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My home has 3-wire single-phase supplied from the power company (Massachusetts, US). Red and black are separated by 180°. Both are 120 V from neutral (white). And in my electrical panel, neutral (white) and ground (uninsulated) are tied to each other and to a copper clad ground spike out in the yard.

Presumably the bare ground wires within the house never carry current except in the event of a short; but it goes back to neutral in the box.

Any 120 V circuit (a light bulb) is wired with one or the other of the two "hot" legs and the neutral; so presumably the original amperage supplied to the light bulb (minus energy dissipated as heat and light) passes thru the neutral line and then to ground. How much current does one actually see on the neutral line from the light bulb to the panel? How much current does one see from the panel ("behind" the ground spike, if you will) back to the electrical company transformer?

Any 220 V circuit (a clothes drier) is wired with both of the two "hot" legs and the neutral. In this case I would expect all current to see-saw between the two hot legs (minus the load again). Is there any current on neutral? Does the energy dissipated by the load appear as current on the neutral? Does any current appear on the neutral between the panel and the transformer?

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    \$\begingroup\$ Current is not consumed by a load, the energy used by a load comes from the difference in voltage across the load. \$\endgroup\$ – Gorloth Sep 2 '14 at 1:36
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    \$\begingroup\$ Just to show that the hot and neutral wires on a single circuit normally carry exactly the same current, add a GFCI outlet or circuit breaker. GFCI works by comparing the current through the hot and neutral wires. If there is a difference (more than a few mA), then the missing current must be flowing through a ground (either the ground wire or maybe a human body) and the GFCI trips. \$\endgroup\$ – DoxyLover Sep 2 '14 at 4:42
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On any individual circuit (lamp or 120V outlet) the current in the neutral in that circuit is equal to the current in the "hot" wire.

If you have equal loads between black and neutral, and between red and neutral, the "black" current and the "red" current will cancel in the neutral - there will be no current in the shared neutral wire.

Anything that only uses 240V (hot water heater?) will not connect to the neutral, and therefore will not cause any neutral current.

An electric stove will use 240 V for the heating elements, but also uses some 120 V for lights and a clock, so will require a neutral connection, and so will generate some neutral current.

The current in the neutral wire between your house and the power company's transformer will depend on how the loads in your house are balanced between the two "hot" wires.

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The neutral carries the difference in amperage between the Black and red if they are on the 2 different legs in the panel. Theoretically it would be near zero. I often will use Black, Red, and White, plus a ground to run 2 separate 120v circuits. I always make sure that the Hot wires (Red, Black) are on Opposing input legs in the breaker panel so that the voltage across the red/black is 220v. This way the neutral carries the difference between the 2 circuits. If the red and black are on the same input leg, the current will be the sum of the 2 circuits.

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