Originally Posted by Bob NH
The basis for the code permitting the "unbalanced load only neutral" to be neglected when using a multiwire branch circuit, or any other case where the neutral carries only the unbalanced load, is that the sum of the
(current squared) values for all of the conductors in the circuit (and therefore the heating) never exceeds the (current squared) value for the ungrounded conductors with balanced load.
For example, it you have a 20 Amp MWBC with balanced load the sum of the
(current squared) = 20x20 + 20x20 + 0x0 = 800 Amps squared.
If there is an unbalanced load, such as 20 Amps on one conductor and 5 Amps on the other, then the sum of the (current squared) = 20x20 + 5x5 +15x15 = 650 Amps Sqaured.
e57 said:
You had me until the parts in red....
The basis for limiting the number of current carrying conductors in a raceway is to limit the heating, which is a result of the power dissipated in the conductors.
The power dissipated in a conductor is: Power = (current sqaured) x Resistance.
Now consider a MWBC of #12 with 20 Amp breakers, and let's calculate the power dissipated in the three conductors for various current conditions. Because the resistance of each conductor is the same and the length is the same we can disregard the actual resistance and calculate the (current squared) = (Amps x Amps) for each of the 3 conductors in the MWBC and add them together. The largest number is the one that provides the greatest heating.
Case 1: First let's take the CODE case of maximum current in each of the ungrounded conductors; which results in zero current in the neutral.
Case 1: Total Amps Squared = 20 x 20 + 20 x 20 + 0 x 0 = 400 + 400 + 0 = 800 Amps squared.
Case 2: 20 Amps in one ungrounded and therefore 20 Amps in the neutral
20 x 20 + 0 x 0 + 20 x 20 = 800 Amps squared.
Case 3: 20 Amps in one ungrounded conductor and10 Amps in the other ungrounded conductor, and therefore 10 Amps in the neutral.
20 x 20 + 10 x 10 + 10 x 10 = 400 + 100 + 100 = 600 Amps squuared.
This is the case with minimum heating when ONE of the ungrounded conductors is carrying 20 Amps. I won't try to show the differential calculus here.
Case 4: 20 Amps in one ungrounded conductor and 15 Amps in the other ungrounded conductor, and therefore 5 Amps in the neutral.
20 x 20 + 15 x 15 + 5 x 5 = 400 + 225 + 25 = 650 Amps squared.
CONCLUSION:
The code permits conductors that carry only the unbalanced portion of the load to be neglected because all cases with an unbalanced load resulting in current in the neutral dissipate LESS ENERGY IN THE CIRCUIT CONDUCTORS than the code case of maximum load in the ungrounded conductors.