That shouldn't be happening. Is it the ductwork itself sweating so much? Is there a coil behind the ductwork? It could be a clogged drainline or the ductwork itself sweating, though if it were the ductwork I'd think the old owners would know something about it. You need to call someone before too much damage is done due to the water.

No that is not normal- something sounds like it is loose or you may be missing a part.

If you are in the NJ area, check out Browns Heating & Cooling. They do air conditioning repairs and installations as well as inspections. They guarantee their work and make sure every problem is fixed before they leave. They are very affordable too.

You just don't want to take the risk and not get it looked at.

Here is a link that might be useful: Browns Heating & Cooling

Most likely a clogged condensate drain.
Look for a 3/4 inch plastic pipe coming from the heater near the AC coil.
Follow it to its end and see if water is coming out when the AC runs.
If there is no water you can try and clear the line with a shop vac.
Wet a rag and use it to create a seal between the shop vac hose and the end of the drain line.
The crud usually comes out with a little slurping and gurgling sound.

i am just a homeowner, but i swear to me it looks like your joints aren't sealed. this allows the cold conditioned air to leak and you get condensation. get some FOIL tape(NOT DUCT TAPE!!!) and/or mastic and seal the joints. or call in a pro to do it for you and pay out the nose for it. you should feel NO air comeing out of any part of the ductwork other than teh vents!

No tape will stop the leak. You can check the drain line. If it's not the drain, then paying for a tech is your best option. The water will do damage to the sensitive controls in your furnace if it isn't taken care of properly.

It's likely a clogged drain line, or a rusted out evaporator coil drain pan. If the drain pan is rusted, it's best to replace the entire coil. Better yet, replace the entire system.

just one question. is it cooling down your home. it looks like there might be a blockage in the orifice or txv, or low on freon. that would cause the freon to evaporate too fast and freeze the a-coil(part in your supply plenum). seen this problem one too many times. let me know what happens

the reason i say airflow is IF the OP's lives in an area like i do. we stay in teh 70-90% RH range most of the time and even a minor cold air leak WILL cause condensation on this level. my unit for the back of my house has done it in teh past. i noticed the backup drain had water coming out, so i figured the main was clogged. go in teh attic and see it is the plenum sweating and pouring water off it. i found the leak, a strap had come undone and allowed it shift a little. resecured the strap, sealed the leak and no more water.

of course, if you live in a normal area that humidity is not so high this may not apply.

regardless, those gaps should be SEALED.