In a balanced three-phase system, which expression gives the total apparent power S?

In a balanced three-phase system, which expression gives the total apparent power S?

• A. S = √3 V_Ph I_Ph
• B. S = 3 V_Ph I_Ph
• C. S = √3 V_L I_L
• D. S = V_L I_L / √3

Answer: (C)

In a balanced three-phase system, the total apparent power is the sum of the powers in all three phases, and using line quantities gives a convenient compact form: S = √3 V_Line I_Line. This works because the line-to-line voltage is related to the phase voltage by V_Line = √3 V_Phase, and the line current relates to the phase current in a way that keeps the total S consistent across connection types. Equivalently, you can express the same total apparent power using phase quantities as S = 3 V_Phase I_Phase. Both forms describe the same power, just in terms of different measured quantities. The line-quantity form is especially convenient for practical measurements, which is why it’s the commonly used expression. The other options either miss the correct factor or mix line and phase quantities in a way that does not yield the total S in general.

In a balanced three-phase system, the total apparent power is the sum of the powers in all three phases, and using line quantities gives a convenient compact form: S = √3 V_Line I_Line. This works because the line-to-line voltage is related to the phase voltage by V_Line = √3 V_Phase, and the line current relates to the phase current in a way that keeps the total S consistent across connection types.

Equivalently, you can express the same total apparent power using phase quantities as S = 3 V_Phase I_Phase. Both forms describe the same power, just in terms of different measured quantities. The line-quantity form is especially convenient for practical measurements, which is why it’s the commonly used expression. The other options either miss the correct factor or mix line and phase quantities in a way that does not yield the total S in general.