A Parallel plate condenser of capacity 100 pF is connected to 230 V of AC supply of 300 rad / sec frequency. The rms value of displacement current

$\begin{array}{rcl}{\mathrm{i}}_{\mathrm{d}} & =& {\in }_0\frac{\mathrm{d\varphi }}{\mathrm{dt}}=\frac{{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}\left(\frac{\mathrm{dV}}{\mathrm{dt}}\right)=\mathrm{C}\frac{\mathrm{dV}}{\mathrm{dt}}=\mathrm{C}\frac{\mathrm{d}}{\mathrm{dt}}\left({\mathrm{V}}_0 \mathrm{sin\omega t}\right)\\ {\mathrm{i}}_{\mathrm{d}} & =& {\mathrm{C\omega V}}_0 \mathrm{cos\omega t}={\mathrm{i}}_0 \mathrm{cos\omega t} \\ {\mathrm{v}}_{\mathrm{rms} }& =& 230 \mathrm{V}\\ {\mathrm{i}}_{\mathrm{rms}} & =& \frac{{\mathrm{i}}_0}{\sqrt{2}}=\frac{{\mathrm{C\omega V}}_0}{\sqrt{2}} \left(\therefore {\mathrm{v}}_{\mathrm{rms}}=\frac{{\mathrm{V}}_0}{\sqrt{2}}\right)\\ & =& \frac{100 \mathrm{x} {10}^{-12} \mathrm{x} 300 \mathrm{x} 230\sqrt{2}}{\sqrt{2}}=6.9 \mathrm{\mu A}\end{array}$