A parallel plate condenser of capacity 10 $\mathrm{\mu }$F is connected to an A.C. supply voltage e = 4 sin(100 $\mathrm{\pi }$t). The maximum displacement current.

Displacement current

$\begin{array}{rcl}{\mathrm{i}}_{\mathrm{d}}& =& {\in }_0\frac{\mathrm{d\varphi }}{\mathrm{dt}}\\ & =& \mathrm{C}\frac{\mathrm{dV}}{\mathrm{dt}}\\ & =& \mathrm{C}\frac{\mathrm{d}}{\mathrm{dt}}\left(4 \sin 100\mathrm{\pi t}\right)\\ & =& \mathrm{C} \mathrm{x} 4 \mathrm{x} 100\mathrm{\pi } \cos \left(100\mathrm{\pi t}\right)\\ & =& 400\mathrm{\pi C} \cos \left(100\mathrm{\pi t}\right)\\ {\mathrm{i}}_{\mathrm{d}}& =& {\mathrm{i}}_0\cos \left(100\mathrm{\pi t}\right) ; \\ \therefore {\mathrm{i}}_0& =& 400\mathrm{\pi C}\\ & =& 400\mathrm{\pi } \mathrm{x} 10 \mathrm{x} {10}^{-6}\\ & =& 4\mathrm{\pi } \mathrm{mA}\end{array}$