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Q.

The current in a conductor varies with time $t$ as $i = 2 t + 3 t^{2}$ where $i$ is in ampere and $t$ in seconds. Electric charge flowing through a section of the conductor during $t = 2 s e c$ to $t = 3 s e c$ is

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a

$44 C$

b

$24 C$

c

$33 C$

d

$10 C$

answer is B.

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Detailed Solution

$q = \int_{t_{1}}^{t_{2}} i d t = \int_{2}^{3} (2 t + 3 t^{2}) d t$

$= {|2 \frac{t^{2}}{2} + 3 \frac{t^{3}}{3}|}_{2}^{3} = (3^{2} + 3^{3}) - (2^{2} + 2^{3})$

$= 24 C$

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