In the three-phase power equations, which statement correctly describes the use of the angle φ for real and reactive power?

• A. P uses cosφ, Q uses sinφ
• B. P uses sinφ, Q uses cosφ
• C. P uses tanφ, Q uses cotφ
• D. P uses cosφ, Q uses cosφ

Answer: (A)

The angle φ is the phase difference between voltage and current, so real power comes from the part of the voltage–current product that lies in phase with the voltage, while reactive power comes from the part that is 90 degrees out of phase. When you break the power into these two components, you project onto the in-phase axis and the quadrature axis. Those projections use cosine for the in-phase (real power) and sine for the out-of-phase (reactive power): P = VI cosφ and Q = VI sinφ. In a balanced three-phase system with line values, this becomes P = √3 V_L I_L cosφ and Q = √3 V_L I_L sinφ. So the real power depends on cosφ and the reactive power on sinφ. For example, φ = 0° gives maximum P and zero Q, while φ = 90° gives zero P and maximum Q. The other options would misassign these relationships or use inappropriate ratios, which doesn’t match how the phasor components project onto the in-phase and quadrature axes.