Question

Two wires A and B made of same material having length 10 cm and 40 cm respectively are connected in parallel to the same source of emf 10 V. What will be the ratio of the drift velocity of the electrons in the wire A to the drift velocity in the wire B?

• A. \( 1:4 \)
• B. \( 1:2 \)
• C. \( 4:1 \)
• D. \( 2:1 \)

Hint:

In parallel circuits, voltage is same, so shorter wire has higher electric field and higher drift velocity.

Answer 1

The Correct Option is C

Step 1: Write drift velocity relation.
\[ v_d \propto E \]

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

Step 3: Since wires are in parallel.
Same voltage across both wires.

Step 4: Write drift velocity dependence.
\[ v_d \propto \frac{V}{L} \]

Step 5: Ratio of drift velocities.
\[ \frac{v_A}{v_B} = \frac{L_B}{L_A} \]

Step 6: Substitute lengths.
\[ \frac{v_A}{v_B} = \frac{40}{10} = 4 \]

Step 7: Final Answer.
\[ \boxed{4:1} \]