# Power in AC Circuit: The Power Factor

The power is defined as the rate at which work is being in the circuit.

The average power in an AC circuit,

Pav = Vrms  irms  cos θ

= \frac{V}{\sqrt{2}} \frac{i}{\sqrt{2}} \cos \theta = \frac{Vi}{2} \cos \theta

Where \cos \theta = \tt \frac{Resistance (R)}{Impedance (Z)} is called the power factor of AC Circuit.

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A voltage v = vm sin ωt applied to a series RLC circuit drives a current in the circuit given by i = im sin (ωt + Φ) where
i_{m} = \frac{v_{m}}{Z} \ {\tt and} \ \phi = \tan^{-1} \frac{X_{C} - X_{L}}{R}