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# Module 5.3

# Phasor Diagrams

**After studying this section, you should be able to:**- • Use Phasor Diagrams to Show Phase Difference.
- • Draw Phasor Diagrams.

## Phasor Diagrams Show Phase Difference

A phasor diagram is used to show the phase relationships between two or more sine waves having the same frequency. Section 5.2 showed a phasor continually rotating, but in use phasor diagrams are static. Imagine that the phasors are rotating in an anticlockwise (counter clockwise) direction.

Every phasor in the diagram will have the same angular velocity because they represent sine waves of identical frequency. The length of the each phasor arm is directly related to the amplitude of the wave it represents, and the angle between the phasors is the same as the angle of phase difference between the sine waves.

### Fig 5.3.1 Showing Phase Relationship with Phasors

Fig 5.3.1 shows how a phasor diagram is used to illustrate the phase difference between waves 1 and 2. In this animation however, you can choose the phase relationship simply by moving the slider control.

The main value of phasor diagrams is that they can be used, not only to represent waveform diagrams, but also in carrying out calculations involving ac waves. The calculations can involve any of the common values (RMS, peak values, phase angles etc.) and will be much quicker and easier than performing the calculations on waveform diagrams.

It can be seen from Fig 5.3.1 that the waveform diagrams can be represented in phasor form without any loss of information. Phasors can be used to calculate unknown values in different types of circuits where capacitors, resistors and inductors may be connected in series or in parallel to achieve different effects, provided some basic rules are followed.

### Five Rules for Drawing Phasor Diagrams.

Rule 1. The length of the phasor is directly proportional to the amplitude of the wave depicted.

Rule 2. In circuits which have combinations of L, C & R in SERIES (studied in AC Theory, Module 9)

it is customary to draw the phasor representing CURRENT horizontally, and call this the REFERENCE phasor. This is because the current in a series circuit is common to all the components.

Rule 3. In parallel circuits, where L, C and R are connected in parallel,(studied in AC Theory, Module 10)

The phasor representing the SUPPLY VOLTAGE is always drawn in the REFERENCE direction. This is because in a parallel circuit it is the supply voltage that is common to all components.

Rule 4. The direction of rotation of all phasors is considered to be ANTICLOCKWISE.

Rule 5. In any one diagram, the same type of value (RMS, peak etc.) is used for all phasors, not a mixture of values.

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