1. Power Factor
The power factor (i-e.cos fi) of a circuit can be defined in one of the following ways:
Power factor= Cos fi= ciosine of angle b/w V & I
Power factor = R / Z = Resistance / Impedance
Power Factor = VI cos fi / VI = True power / Apparent power
For example, in a resistor, the current & voltage are in phase i.e. fi = 0 degree.
Therefore, power factor of a pure resistive circuit is cos 0 degree = 1.
Similarly, phase difference b/w voltage & currentin a pure inductance or capacitance is 90 degree.
Hence power factor of pure L or C is zero.

2. This is the reason that power consumed by pure L or C is zero.
For a circuit having R, L & C is varying proportions, the value of power factor will lie b/w 0 & 1.
It may be noted that power factor can never have value greater than 1.
It is a usual practice to attach the word ‘lagging or leading ‘with the the numerical value of power factor to signify wether the current lags or leads the voltage.thus if a circuit has a p.f of 0.5 & the current lags the voltage, we generally write p.f as 0.5 lagging.
Sometimes p.f is experesed as a percentage. Thus 0.8 lagging p.f may be expressed as 80 % lagging.

3. True power & Reactive power
The purpose of passing current through a circuit is to transfer power from the source to the circuit.
The power which is actually consumed in the circuit is called true power or active power.
As power is consumed only in resistance since neither pure inductor nor the capacitor consumes any active power.
The power consumed ( or true power ) in L & C is zerob/c all the power received from the sourcein one-quarter cycle is returned to the sourcein the next-one quarter cycle. This circulating power is called the reactive powerand does no useful work in the circuit.

4. As the current & voltage are in phase in a resistance where as they are 90 degree out of phase in L & C. Therefore, we come to the conclusion that I in phase with voltage produces true or active power whereas current 90 degree out of phase with voltage contributes to reactive power, i.e;
True power = V * I in phase with voltage
Reactive power = V * I 90 degree out of phase with voltage.
Consider an inductive circuit in which I lags behind the applied voltage V by fi degree.
The current I can be resolved into two rectangular components viz,
I cos fi in phase with V and
I sin fi; 90 degree out of phase with V.

5. True power, P = V. I cos fi watts or KW Reactive power, Q = V
True power, P = V * I cos fi watts or KW Reactive power, Q = V*I sin fi VAR or KVAR Apparent power, S = V * I = VI VA or KVA