Why is there a neutral wire?
Not all systems of electrical
distribution use a grounded neutral if they have a neutral at all. In
Europe, there is no neutral wire.

The three wires come into your
house, the neutral wire is connected to the ground both at the pole and in the
house (water pipe, ground rod, etc). If for example you now hook your coffee
maker to the left wire and neutral, the current flows back and forth into the
toaster on one wire and out of the toaster on the other wire.
However, you now hook your toaster
to the right wire and neutral, the current flows as before, but since the left
and right wires have opposite phase, there will actually be no current flowing
on the neutral wire. The two out-of-phase flows cancel each other out. This is
why the wire is referred to as "neutral" If loads are exactly balanced,
there is no current flow along it. The fact that it is grounded is irrelevant.
At the transformer on the pole
outside the house, there is a coil, and the average voltage measured between the
ends of this coil is 240V AC, meaning that the voltage difference measured
between these wires which fluctuates 60 times a second and ranges from +339V to
-339V. 240 V is a nominal voltage or average voltage.
The third wire (the neutral)
connected to the middle of this coil, and the voltage between this wire and one
of the ends ranges from +169 to -169, 169 is an average, the nominal voltage is
120V. That is, when the center and the left end are 169 apart, the
center and right end are -169 apart.
Three phase systems have three
power wires instead of two and also have a neutral wire.
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