In a Y-connected circuit, how does the magnitude of each line current relate to the corresponding phase current?

In a Y-connected circuit, the relationship between line currents and phase currents is such that the magnitude of each line current is equal to the corresponding phase current. This occurs because in a Y connection, each line current flows directly through one phase of the load without any branching or splitting at the connection point.

When you consider the phasor representation of a Y-connected system, each line current is drawn from the neutral point to each respective phase load. In mathematical terms, if you denote the phase currents as (I_a), (I_b), and (I_c) for each phase, then the line currents (I_{L_a}), (I_{L_b}), and (I_{L_c}) are equal to (I_a), (I_b), and (I_c) respectively. This leads to the conclusion that:

[ I_{L_a} = I_a ] [ I_{L_b} = I_b ] [ I_{L_c} = I_c ]

Consequently, any load changes affecting the individual phase currents will also reflect directly on the corresponding line currents, ensuring their magnitudes remain equal. This fundamental principle simplifies the calculations of current in Y-connected circuits and is pivotal