In the power formula P = √3 V_L I_L cosφ, cosφ represents what electrical quantity?

In the power formula P = √3 V_L I_L cosφ, cosφ represents what electrical quantity?

• A. Power factor
• B. Voltage magnitude
• C. Current magnitude
• D. Impedance

Answer: (A)

Cosφ is the power factor, the cosine of the phase angle between voltage and current in an AC system. In a balanced three‑phase circuit, real power P equals √3 V_L I_L cosφ because only the in‑phase component of voltage and current does useful work. When the load is purely resistive, φ is zero and cosφ equals one, so all the apparent power √3 V_L I_L becomes real power. When inductive or capacitive elements cause a phase difference, cosφ is less than one (and can even be negative in some conditions), meaning not all of the apparent power is doing real work—the rest is reactive power circulating between the source and the energy-storage elements.

Cosφ is the power factor, the cosine of the phase angle between voltage and current in an AC system. In a balanced three‑phase circuit, real power P equals √3 V_L I_L cosφ because only the in‑phase component of voltage and current does useful work. When the load is purely resistive, φ is zero and cosφ equals one, so all the apparent power √3 V_L I_L becomes real power. When inductive or capacitive elements cause a phase difference, cosφ is less than one (and can even be negative in some conditions), meaning not all of the apparent power is doing real work—the rest is reactive power circulating between the source and the energy-storage elements.