Question

Which of the following characteristics of electrons determines the current in the conductor?

• A. Drift velocity only
• B. Thermal velocity only
• C. Both drift velocity and thermal velocity
• D. Neither drift nor thermal velocity

Hint:

Use I = n e A v_d. Thermal velocity is random and averages to zero, so only drift velocity decides the current.

Answer 1

The Correct Option is A

Step 1: Count the charge crossing a section:
Take a cross-section $A$ of a wire. In a time $\Delta t$, the electrons that cross it are those within a distance $v_d \Delta t$ of it, on the correct side.
The charge crossing is $\Delta Q = n e A v_d \Delta t$, so $I = \Delta Q/\Delta t = n e A v_d$.

Step 2: Look at what the formula contains:
Only the drift velocity $v_d$ appears. The thermal speed does not appear anywhere in the expression for the current.

Step 3: Why the random motion cancels:
At room temperature thermal speeds are about $10^{5}$ m/s, while drift speeds are only a few mm/s. Still, thermal motion points in all directions equally.
In any short time, as many electrons cross the section from the left as from the right, so the net charge carried is zero.

Step 4: Decide:
Only the drift velocity decides the current. Options (B), (C) and (D) are false, so the answer is option (A).

Final Answer:
Only the drift velocity appears in the current, because random thermal motion averages to zero. This is option (A). \[ \boxed{\text{(A) Drift velocity only}} \]