Phase, Reactance, Impedance, and Power Factor

 Phase of a wave is the angular displacement of a sinusoid from a reference point or time. Phase in the context of alternating current can be considered as corresponding to the angular position of the armature in the AC generator. Armature is the part which generates an electric current when it rotates in a magnetic field. Armature is made of a coil of wire wound around an iron core. Instead of the armature rotating, magnetic field can be made to rotate by rotating the permanent magnet which produces the magnetic field. The term phase is also used to denote the live wire in home electrical wiring.

Usual large generators generate alternating current with three phases so that three lines run along the high tension and low tension supply lines in addition to the ground or neutral line. Simplest way to generate three phase alternating current is by having three sets of coils in the generator, physically offset by an angle of 120 degrees to each other, which is one third of a complete 360 degrees. The three current waveforms produced by the generator will be equal in magnitude, but 120 degrees out of phase to each other. In actual practice, generators have coil numbers in higher multiples of three to generate same frequency of AC with lower number of rotations per minute (RPM).

This diagram illustrates one voltage cycle in a three phase system, which has been labeled from zero to 360 degrees along the horizontal X-axis which represents time. Expressed in radians, 360 degrees will correspond to 2π radians. Vertical Y-axis shows the change in voltage or current with respect to time. The peaks and troughs of the three phases differ by an angle of 120 degrees. The duration of each cycle will depend on the frequency of the supply, whether it is 50 or 60 Hz. The duration or period of one cycle will be 0.02 s for a 50 Hz supply.

If an alternating current is fed to a resistor, voltage and current will be in phase, meaning that they will rise and fall in the same pattern. But if it is fed to a capacitor or inductor, there will be a phase difference between the two, known as the phase angle. Phase angle can be expressed in degrees or radians. For an ideal inductor with no resistance, the current will lag the voltage by a quarter cycle or 90 degrees. This is because of the inhibitive effect of the inductance on change in current flow, causing a phase shift of the alternating current with respect to alternating voltage. In case of an ideal capacitor, it is the other way round, with the alternating current leading the voltage by a quarter cycle or 90 degrees. This is because of inhibitive effect of capacitance on change in voltage.

Reactance is the property of inductors and capacitors to reduce the flow of alternating current in a circuit, represented by the letter X. The alternating current could be of line supply, audio frequency or radio frequency. Reactance does not apply to direct current. Inductive reactance can be calculated by the formula 2πfL, where f is frequency in hertz and L the inductance in henries. Capacitive reactance is 1/(2πfC), where C is the capacitance in farads.

Impedance of a circuit represented by Z, is the sum total of contributions of resistive, capacitive and inductive elements in the circuit. But it is not a simple mathematical sum as in case of resistors connected in series. When a capacitor is placed in series with an inductor, their contributions to the total impedance of the circuit are opposite. Impedance Z = R + jX, where ‘j’ is the square root of minus one (In non-electrical formulas, it is written as ‘i’, the imaginary unit. In electrical formulas, ‘j’ is used to avoid confusion with current).

Power factor in an alternating current circuit measures how efficiently it uses the power it receives. Power factor is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit. Thus a high power factor would indicate that the power supplied to the electrical circuit is being used efficiently by the load. A power factor less than one indicates that the voltage and current are not in phase and reduces the average product of the two. For a single phase circuit, the power factor can be considered as the ratio of watts consumed by the circuit to the volt-amperes delivered to the load. Another way to calculate power factor is as the cosine of the phase angle between voltage and current. It is also the ratio of the resistance to the impedance of the circuit. A purely resistive load will have a power factor of one. As there is no reactive component in  a purely resistive load, resistance and impedance are equal.