Question

Two identical conductors of lengths \(l\) and \(3l\) respectively are maintained at the same temperature. They are given potential differences in the ratio \(1:3\). The ratio of their drift velocities is

• A. \(1:9\)
• B. \(9:1\)
• C. \(1:1\)
• D. \(1:3\)

Hint:

Drift velocity depends on \( \frac{V}{L} \). If both scale equally, velocity remains same.

Answer 1

The Correct Option is C

Step 1: Drift velocity relation.
\[ v_d = \mu E \]

Step 2: Electric field expression.
\[ E = \frac{V}{L} \]

Step 3: Write drift velocity.
\[ v_d = \mu \frac{V}{L} \]

Step 4: Substitute values.
For first conductor:
\[ v_1 = \mu \frac{V}{l} \]
For second conductor:
\[ v_2 = \mu \frac{3V}{3l} \]

Step 5: Simplify.
\[ v_2 = \mu \frac{V}{l} \]

Step 6: Compare velocities.
\[ v_1 = v_2 \]

Step 7: Final conclusion.
\[ \boxed{1:1} \] Hence, correct answer is option (C).