area:

- The voltage $$V$$ and length $$L$$ remain the same, so the electric field $$E = V/L$$ is unchanged.

- The relaxation time $$\tau$$ depends only on the material, which is the same.

Therefore, the drift velocity formula gives the same value:

$$ V_d' = \frac{eE\tau}{m} = V_d $$

The new drift velocity remains $$V_d$$.

Note: While the resistance decreases (halves) and the current increases (doubles), the drift velocity depends on the electric field (not current), which remains unchanged.