Question

If the length of a conductor is doubled while keeping the potential difference across it constant, then the drift velocity of electron will

• A. remain the same
• B. be double
• C. be halved
• D. increase fourfold

Hint:

The drift velocity is inversely proportional to the length of the conductor, given that other factors remain constant.

Answer 1

The Correct Option is C

Step 1: Understanding the relation between drift velocity and length of conductor.
The drift velocity (\( v_d \)) of electrons is given by the formula: \[ v_d = \frac{I}{nA e} \] where: - \( I \) is the current, - \( n \) is the number of electrons per unit volume, - \( A \) is the cross-sectional area of the conductor, - \( e \) is the charge of an electron. In the case of a conductor with a constant potential difference, the current remains the same because \( I = \frac{V}{R} \). However, the resistance of the conductor (\( R \)) is given by: \[ R = \rho \frac{L}{A} \] where \( L \) is the length of the conductor and \( \rho \) is its resistivity. If the length \( L \) is doubled, the resistance doubles, which means the drift velocity is inversely proportional to the length of the conductor. Step 2: Conclusion.
Thus, if the length of the conductor is doubled, the drift velocity of electrons will be halved.
\[ \boxed{\text{be halved}} \]