A parallel plate of capacitor made of circular plates each of radius $20.0cm$ has a capacitance $100pF$. The capacitor is connected to a source of 220 V and angular frequency of  $200rad/s$, the rms value of the displacement current is __________$\mathrm{\mu A}$ 

Given : ${\mathrm{E}}_{\mathrm{rms}}=220 \mathrm{V},\mathrm{\omega }=200 \mathrm{rad}/\mathrm{s}$

Capacitance,  $\mathrm{C}=100 \mathrm{pF}=100\times {10}^{-12} \mathrm{F}$
RMS value of the displacement current is same as  conduction current,

  ${\mathrm{I}}_{\mathrm{rms}}=\frac{{\mathrm{E}}_{\mathrm{rms}}}{{\mathrm{X}}_{\mathrm{C}}}$
$\begin{array}{rcl} & \Rightarrow & {\mathrm{I}}_{\mathrm{rms}}=\frac{{\mathrm{E}}_{\mathrm{rms}}}{1/\mathrm{\omega C}} \\ & \Rightarrow & {\mathrm{I}}_{\mathrm{rms}}={\mathrm{E}}_{\mathrm{rms}}\times \mathrm{\omega C} =220\times 200\times 100\times {10}^{-12}=44\times {10}^{-7}=4.4\times {10}^{-6} \end{array}$     
$\Rightarrow {\mathrm{I}}_{\mathrm{rms}}=4.4\mathrm{\mu A}$