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(B) The relationship between current $I$ and charge $Q$ is given by $I = \frac{dQ}{dt}$,which implies $dQ = I \ dt$.To find the total charge $Q$ passi

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$24$

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(B) The relationship between current $I$ and charge $Q$ is given by $I = \frac{dQ}{dt}$,which implies $dQ = I \ dt$.To find the total charge $Q$ passing through the cross-section between time $t_1 = 2 \ s$ and $t_2 = 3 \ s$,we integrate the current with respect to time:$Q = \int_{2}^{3} I \ dt = \int_{2}^{3} (2t + 3t^2) \ dt$Performing the integration:$Q = [t^2 + t^3]_{2}^{3}$$Q = (3^2 + 3^3) - (2^2 + 2^3)$$Q = (9 + 27) - (4 + 8)$$Q = 36 - 12 = 24 \ C$.Thus,the total charge passed is $24 \ C$.

The electric current in a conductor varies with time $t$ as $I = 2t + 3t^2$,where $I$ is in amperes and $t$ is in seconds. Find the total charge $Q$ (in $C$) that passes through the cross-section of the conductor from $t = 2 \ s$ to $t = 3 \ s$.

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