Filter Capacitors and Ripple

The capacitor charges to the peak, then supplies the load until the next peak. For a full-wave rectifier:

$V_{ripple(p\text{-}p)} \approx \frac{I_{load}}{2 f C}$

(use $f C$ instead of $2fC$ for half-wave). Example: 1 A load, 50 Hz mains, 4700 µF → ripple ≈ 1/(2·50·0.0047) ≈ 2.1 V.

Choose the capacitor's voltage rating above the peak and check its ripple current rating — the charging pulses are large and heat electrolytic capacitors.