Power in AC Circuits

 

Power in AC Circuits

Definition:
The power in an AC circuit is made up of:

• Active Power (P): The actual power consumed by resistive elements, measured in watts (W).
• Reactive Power (Q): The power stored and returned by reactive elements like capacitors and inductors, measured in volt-amperes reactive (VAR).

The total power is represented as apparent power (S), measured in volt-amperes (VA).

$$S = P + jQ$$

Example:
For an AC circuit with voltage $V = 100V$, current $I = 5A$, and a phase angle $\theta = 30^\circ$, the active and reactive power can be calculated as:

$$P = VI \cos \theta = 100 \times 5 \times \cos 30^\circ = 433W$$ $$Q = VI \sin \theta = 100 \times 5 \times \sin 30^\circ = 250VAR$$