Drift Velocity

Step 1: Calculate the drift velocity ( ) of electrons.

The drift velocity is related to the current density ( ), number density of electrons ( ), and charge of an electron ( ) by the formula:

Current density , where is the current and is the cross-sectional area. So,

Step 2: Calculate the drift velocity using given values.

Step 3: Calculate the time ( ) taken to drift the length of the wire.

Time = Distance / Speed

The correct answer is (D) .

Given: Drift velocity = , Mobility =

Step-by-step Explanation:

Step 1: The relationship between drift velocity and current is given by: where,
= number density of electrons (constant for a material),
= electronic charge (constant),
= cross-sectional area (constant for a wire).

From this relation, if the current increases, clearly the drift velocity must also increase since all other parameters ( ) are constant.

Thus, increases as current increases.

Step 2: Mobility is defined as: where,
= Electric field inside the conductor.

Mobility depends only on the material properties and temperature, not on current. Since temperature is constant (as given), mobility remains constant.

Thus, the mobility remains the same.

Final conclusion: Drift velocity increases and mobility remains unchanged.

Correct Option: increases, remains the same