The current flowing through a wire depends on time as l = 3t2 + 2t + 5. The charge flowing through the cross-section of the wire in time from t = 0 and t = 2 sec. is

strong{font-weight:bold !important} Given i=3t2+2t+5⇒dqdt=3t2+2t+5∴q=∫idt=∫023t2+2t+5dt=3t33+2t22+5t02=t3+t2+5t02=8+4+10=22C

The current flowing through a wire depends on time as l = 3t2 + 2t + 5. The charge flowing through the cross-section of the wire in time from t = 0 and t = 2 sec. is

strong{font-weight:bold !important} Given i=3t2+2t+5⇒dqdt=3t2+2t+5∴q=∫idt=∫023t2+2t+5dt=3t33+2t22+5t02=t3+t2+5t02=8+4+10=22C

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The current flowing through a wire depends on time as l = 3t² + 2t + 5. The charge flowing through the cross-section of the wire in time from t = 0 and t = 2 sec. is

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20 C

22 C

18 C

5 C

answer is A.

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Detailed Solution

$Given i = 3 t^{2} + 2 t + 5 \Rightarrow \frac{dq}{dt} = 3 t^{2} + 2 t + 5$

$∴ q = \int i d t = \int_{0}^{2} (3 t^{2} + 2 t + 5) d t$

$= {[3 (\frac{t^{3}}{3}) + 2 (\frac{t^{2}}{2}) + 5 t]}_{0}^{2} = {[t^{3} + t^{2} + 5 t]}_{0}^{2}$

$= 8 + 4 + 10 = 22 C$

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