b
Given that

Current \(I=I_0+\beta t\)

\( I_0=20 \mathrm{~A} \)

\( \beta=3 \mathrm{~A} / \mathrm{s}\)

\( \mathrm{I}=20+3 \mathrm{t} \)

\( \frac{\mathrm{dq}}{\mathrm{dt}}=20+3 \mathrm{t} \)

\( \int_0^q \mathrm{dq}=\int_0^{20}(20+3 \mathrm{t}) \mathrm{dt} \)

\( \mathrm{q}=\int_0^{20} 20 \mathrm{dt}+\int_0^{20} 3 \mathrm{tdt} \)

\( \mathrm{q}=\left[20 \mathrm{t}+\frac{3 \mathrm{t}^2}{2}\right]_0^{20}=1000\  \mathrm{C}\)