Question

The relation between drift velocity \( v \) of free electrons in conductor and potential difference \( V \) between ends of conductor is

• A. proportional to \( V \)
• B. inversely proportional to \( V \)
• C. proportional to \( V^2 \)
• D. inversely proportional to \( V^2 \)

Hint:

Drift velocity in a conductor increases with the applied potential difference, following a direct proportionality as per Ohm's law.

Answer 1

The Correct Option is A

Step 1: Drift velocity and potential difference.
In electric conduction, the drift velocity \( v \) of free electrons in a conductor is directly proportional to the applied potential difference \( V \). This is a consequence of Ohm's law, which states that current \( I \) is proportional to the potential difference \( V \), and since current is related to drift velocity, the drift velocity follows the same relationship.
Step 2: Explanation of the relationship.
The drift velocity \( v \) is given by the formula \( v = \mu E \), where \( \mu \) is the mobility of the electrons and \( E \) is the electric field, which is related to the potential difference by \( E = \frac{V}{L} \), where \( L \) is the length of the conductor. Hence, \( v \) is proportional to \( V \).
Step 3: Conclusion.
Thus, the correct relationship is that drift velocity is proportional to the potential difference \( V \).
\[ \boxed{\text{Correct Answer: Proportional to V}} \]