Apparent Power and Power Factor

Apparent Power

The apparent Power ( in VA) is the product of the rms values of voltage and current. It is measured in colts-amperes or VA to distinguish it form the average power, which is measured in watts. 
Apparent power is a measure of alternating current (AC) power that is computed by multiplying the root-mean-square (rms) current by the root-mean-square voltage. In a direct current (DC) circuit, or in an AC circuit whose impedance is a pure resistance, the voltage and current are in phase.

Power Factor

The power factor is the cosine of the phase difference between voltage and current. It is the cosine of the angle of the load impedance.
 The power factor is the ratio of the real power that is used to do work and the apparent power that is supplied to the circuit. The power factor can get values in the range from 0 to 1.

In sinusoidal, power factor is

• θ - ϕ is the angle the voltage leads the current: PF angle

MAXIMUM AVERAGE POWER TRANSFER

A simple loop circuit used to illustrate the derivation of the maximum power transfer theorem as it applies to circuits operating in the sinusoidal steady state.

  

To get the maximum average power transferred from a source to a load, the load impedance should be equal to the conjugate of the Thevenin equivalent impedance of the network or circuit.

Instantaneous and Average Power

Instantaneous Power

Instantaneous power p(t) absorbed by an element is the product of the instantaneous voltage v(t) across the element and the instantaneous current i(t) through it.

This definition of instantaneous power is valid for signals of any waveform.

From the formula above, this shows us that the instantaneous power has two parts. The first part is constant or time independent. Its value depends on the phase difference between the voltage and current. The second part is a sinusoidal function whose frequency is 2ω, which is twice the angular frequency of the voltage or current.

Average Power

P can be defined in two ways: as the real part of the complex power or as the simple average of the instantaneous power. The second definition is more general because with it we can define the instantaneous power for any signal waveform, not just for sinusoidal.

The instantaneous power changes with time and therefore difficult to measure. The average power is more convenient to measure.

NOTE: A resistive load absorbs power at all times, while a reactive load ( L or C) absorbs zero average power.