This drawing illustrates the wiring for a split receptacle controlled by a switch. The tab connecting the hot terminals on the receptacle is removed and the source hot is connected to the bottom half. The source neutral is connected to one of the neutral terminals on the receptacle.
The neutral and ground wires for the circuit are connected to a bar along the side of the service panel box. The neutral and grounding bars in the box may be separate or, in the case of older service panels, the same bar may be used for both purposes.
This diagram shows the wiring for a switch to control multiple receptacles. The source for the circuit is at the switch and the receptacles are wired using pigtail splices to make the connections.
This type of switch will be referred to as a 2 circuit lamp switch when shopping at home stores. Don’t mistake this for a three way switch (pictured below), the two do not function in the same way.
Here 3-wire cable serves a split receptacle. The bottom half of the receptacle is controlled by a switch and the top half is always-hot.
A doorbell circuit for two or more doors will have a separate contact on the chimes for each button included. At the chimes, one wire from each button is spliced to the output wire on the transformer. The second wire is connected to one of the contact screws on the chimes.
This diagram shows the wiring for a new receptacle added from a light switch. The switch must have an always-hot wire for the source and a neutral wire must be present for the return path. The hot source is spliced with a pigtail back to the switch, and to a new 2-wire cable running to the new outlet. The neutral is spliced in the switch box to both the existing light, and the cable to the new receptacle.
The battery is the weakest link here and should be the first place to look for trouble. The battery can be replaced with a large flashlight-type dry cell rated at 12 to 16 volts and if the wires are still intact and the contacts clean, the doorbell should come back to life.