Cosphi

Cosphi, often written as cosφ, denotes the cosine of the phase angle φ between voltage and current in alternating current circuits. It is most commonly used to describe the power factor of an electrical system.

In sinusoidal steady state, voltage and current can be represented as phasors V and I with a phase difference φ. The power factor is PF = P/(VI) = cosφ, where P is real power, V is RMS voltage, and I is RMS current. The real power, reactive power Q, and apparent power S relate to cosφ by:

- P = VI cosφ

- Q = VI sinφ

- S = VI

The magnitude of cosφ lies between 0 and 1 for typical passive loads, with cosφ = 1 indicating unity power factor (a purely resistive load). If the load is capacitive, φ can be negative (current leads voltage); if inductive, φ is positive (current lags voltage). Because cosφ is symmetric with respect to the sign of φ, leading or lagging is usually described by the sign of Q rather than cosφ itself.

In practice, a high cosφ (close to 1) means more efficient use of electrical power, as less energy is wasted in reactive power. Low cosφ indicates a need for power factor correction, commonly achieved with capacitors, reactors, or other devices to reduce reactive power and improve voltage regulation and system capacity.

Cosphi also appears as a general mathematical symbol for the cosine of an angle φ in contexts beyond electrical engineering, including physics and engineering disciplines.