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Question:

What role does the neutral wire play?

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Answer:

A neutral conductor is used to provide two different supply voltage levels. Three-phase application: A 3-phase transformer with the secondary windings connected Wye with a line-to-line voltage of 480 V. If a neutral conductor is connected, the secondary would supply 480 V and 277 V (line-to-neutral). 480/1.732 = 277. Single-phase application: A single-phase distribution transformer with a secondary voltage of 240 V. If a neutral conductor is connected at the middle (center tap) of the secondary winding, the secondary of the transformer would supply 240 V and 120 V.
It provides the return current path. Without it positive current would have no where to flow once it enters a device. Here's why: Think about you sink... you need a pipe to bring the water in, this is the hot wire. Without a drain the water has no where to go to, this is the neutral wire. Without a drain there is no net flow of water.
An electrical circuit requires at least two wires, whether it be ac or dc. In mains ac, one of the wires is connected to ground for safety. This is called the neutral. So the circuit will still work without the neutral connected to ground but not be so safe. The reason the neutral makes it safer is that a current will flow in the event of a fault on the hot wire and cause the protection (fuse or breaker) to operate.
Commercial city electricity comes from the power plant in the form of three-phase current. Each phase requires one wire, and the neutral is the common return path for all three. It's more complicated than that, but that will get you started. Near your house there is a transformer that takes one leg of the three-phase power line and reduces it to the voltages used by your household lights and appliances. The neutral wire is grounded at the pole and at your house, and connected to the neutral line in the three-phase wiring, so that it provides a safety ground connection and a return path for electric current. IT IS VERY IMPORTANT that the neutral wire be connected correctly and properly maintained. Never let anyone fool with it unless you are sure they know what they are doing. A bad neutral can burn your house down, very quickly. It's much easier to explain city wiring and house wiring with diagrams and pictures. Try an internet search on house wiring. Good luck.

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