The given equation of alternating voltage is,
       $\mathit{\text{e}}=200\sqrt{2}\text{ sin }100t ...\left(\mathrm{i}\right)$
The standard equation of alternating voltage is,
      $\mathit{\text{e}}={\mathit{\text{e}}}_0\text{sin}\omega t ...\left(\mathrm{ii}\right)$
Comparing equations $\left(\mathrm{i}\right)$ and $\left(\mathrm{ii}\right)$, we get,
    ${\mathit{\text{e}}}_0=200\sqrt{2}\text{ V}\text{, }\omega =100\text{ rad}{\text{ s}}^{-1}$
The capacitive reactance is,
    ${\mathit{\text{X}}}_{\mathit{\text{C}}}=\frac{1}{\omega \mathit{\text{C}}}=\frac{1}{100\times 1\times 10^{-6}} \mathrm{\Omega }$
The rms value of current in the circuit is,
    $i_{rms}=\frac{v_{\text{rms}}}{{\mathit{\text{X}}}_{\mathit{\text{C}}}}=\frac{{\mathit{\text{e}}}_0/\sqrt{2}}{1/\omega \mathit{\text{C}}}=\frac{\left(200\sqrt{2}/\sqrt{2}\right)}{1/100\times 10^{-6}}$
             $=200\times 100\times 10^{-6} \text{A}=2\times 10^{-2} \text{A}=20\text{ mA}$