Power supply smoothing capacitor
The capacitor is a water tank filled in short bursts. A bigger tank, or a smaller tap on the way out, keeps the level from dipping between refills.
C = I / (2 × f × Vr) (full-wave rectifier)
Full-wave rectifier approximation: constant load current, ripple much smaller than the peak. Use the mains frequency, not the ripple frequency. Mains-powered circuits are dangerous; consider a sealed power module.