Final answer:
The average power factor often taken for calculations is 0.85. It measures the efficiency of power conversion in an AC circuit, with values closer to 1 indicating higher efficiency; at resonance, the power factor is 1.
Step-by-step explanation:
The average value often taken for the power factor in making calculations is 0.85. This value is commonly used because it falls within the typical range of 0.70 to 1.00 lagging power factors found in many electric power systems and represents a conservative average that allows for simplified calculations in the absence of more specific data.
The power factor is defined as the cosine of the phase difference between the voltage and the current in an AC circuit, and it essentially measures how effectively the circuit is converting electric power into useful work output. A power factor closer to 1 indicates a more efficient circuit where most of the power is being used to do work, while a lower power factor indicates a less efficient circuit with more power being wasted. Engineers often aim for a power factor as close to 1 as possible to reduce losses and improve system efficiency.
For instance, when calculating the average power (Pave) delivered to an RLC circuit, you use the formula Pave = Irms Vrms cos ϕ, where ϕ is the phase angle between the voltage and current, and cos ϕ is the power factor. At the resonant frequency of the RLC circuit, the power factor is 1 since the voltage and current are in phase.