Power in AC Circuits

Introduction

The rate of doing work or the amount of energy transferred by an electrical circuit per unit time is known as electrical power. In AC circuits, power is used to calculate the total power required to supply a load. In a DC circuit, the power consumed is simply the product of the DC voltage and DC current, expressed in watts. However, in AC circuits containing reactive components, the calculation of power becomes more complex.

Power in DC Circuits

In DC circuits, voltage and current remain constant with time. Therefore, power calculation is straightforward.

Electrical Power:

P = V × I = V² / R = I² × R (Watts)

Where:

V = DC voltage
I = DC current
R = Resistance

Power exists in a circuit only when both voltage and current are present. Therefore, there is no power consumption under open-circuit or no-current conditions.

In AC circuits, voltage and current vary continuously with time due to the sinusoidal nature of the AC supply. As a result, the instantaneous values of voltage, current, and power are constantly changing. The amount of power at any instant of time is called instantaneous power. It is given by the well-known relationship:

p = v × i

where v is the instantaneous voltage and i is the instantaneous current.

Effect of Reactance in AC Circuits

AC circuits often contain reactive components such as inductors and capacitors. These components introduce reactance, which causes a phase difference between voltage and current. Due to this phase difference, a portion of power is alternately stored and returned to the supply in the form of magnetic and electric fields during each cycle of the AC waveform. Unlike purely resistive circuits, this stored energy does not perform useful work but circulates between the source and the reactive components.

Average Power in AC Circuits

The average power absorbed by an AC circuit is defined as the average value of the instantaneous power over one complete cycle. Since the AC waveform is periodic and continuous, the average power over one cycle is the same as the average power over any number of cycles. Therefore, the average power consumption of an AC circuit is determined by averaging the instantaneous power over a full cycle of the waveform.