Why is the factor 1.73 used when solving for kW in a three-phase circuit?

Why is the factor 1.73 used when solving for kW in a three-phase circuit?

• A. Because it is the square root of 3 used to obtain the average across all phases.
• B. It is a constant used to convert line-to-line voltage to line-to-neutral voltage.
• C. It is a rounded value of pi used in power calculations.
• D. It is an efficiency factor for three-phase systems.

Answer: (A)

The 1.73 comes from the relationship between line and phase quantities in a balanced three-phase system. Real power in a three-phase circuit can be written as P = 3 V_Ph I_Ph cosφ. In a wye (star) connection, the line voltage V_L is √3 times the phase voltage V_Ph, and the line current I_L equals the phase current I_Ph. Substituting V_Ph = V_L/√3 and I_Ph = I_L gives P = 3 (V_L/√3) I_L cosφ = √3 V_L I_L cosφ. Since √3 is about 1.732, we use the factor 1.73 when calculating kilowatts from line voltage, line current, and power factor. This reflects the geometric relationship of the three phase voltages, not an efficiency or pi-based constant. It’s valid for balanced loads; unbalanced cases require per-phase calculations.

The 1.73 comes from the relationship between line and phase quantities in a balanced three-phase system. Real power in a three-phase circuit can be written as P = 3 V_Ph I_Ph cosφ. In a wye (star) connection, the line voltage V_L is √3 times the phase voltage V_Ph, and the line current I_L equals the phase current I_Ph. Substituting V_Ph = V_L/√3 and I_Ph = I_L gives P = 3 (V_L/√3) I_L cosφ = √3 V_L I_L cosφ. Since √3 is about 1.732, we use the factor 1.73 when calculating kilowatts from line voltage, line current, and power factor. This reflects the geometric relationship of the three phase voltages, not an efficiency or pi-based constant. It’s valid for balanced loads; unbalanced cases require per-phase calculations.