In the same delta-connected system, how are line current and phase current related?

In the same delta-connected system, how are line current and phase current related?

• A. I_line = √3 I_phase
• B. I_line = I_phase
• C. I_line = I_phase / √3
• D. I_line = 3 I_phase

Answer: (C)

In a delta-connected system, the current in each line is the phasor sum of the two currents in the adjacent delta legs. For a balanced delta, those two leg currents are 60 degrees apart, so their vector sum has a magnitude of √3 times the magnitude of either leg current. That means the line current is √3 times the phase (branch) current, with a 30-degree phase difference between them. So the correct relationship is I_line = √3 I_phase, unlike the equal or smaller multiples you might see in other configurations.

In a delta-connected system, the current in each line is the phasor sum of the two currents in the adjacent delta legs. For a balanced delta, those two leg currents are 60 degrees apart, so their vector sum has a magnitude of √3 times the magnitude of either leg current. That means the line current is √3 times the phase (branch) current, with a 30-degree phase difference between them. So the correct relationship is I_line = √3 I_phase, unlike the equal or smaller multiples you might see in other configurations.