The a/c in my apartment is in the hallway ceiling,and I can hear a gurgling in my bathroom drain. This bathroom is the one closest to the a/c unit. What causing this noise??

Possible wired neg to pos and pos to negative.

check the circut breakers too.

Most likely the problem is a leaking drain pipe in the wall, perhaps because of a failed joint. The reason it's not going down the wall to the floor of the dining room is because there is a top plate on the wall. Most likely the water is running down the bathroom wall, then out over the dining room drywall ceiling. It is finding the lowest spot in the area to accumulate and is soaking into the drywall. Since it is drain water, it is dirty and is picking up additional contaminates from the wall and causing the brown stain. It may or may not be soft, depending on how much water accumulates at one time, but it is slowly breaking down the ceiling where the stain is.
That said, are you sure it's a leak, or are you assuming that since you see the stain on the ceiling. I say this because mice, like many other rodents, usually pick one location to use as their bathroom. If you have mice in the ceiling and this is where they do their thing, you will get the same type of indication.

where is the duct work located? In an attic, crawlspace? It sounds as if part of the system is disconnected. Are the outlets at the floor or in the ceiling? Is the duct work insulated? Can you take actual air temperatures at the outlets?

I would think that it is the ac evaporator unit and condensate in the ac box that is unable to get out the drain pipe from a blockage . It could be ice melting off the ac unit fins . check that the ac is operating properly

It sounds like a vent problem.
On top of each house is a vent stack.
There should be a vent stack above each toilet, and above kitchen sink.
Look for pipes sticking out of roof.
These pipes are open to the sewer line.
When you run a column of water down a drain, the vent stack lets air flow in front of and behind the column of water.
This air flow prevents the gurgling sound.
The gurgling sound is the drain water pushing air in front of it because of a clogged vent.
If you have a two story house, there are vents that run between floors to prevent the air flow from gurgling or bubbling sewer air into each drain as water column moves down pipe.

http://www.bradyinspects.com/plumbing-vents.html
http://chestofbooks.com/home-improvement/construction/plumbing/Standard-Practical/Venting-Part-3.html

Look for bird nest over vent pipe on top of house.
Run a snake down into pipe from roof and see if the is a stoppage.
You many need to call plumber to track down each vent and the cause.
For example if there are quick-vents installed inside a wall and the quick vent is no longer working.

You can also take advantage of fixya phone support.
Fixya expert will walk you through the steps for a price.

Is the bathroom light controlled by two switches?
Is the hallway light controlled by two switches?
What color wires are in the bathroom light switch that you changed?
Side wiring will not change the way the switch works.

The drain from your washer is tied to your shower drain and it is receiving air from your shower drain. Maybe your washer drain is not vented. This should not be a major concern if you can live with the noise.

try climbing on to your roof with the hose and give it a good flushing, otherwise you'll want to locate the cleanout and snake it out

The air handler has either a drip pan with exit pipes on the side or a drain pipe and any of which could be clogged.. Find out were the water is supose to exit,, and at that end - tape a strong wet vac to suk out any clog or debris..

Rate well ;o)

You'll be able to access the motor to service it and the wiring junction box from inside the bathroom. Please rate this answer if it was at all helpful.