Exam Question

### Principle and Concept
In a balanced 3-phase, 4-wire system, the vector sum of the three phase currents is zero, and therefore, no current flows in the neutral wire. However, when the loads are unbalanced (i.e., different magnitudes or power factors), the vector sum of the phase currents is not zero. The neutral wire provides a return path for this resultant current, known as the neutral current ($$I_n$$).
The neutral current is the phasor sum of the three line currents. By Kirchhoff's Current Law applied at the neutral point, the sum of currents entering the node is zero:
$$ \vec{I_r} + \vec{I_y} + \vec{I_b} + \vec{I_n} = 0 $$