Clearly, an activated carbon filter can be expected to collect what comes from the cooking plate with the air. But what happens to the moisture, how much of it will leave the hood?
All the moisture will head right back around if you are (as seems to be the case) talking about one of those useless hood-shaped objects that don't actually vent outside. Carbon does not trap water, and if it did, or you put in something that did, you'd have to change it very, very frequently.
Indeed, the "filtration" provided by such hood-shaped objects is fairly ineffective, period. Burn something on the stove and the smoke will hang around for a long time.
Activated carbon filters are supposed to remove smell. In reality it's just a fancy sounding name. If your fan is recirculating then it's the same thing as having a convenient oscillating fan above your stove. The filters may, perhaps trap some smell. If your fan is ducted to outside you don't need the activated carbon filter at all.
Oscillating fan from www.Wayfair.cahttps://www.wayfair.ca