In a three-phase system, the expression S = √3 V_L I_L is used to determine which quantity?

In a three-phase system, the expression S = √3 V_L I_L is used to determine which quantity?

• A. Real power
• B. Reactive power
• C. Apparent power
• D. Power factor

Answer: (C)

In a balanced three-phase system, the total power that appears as a combination of real and reactive parts is captured by the apparent power. The quantity S represents the magnitude of the complex power P + jQ, and when you’re using line values, it simplifies to S = √3 V_L I_L. This is because P = S cos φ and Q = S sin φ, where φ is the angle between voltage and current (the power factor angle). The expression √3 V_L I_L does not include the cos φ or sin φ terms, so it gives the apparent power, not the real or reactive components. If you used phase quantities instead, you'd have S = 3 V_Ph I_Ph, which is consistent for a balanced system.

In a balanced three-phase system, the total power that appears as a combination of real and reactive parts is captured by the apparent power. The quantity S represents the magnitude of the complex power P + jQ, and when you’re using line values, it simplifies to S = √3 V_L I_L. This is because P = S cos φ and Q = S sin φ, where φ is the angle between voltage and current (the power factor angle). The expression √3 V_L I_L does not include the cos φ or sin φ terms, so it gives the apparent power, not the real or reactive components. If you used phase quantities instead, you'd have S = 3 V_Ph I_Ph, which is consistent for a balanced system.