In an AC circuit, I = 100 sin($200 \mathrm{\pi t}).$ The time required for the current to achieve its peak value will be

The current takes $\frac{\mathrm{T}}{4}$ sec to reach the peak value.

In the given question, $\frac{2\mathrm{\pi }}{\mathrm{T}}=200 \mathrm{\pi }\Rightarrow \mathrm{T}=\frac{1}{100} \sec$

$\therefore$       Time to reach the peak value $=\frac{1}{400} \sec$