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