TS EAMCET · Physics · Current Electricity
The relation between the current \(i\) (in ampere) in a conductor and the time \(t\) (in second) is \(i=12 i+9 t^2\). The charge passing through the conductor between the times \(t=2 \mathrm{~s}\) and \(t=10 \mathrm{~s}\) is
- A 3720 C
- B 3648 C
- C 3600 C
- D 3552 C
Answer & Solution
Correct Answer
(D) 3552 C
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Current, } i=12 t+9 t^2, t_1=2 \mathrm{~s}, t_2=10 \mathrm{~s} \\ & \therefore \text { Charge, } q=\int_{t_1}^{t_2} i d t=\int_2^{10}\left(9 t^2+12 t\right) d t \\ & =\left[9 \frac{t_3}{3}+12 \cdot \frac{t^2}{2}\right]_2^{10}=3552 C\end{aligned}\)
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