Write value of neutral current and neutral voltage in balanced load
Answers
Every other answer that says zero amperes or no current is partially correct and partially incorrect.
One dependency is whether that three phase circuit is a delta-connected system, or a wye-connected system.
In a wye system, if the current load is equal on each of the three phases, AND the power factor is zero, the neutral load should be zero.
But in a delta connected system, you can have equal loads on the three phases PLUS a load on the high leg that returns via the neutral. Then you have a current on the neutral, even though the current on each of the three phase legs is the same.
The second dependency is power factor. If you have multiple single-phase loads with power factors other than zero (where the current waveform does not exactly track the voltage waveform) on your three phase circuit, then you can indeed have a current on the neutral conductor even when the current on each of the phase conductors is equal. This is a common problem with switched-mode power supplies, and can require a neutral conductor be sized LARGER than the phase conductors in a circuit. (Look up triplen harmonics.)
If the question is from your engineering homework or exam, the other answers are probably what your instructor is looking for. These issues where the neutral current could be something else will likely be covered in advanced electrical engineering classes. (And if they aren't, they should be.)
P.S. — If you copy this answer verbatim, your instructor will ask you to prove it mathematically. I can't help you there!
One other thing: the answers that say “zero volts” are completely incorrect, because the question was about current, which is measured in amperes, not voltage, which is measured in volts.