A little clarification here:
Typical US 120/240Vac residential power is termed "split phase". The POCO service drop to your house from the secondary side of a center-tapped pole transformer consists of 4 wires. There are two legs (L1 and L2), which are 180 degrees out of phase with each other, and are connected to the "ends" of the transformer secondary winding. Then there is the neutral (N), sourced at the center tap of the transformer secondary winding. And finally there is ground (G).
Due to the 180 degree phase difference between L1 and L2, the following voltages result:
L1<->L2 = 240Vac
L1<->N = 120Vac
L2<->N = 120Vac
In a residential circuit breaker panel, every other breaker location is on the same leg (either L1 or L2). Ergo, a double-width breaker picks up both L1 and L2, and is thus used for a 240Vac branch circuit (and also used for an MWBC but that is another topic altogether).
The primary advantage of split phase power distribution is reduction in the amount of copper (or aluminum) needed in the service drop. For a given amount of power delivered to the residence, split phase minimizes the aggregate size of the conductors and therefore the overall amount of (expensive) conductor material required.
This is because with split phase power, the N carries only the *difference* between the L1 and L2 currents, and not the *sum* of the L1 and L2 currents. In other service drop schemes, the N would have to carry the total current sourced by L1 and L2, and the result would be that the size of the N conductor would have to be increased accordingly.
As you can see by inspection of your home's service drop, the L1, L2, and N conductors are all the same gauge. As noted above, this is the beneficial side effect of split phase power distribution. At worst case for the N conductor, L1 = I(max), L2 = 0, and therefore N = I(max). Otherwise, current in the N conductor is L1-L2, and lower. You can see by extension that when the total load on the residence is at it's maximum, the N carries no current.
It may also be useful to understand what is meant by "100A service" (or insert your residential service drop ampacity, which could be 150A, or 200A, et, in the example).
This term of "100A" means you can draw 100A x 240Vac = 24,000W from the utility service drop. (Which, by the way, is a lot!)
You can split up this power however you need in terms of the voltages, but you can not exceed the maximum above, nor can you exceed 100A at 120Vac on either L1 or L2.
Example:
30A at 240Vac = 7200W
50A at 120Vac = 6000W on L1
60A at 120Vac = 7200W on L2
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Total 20,400W
ps:
In the example above, the N conductor is carrying 10A.
Wrooster