Q.A capacitor of capacitance 0.5 $\mu$F is connected to a source of alternating e.m.f. of frequency 100 Hz. What is the capacitive reactance? ($\pi = 3.142$)

For a capacitor of capacitance C connected to $e=e_0\sin\omega t$ (with no series resistance, so the instantaneous voltage across the plates always equals the source emf), the instantaneous charge is $q=Ce=Ce_0\sin\omega t$, and differentiating gives the instantaneous current $i=\dfrac{dq}{dt}=\omega C\,e_0\cos\omega t=i_0\sin\left(\omega t+\dfrac{\pi}{2}\right)$, with peak current $i_0=\omega C\,e_0$ -- the current LEADS the emf by a phase angle of $\pi/2$ ($90^\circ$), the exact mirror image of the inductor's lagging behaviour. …