About battery and power grid circuits
In your home, the AC mains use the neutral as a return path in an unbalanced load. There is current flowing through the neutral wire, but it is very slow. An equation factoring in the current, charge of electrons per CC, and wire gauge can calculate the current flowing in a 100watt lightbulb to be about 3 inches per hour. It is slow like molasses.
In North America, your house panel is fed by two 120volt conductors and 1 neutral conductor. To get 120 volts, one of the hot phases is connected through a load back to the neutral conductor. The neutral conductor comes from a center-tapped winding on the secondary side of the distribution transformer. The neutral is earthed at your panel and at the transformer to prevent any situation where the neutral could carry a voltage higher than ground potential. For a 220volt potential, the load is connected between the two 120volt phases which create a 220 volt potential. You can think of the neutral as being half-way between the two phases, thus creating half the voltage. So in a 120 volt circuit, the current flows from one of the hot conductors, through the load, and back to the transformer via the neutral wire.