Question

Choose the correct option with respect to the statements A and B.

• A. : When no electric field is applied across a conductor, the path of free electrons between two successive collisions in it is straight.
• B. : When an electric field is applied across a conductor, the drift velocity of electrons is independent of time.
• C. A and B are true
• D. A is true and B is false

Hint:

In conductors, free electrons follow straight paths between collisions without an electric field, and with a field, their steady-state drift velocity becomes constant after a brief transient period.

Answer 1

The Correct Option is A

Step 1: Evaluate statement A.
Statement A claims that when no electric field is applied across a conductor, the path of free electrons between two successive collisions is straight. Without an electric field, free electrons in a conductor undergo random thermal motion. Between collisions with lattice ions, there are no external forces (neglecting magnetic fields or other influences). Thus, their motion follows Newton’s first law, and the path is straight. Statement A is true.
Step 2: Evaluate statement B.
Statement B claims that when an electric field is applied across a conductor, the drift velocity of electrons is independent of time. When an electric field \( E \) is applied, electrons experience a force \( F = -eE \), causing an acceleration \( a = \frac{-eE}{m} \). Without collisions, the velocity would increase linearly with time. However, in a conductor, electrons collide with lattice ions, leading to a steady-state drift velocity \( v_d = \frac{eE\tau}{m} \), where \( \tau \) is the average time between collisions. This steady-state is reached after a short transient period (typically \( 10^{-14} \) seconds). In most physics problems, “drift velocity” refers to this steady-state value, which is constant and thus independent of time after the transient. Given the context of the correct answer, the statement likely assumes steady-state conditions, making statement B true. Final Answer: Both A and B are true, so the correct option is \( \boxed{\text{1}} \).