A $100\Omega$ resistance and a capacitor of $100\Omega$ reactance are connected in series across a 220 V source. When the capacitor is 50 % charged, the peak value of the displacement current is

Reactance X_C = $\mathrm{\omega C}$
It does not depend on charge. It depends
on angular frequency$\mathrm{\omega }$and capacity C.
Given reactance X_C = 100 Ω
Resistance R = 100 Ω
$\begin{array}{l}\therefore \text{ Impedence }\mathrm{Z}=\sqrt{{\mathrm{R}}^2+{\mathrm{X}}_{\mathrm{c}}^2}\\ \therefore \mathrm{Z}=\sqrt{{100}^2+{100}^2}\\ \mathrm{Z}=100\sqrt{2}\mathrm{\Omega }\end{array}$
Given, ${\mathrm{V}}_{\mathrm{rms}}=220=\frac{{\mathrm{V}}_0}{\sqrt{2}}$
Peak value of displacement current
 ${\mathrm{i}}_0=\frac{{\mathrm{V}}_0}{\mathrm{Z}}=\frac{220\sqrt{2}}{100\sqrt{2}}=2.2\mathrm{A}$