Compare with the standard AC current form

The given current is $i = 100\sqrt{2}\sin(100\pi t)\;\text{A}$

Standard form of alternating current is $i = I_0 \sin(\omega t)$

So, by comparison: $I_0 = 100\sqrt{2}\;\text{A}, \qquad \omega = 100\pi\;\text{rad/s}$

Find the RMS current

RMS current is given by $I_{\text{rms}} = \frac{I_0}{\sqrt{2}}$

Substituting $I_0 = 100\sqrt{2}$: $I_{\text{rms}} = \frac{100\sqrt{2}}{\sqrt{2}} = 100\;\text{A}$

Find the frequency

We know $\omega = 2\pi f$

Hence, $f = \frac{\omega}{2\pi} = \frac{100\pi}{2\pi} = 50\;\text{Hz}$

Match with the options

We obtained: $I_{\text{rms}} = 100\;\text{A}, \qquad f = 50\;\text{Hz}$

This matches Option D.

Verification with stored answer

Stored correct answer: D

Derived answer: D

So, the derived answer agrees with the stored answer.