The current in a conductor is expressed as , where is in Ampere and is in second. The amount of electric charge that flows through a section of the conductor during to is _________ C

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Solution

Q.
The current in a conductor is expressed as $I = 3 t^{2} + 4 t^{3}$ , where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t = 1 s$ to $t = 2 s$ is _________ C. [2024]

Ans.
(22) $I = 3 t^{2} + 4 t^{3}$

   $\int d Q = \int I d t$

   $Q = \int_{1}^{2} (3 t^{2} + 4 t^{3}) d t$

$= {[t^{3} + t^{4}]}_{1}^{2}$

   $= (8 + 16) - (2) = 22 C$

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