AC FUNDAMENTALS – PART – 03 – REPRESENTATION OF AC QUANTITIES

SCALAR

Some physical quantities are described completely by a single number with a unit, examples are temperature, density and quantity of electric discharge.

VECTOR

Many other quantities have both magnitude and direction, examples are velocity, force and displacement.

PHASORS

In the theory of electric circuits, voltages and current can be represented in the complex plane by radius vectors characterized by a magnitude and phase with respect to a reference angle. Such radius vectors representing complex numbers are called phasors.

[OR]

A sinusoidal quantity may be represented by a line fixed at one end and rotating counterclockwise at a velocity equal to the angular velocity (ω rad/s) of the sinusoidal quantity. This rotating line is called the phasor.

Phasor is a complex quantity while a vector is a simple quantity. Phasors are actually moving with time. By convection, phasors are assumed to rotate in a counterclockwise direction.

REFERENCE PHASOR

Since the phase difference remains constant, any phasor may be drawn along the convenient direction. This phasor will be called a reference phasor.  The position of other phasors relative to the reference phasor becomes fixed.

PHASE – The orientation of a rotating vector in space at any particular instant is called its ‘phase’.

If we are considering a single rotating vector, we are not concerned with its phase; but if there are two or more rotating vectors then the difference between their orientations is extremely important.

The phase angle is taken positive when measured counter clockwise and negative in the clockwise direction. The angular position of the phasor represents a position in time, not space.

PHASE DIFFERENCE – It is an angular displacement of ɸ will remain constant as the two vectors rotate in space. The angle ɸ is called phase difference.

PHASOR DIAGRAM

The graphic representation of the phasors of sinusoidal quantities taken all at the same frequency and with proper phase relationships with respect to each other is called phasor diagram.

It is a common practice to draw the phasor diagrams in terms of effective value (RMS value) rather than maximum values.

LIMITATIONS OF PHASOR DIDAGRAMS

1. A phasor represents only one position (per cycle) of the waveform and therefore it does not give a complete description of a sinusoidal quantity.

2. A phasor diagram is drawn to represent phasors at one frequency only.

METHODS OF RESPRESENTATION OF SINUSOIDAL WAVEFORM

1. Mathematical equation

2. Waveform representation

3. Phasor representation