In an $$AC$$  circuit an alternating voltage $$e = 200\sqrt 2 \sin 100t\,volt$$     is connected to a capacitor of capacity $$1\,\mu F.$$  The $$rms$$  value of the current in the circuit is

Solution :
Problem Solving Strategy
Compare the given equation with the equation of alternating voltage i.e. $$e = {e_m}\sin \omega t$$
where, $${e_m} = {e_{rms}}$$
Given,
emf, $$e = 200\sqrt 2 \sin 100\,t$$
and $$C = 1\mu F = 1 \times {10^{ - 6}}F$$
As $${e_{rms}} = 200\,V\,{\text{and}}\,\omega = 100$$
$$\eqalign{ & \therefore {X_C} = \frac{1}{{\omega C}} = \frac{1}{{1 \times {{10}^{ - 6}} \times 100}} = {10^4}\,\Omega \cr & {i_{rms}} = \frac{{{e_{rms}}}}{{{X_C}}} = \frac{{200}}{{{{10}^4}}} = 2 \times {10^{ - 2}}A = 20\,mA \cr} $$