In three-phase calculations, what factor is used to convert line current to feeder current?

In three-phase calculations, what factor is used to convert line current to feeder current?

• A. 1.0
• B. 1.732
• C. 3.0
• D. 0.577

Answer: (B)

In a balanced three-phase system, the three phase currents are equal in magnitude and 120 degrees apart. The feeder current that carries all three phases is basically the vector sum of those three currents. When you do that vector sum, the resulting magnitude is √3 times the current of one line. That’s why the factor used to convert line current to feeder current is √3 (approximately 1.732). For context, this same √3 factor appears in power calculations as S = √3 V_L I_L, which reflects the same phasor geometry. (If you were converting in a delta connection from line current to phase current, you’d use 1/√3, about 0.577, but for converting line current to feeder current in a balanced 3-phase feeder, the factor is √3.)

In a balanced three-phase system, the three phase currents are equal in magnitude and 120 degrees apart. The feeder current that carries all three phases is basically the vector sum of those three currents. When you do that vector sum, the resulting magnitude is √3 times the current of one line. That’s why the factor used to convert line current to feeder current is √3 (approximately 1.732).

For context, this same √3 factor appears in power calculations as S = √3 V_L I_L, which reflects the same phasor geometry. (If you were converting in a delta connection from line current to phase current, you’d use 1/√3, about 0.577, but for converting line current to feeder current in a balanced 3-phase feeder, the factor is √3.)