The current flowing through a wire as a function of time is given as: \( I = 3t^{2} + 2t + 5 \) The charge flowing through any cross-section of the wire in first 2 s is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 22 C
Current is the rate of flow of charge, \( I = dq/dt \), so the charge that crosses a section in a time interval is the integral of the current over that interval.
\( \displaystyle q = \int_{0}^{2}\left(3t^{2} + 2t + 5\right)dt = \left[t^{3} + t^{2} + 5t\right]_{0}^{2} \)
\( q = (8 + 4 + 10) - 0 = 22\,\mathrm{C} \)