Question

Charge passing through a conductor of crosssection area \( A = 0.3 \, \text{m}^2 \) is given by \( q = 3t^2 + 5t + 2 \, \text{C} \), where \( t \) is in seconds. What is the value of drift velocity at \( t = 2 \) seconds?

• A. \( 0.77 \times 10^{-5} \, \text{m/s} \)
• B. \( 1.77 \times 10^{-5} \, \text{m/s} \)
• C. \( 2.08 \times 10^{-5} \, \text{m/s} \)
• D. \( 0.57 \times 10^{-5} \, \text{m/s} \)

Hint:

To calculate drift velocity, use the relationship between charge, current, and area of the conductor.

Answer 1

The Correct Option is B

The drift velocity is related to the current by \( I = n A e v_d \), where \( I \) is the current, \( n \) is the number of charge carriers, \( e \) is the charge of an electron, and \( v_d \) is the drift velocity. We can calculate \( v_d \) using the given charge function.

Step 2: Conclusion.
The drift velocity at \( t = 2 \) seconds is \( 1.77 \times 10^{-5} \, \text{m/s} \), corresponding to option (b).