An $AC$ current is given by the expression, $I\left(t\right)=50\sin \left(200\pi t\right)$ in amperes. The frequency and RMS value of the current respectively are

Standard equation of the current variation in an AC supply can be written as,

$I=I_0\sin \left(\omega t\right)$, where $I_0=$peak current and $\omega =$angular frequency.

Comparing it with the given expression of current, we get

$I_0=50 \mathrm{A}$.

Therefore, RMS current

$I_{RMS}=\frac{I_0}{\sqrt{2}}=25\sqrt{2} \mathrm{A}$

Similarly, $\omega =200\pi$

$$\begin{gathered} \Rightarrow 2\pi f=200\pi \\ \Rightarrow f=100 \mathrm{Hz} \end{gathered}$$