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(B) Given that the current $I$ varies with time $t$ as $I = I_0 + \beta t$.Here,$I_0 = 20 \ A$ and $\beta = 3 \ A/s$.So,$I = 20 + 3t$.We know that cur

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$1000$

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(B) Given that the current $I$ varies with time $t$ as $I = I_0 + \beta t$.Here,$I_0 = 20 \ A$ and $\beta = 3 \ A/s$.So,$I = 20 + 3t$.We know that current $I = \frac{dq}{dt}$,which implies $dq = I \ dt$.To find the total charge $q$ that crosses a section in time $t = 0$ to $t = 20 \ s$,we integrate the expression:$q = \int_{0}^{20} I \ dt = \int_{0}^{20} (20 + 3t) \ dt$$q = \left[ 20t + \frac{3t^2}{2} ight]_{0}^{20}$$q = \left( 20(20) + \frac{3(20)^2}{2} ight) - 0$$q = 400 + \frac{3 	imes 400}{2} = 400 + 600 = 1000 \ C$.

The electric current through a wire varies with time as $I = I_0 + \beta t$,where $I_0 = 20 \ A$ and $\beta = 3 \ A/s$. The amount of electric charge that crosses through a section of the wire in $20 \ s$ is: (in $C$)

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