Question

The relation between the current \( i \) (in ampere) in a conductor and the time \( t \) (in second) is given by \( i = 12t + 9t^2 \). The charge passing through the conductor between the times \( t = 2 \, \text{s} \) and \( t = 10 \, \text{s} \) is.

• A. \( 3720 \, \text{C} \)
• B. \( 3648 \, \text{C} \)
• C. \( 3600 \, \text{C} \)
• D. \( 3552 \, \text{C} \) \bigskip

Hint:

To calculate the charge, integrate the current function with respect to time over the given limits.

Answer 1

The Correct Option is D

Step 1: The charge passing through the conductor is given by the integral of the current with respect to time: \[ Q = \int_{t_1}^{t_2} i \, dt = \int_{2}^{10} (12t + 9t^2) \, dt \] \[ Q = \left[ 6t^2 + 3t^3 \right]_2^{10} \] \[ Q = \left( 6 \times 10^2 + 3 \times 10^3 \right) - \left( 6 \times 2^2 + 3 \times 2^3 \right) \] \[ Q = (600 + 3000) - (24 + 24) = 3600 - 48 = 3552 \, \text{C} \] Thus, the charge passing through the conductor is \( \boxed{3552 \, \text{C}} \). \bigskip