What is the power factor in a sinusoidal AC system?

• A. φ
• B. cos φ; it's the cosine of the phase angle between voltage and current.
• C. sin φ
• D. tan φ

Answer: (B)

Power factor measures how effectively the current supplies real power to the load. In a sinusoidal system, if the voltage is v(t) = Vm cos(ωt) and the current is i(t) = Im cos(ωt − φ), the average real power is P = Vrms Irms cos φ, while the apparent power is S = Vrms Irms. Therefore, the power factor, defined as P/S, simplifies to cos φ. This means the power factor is the cosine of the phase difference between voltage and current. When they are in phase (φ = 0), the power factor is 1, indicating full active power transfer. If the current lags or leads (φ ≠ 0), the power factor drops below 1, reflecting that some of the apparent power is reactive. Sin φ would relate to reactive aspects (Q = Vrms Irms sin φ), and tan φ would relate to the ratio of reactive to real power, not the power factor itself.