Read the passage below and answer following questions
The current through a wire depends on time as i=i0 + 3 αt2, where i0 = 10 A and α = 0.5 A/sec2.
What is the charge passing through the wire for that interval t = 0 to t = 2s ?
Answer & explanation
Correct answer: option 3
$Charge , dq = Idt = (I_0 + 3\alpha t^2)dt $
$\text{Integrating both sides,}$
$ q = I_0t+\alpha t^3 = 24C$