What I don't understand is why each hot wire is allowed to carry x amps of current, but the single neutral is allowed to carry 2x amps of current, the current carried simultaneously by both hot wires.
The neutral doesn't carry 2x the amps, it only carries the differential (difference) between the two circuits.
What makes this work is, THE TWO CIRCUITS MUST BE ON DIFFERENT LEGS WHICH MEANS THERE MUST BE 240 VOLTS ACROSS THE TWO CIRCUITS AND NOT 0 VOLTS. In this configuration the neutral only carries the difference. If one leg is pulling 15 amps and the other leg is pulling 13 amps, the neutral will see 2 amps. (The two circuits push/pull amps to/from each other.)
If the two circuits are on the same leg, then the neutral will carry the sum amps of the two circuits. This is dangerous and against code because the neutral will be undersized.
If wired correctly, it is completely legal and safe.
The downside to this "Edison circuit" (or multi-wire branch), is:
You are "sharing" the neutral which will trip GFCI and AFCI devices.
Does not save you very much money/labor vs running a second Romex.
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