The electric current through a wire varies with time as $I=I_0+\beta t$. where $I_0=20 \mathrm{~A}$ and $\beta=3 \mathrm{~A} / \mathrm{s}$. The amount of electric charge crossed through a section of the wire in $20 \mathrm{~s}$ is :
JEE MAIN 2024, Diffcult
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Given that
Current $I=I_0+\beta t$
$ I_0=20 \mathrm{~A} $
$ \beta=3 \mathrm{~A} / \mathrm{s}$
$ \mathrm{I}=20+3 \mathrm{t} $
$ \frac{\mathrm{dq}}{\mathrm{dt}}=20+3 \mathrm{t} $
$ \int_0^q \mathrm{dq}=\int_0^{20}(20+3 \mathrm{t}) \mathrm{dt} $
$ \mathrm{q}=\int_0^{20} 20 \mathrm{dt}+\int_0^{20} 3 \mathrm{tdt} $
$ \mathrm{q}=\left[20 \mathrm{t}+\frac{3 \mathrm{t}^2}{2}\right]_0^{20}=1000\ \mathrm{C}$
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