Question

The drift velocity of electrons for a conductor connected in an electrical circuit is $V _{ d }$ The conductor in 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

• A. $\frac{V_{ d }}{4}$
• B. $\frac{ V _{ d }}{2}$
• C. $2 V _{ d }$
• D. $V _{ d }$

Hint:

Drift velocity is independent of the cross-sectional area of the conductor. It depends on the electric field and the relaxation time.

Answer 1

The Correct Option is D

The drift velocity \( V_d \) is given by the formula:

\[ V_d = \frac{eE\tau}{m} \]

where \( e \) is the charge of the electron, \( E \) is the electric field, \( \tau \) is the relaxation time, and \( m \) is the mass of the electron. The drift velocity is independent of the area of cross-section of the conductor. Therefore, the new drift velocity will remain the same as \( V_d \).