## Alternating Current

# 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,

*P*_{av }= *V*_{rms }*i*_{rms }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.

### View the Topic in this video From 31:38 To 59:00

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A voltage *v* = *v _{m}* sin ω

*t*applied to a series

*RLC*circuit drives a current in the circuit given by

*i*=

*i*sin (ω

_{m}*t*+ Φ) where

i_{m} = \frac{v_{m}}{Z} \ {\tt and} \ \phi = \tan^{-1} \frac{X_{C} - X_{L}}{R}