Question

For a given electric current the drift velocity of conduction electrons in a copper wire is v_d and their mobility is μ . When the current is increased at constant temperature

• A. v_d remains the same, μ increases
• B. v_d decreases, μ remains the same
• C. v_d remains the same, μ decreases
• D. v_d increases, μ remains the same

Answer 1

The Correct Option is D

Given: Drift velocity = \( v_d \), Mobility = \( \mu \) 

Step-by-step Explanation:

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

From this relation, if the current \( I \) increases, clearly the drift velocity \( v_d \) must also increase since all other parameters (\( n, e, A \)) are constant.

Thus, \( v_d \) increases as current increases.

Step 2: Mobility \( \mu \) is defined as: \[ \mu = \frac{v_d}{E} \] where,
\( E \) = Electric field inside the conductor.

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

Thus, the mobility \( \mu \) remains the same.

Final conclusion: Drift velocity \( v_d \) increases and mobility \( \mu \) remains unchanged.

Correct Option: \( v_d \) increases, \( \mu \) remains the same

Answer 2

The drift velocity \( v_d \) of conduction electrons in a wire is given by the relation: \[ v_d = \frac{I}{n A e} \] where:
 \( I \) is the electric current,
\( n \) is the number of free electrons per unit volume,
\( A \) is the cross-sectional area of the wire,
\( e \) is the charge of an electron.
When the current \( I \) is increased, at constant temperature, the drift velocity \( v_d \) increases. This is because the increase in current means a higher flow of electrons, resulting in a higher drift velocity. Also, the mobility \( \mu \) of the conduction electrons, defined as: \[ \mu = \frac{v_d}{E} \] where \( E \) is the electric field, typically remains constant with respect to the change in current at constant temperature, since it is a material property. Thus, when the current is increased:
The drift velocity \( v_d \) increases,
The mobility \( \mu \) remains the same.

\(\textbf{Correct Answer:}\) (D) \( v_d \) increases, \( \mu \) remains the same