The FCU in my apartment ceiling is dripping water onto the floor — how do I stop it?

First thing: switch that FCU off at the thermostat to stop the drip while you sort it — standing water will keep spreading on the ceiling and can reach the light fittings.

Nine times out of ten this is a blocked condensate drain, and here's the logic: your fan-coil unit chills the air, and that pulls a surprising amount of water out of our humid air. That water is supposed to run out through a small drain line. When dust and algae block that line, the water has nowhere to go — it backs up in the drain tray and overflows through the ceiling. Exactly your symptom, and exactly why it only drips when the cooling's running.

The fix is to clear and flush the drain line and clean the tray — straightforward for the right person, and they'll usually add a slope/anti-algae treatment so it doesn't recur.

Less common causes if the drain's clear: chilled-water pipes sweating because their insulation has failed (they drip along their length, not just at the FCU), or a cracked drain pan.

This is a chilled-water / FCU job rather than a general handyman one — the FCU sits above a false ceiling and the drain and pan need doing properly. Background on why there's so much water in the first place: the condensate drain explainer.