This is where semantics count
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If you run "a ground" per NEC definition I guess that means you are filling your conduit with soil
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(NEC: Ground= earth). If you are installing an equipment ground
ing conductor, that conductor would need to be taken into account as number of conductors allowed in the conduit, but would not be taken into account for derating. If you are installing a ground
ed conductor it might or might not be taken into account in derating.
Jumper (Derek) has a very nice explanation chart:
Here's some examples of when to count the neutral as a CCC:
208Y/120 volt system-different circuit types:
A)- 2 wire circuit w/ 1 ungrounded, 1 neutral = 2 CCC's
B)- 3 wire circuit w/ 2 ungrounded, 1 neutral = 3 CCC's
C)- 4 wire circuit w/ 3 ungrounded, 1 neutral = 3 CCC's*
Notes:
A)- A normal 2 wire circuit has equal current flowing in each of the circuit conductors so they both count as CCC's.
B)- In this circuit the neutral current will be nearly equal to the current in the ungrounded conductors so the neutral counts as a CCC
C)- In this circuit the neutral will only carry the imbalance of the current between the three ungrounded conductors so it is not counted as a CCC, with one exception, *if the current is more than 50% nonlinear then the neutral would count as a CCC.
120/240 volt system-different circuit types:
D)- 2 wire circuit w/ 1 ungrounded, 1 neutral = 2 CCC's
E)- 3 wire circuit w/ 2 ungrounded, 1 neutral = 2 CCC's
Notes:
D)- A normal 2 wire circuit has equal current flowing in each of the circuit conductors so they both count as CCC's.
E)- In this circuit the neutral will only carry the imbalance between the two ungrounded conductors so the neutral is not counted as a CCC.