# Why is the neutral wire the same size as hot wire in a 3C cable?

I thought that the wire size depends on the amperage that the current passes. However in a 3 conductor cable, the size of the neutral wire is the same as the hot wire; which puzzles me. If both hot wires carry 15A current, the neutral wire will carry 30A current.

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A simplified representation of a multi-wire branch circuit, would look something like this.

If each part of the circuit had a 120 Watt light bulb installed, it would look like this.

If the switch on `L1` was closed, you'd see 1 ampere on the circuit.
Ohm's law I=P/E

`L1` = 1A, `N` = 1A, `L2` = 0A

If both switches were closed, you'd still see 1 ampere on the circuit. However, in this case the current flows line to line, and there will be no current on `N`.

`L1` = 1A, `N` = 0A, `L2` = 1A

If we replace one of the 120 Watt bulbs with a 240 Watt bulb, you'll see that the unbalanced load flows on `N`.

'L1' = 2A, `N` = 1A, `L2` = 1A

So as you can see, the neutral (`N`) will never carry more than either line (`L`). At least not in a properly wired circuit. This is because of the nature of alternating current, and the properties of a split-phase system.

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When it is said that the current cancels each other out, it means that the neutral of a multi-wire branch circuit only carries the imbalance of the current between the two circuits of a properly wired MWBC.

So a load of 5A on one leg, and 15A on the other leg, will result in a load of 10A on the neutral.

For a typical MWBC it is extremely rare that both legs will be 100% balanced, so the neutral will almost certainly carry some current. This is why a straight 240V circuit (which is a line-to-line circuit as opposed to a line-to-neutral) requires no neutral wire. It is a 100% balanced line-to-line circuit.

See?

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"This is why a straight 240V circuit requires no neutral wire. It is a 100% balanced line-to-line circuit." - This statement is confusing. If there were a neutral wire, it wouldn't carry a current, but it's not because both legs are balanced; it's because the neutral wouldn't be connected to anything (which is why both legs are balanced...) – BlueRaja - Danny Pflughoeft Feb 14 '14 at 16:51
Well, it would not be connected to anything, true, because it is not needed. – Speedy Petey Feb 14 '14 at 16:52

No, because the two hot legs are out of phase. So 15 amps on one side will cancel out the 15 amps on the other side.

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3 conductor cable is usually used for one of two purposes: An additional/dedicated hot (i.e. feeding a switched light and an always-on receptacle), or a multi-wire branch circuit. In the case of a multi-wire branch circuit, the two hot legs come from different legs of your supply (+120V, -120V), so they actually cancel each other out when properly balanced.

You are correct in that you would not want to return 2 15 amp circuits on the same leg via a single neutral.

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Isn't longneck's answer below correct? – bib Feb 13 '14 at 19:57
yes, Longneck is correct. The two legs are 180 degrees out of phase. there is no - or + leg, they both supply 120 volts of alternating voltage both + and -, but reversed polarity from eachother, 60 times a second. – shirlock homes Feb 13 '14 at 22:06
correct me if i'm wrong, but residential supply is not two phases but rather one phase stepped down via a center tap transformer, unlike 3-phase supply where your phases are 120 degrees apart – Steven Feb 13 '14 at 23:48
@Steven 120/240V Split-phase systems supply a single 240 circuit line to line, but since the neutral is a center tap on the transformer you end up with two 120V circuits line to neutral. Since it's alternating current, when line1 is "pushing", line2 is "pulling". Because of all this line1 and line2 appear to be 180 degrees out of phase. While in fact it's just the nature of an alternating current circuit. – Tester101 Feb 14 '14 at 1:33

The two hot legs are NOT out of phase! They are completely in-phase. No current flows through the neutral when the same load is applied to both legs of the hots because all of the current flows through the hots (only) from one end to the other across the entire length of the (power pole) transformer secondary winding. A difference current flows through the neutral only when the loads on the two legs of the hot are not equal --- not because they are out of phase (because they are not out of phase) but because they are out of balance!

If the two hot wires were out of phase then no current at all would flow into a 240-volt motor when it is wired across the hots.

I'm not an electrician, but I am a certified electronic technician and I do know electricity. I've been wiring circuits since before the Beatles were a band.

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I stand corrected by myself. The two hots are indeed out of phase with each other. When they are connected across a load, the load current is in phase with the current in each hot leg, and this is the source of the confusion. In other words, the current at every point in the loop is "in phase" with the current at every other point in the loop. But the two hot wires are "out of phase" with respect to each other even though they both source a single phase of current through a load. It depends on one's point of view when looking at the meaning of the word "phase". – John May 21 '15 at 5:05
You can edit your own post to include your comments by clicking the "edit" button on the bottom left. – Doresoom May 21 '15 at 13:44

As others have said the 3 conductor cable could be used for feeding two circuits on split phases. Transformer on the pole (or in the ground) is used as shown in Tester101's diagrams. However, you must be sure that the breakers in the panel are on two different phases. Generally breakers that are adjacent to one another are on different phases but not always. Some panels have alternating phases at the top of the panel and some at the lower end adjacent breakers are the same phase. Also a dual breaker that fits in a single slot would not be on separate phases.

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The exception to this rule is harmonics. Triplet harmonics will SUM in the neutral, in a 3 phase supply. Triplets come from single phase rectifiers (eg most electronic power supplies for computers, TV's, microwaves, etc). In years gone by when there were less electronic consumer products, half size neutrals were used in 3P supplies. Today the minimum is same size neutrals, and even double size in some installations, depending on the nature of the expected load.

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There are many varieties of three and four conductor cables that have unequal size conductors for this very reason:

http://www.wireandcabletogo.com/Underground-Secondary-Distribution-Cable/

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