Page 279 - Basic Electrical Engineering

fundamental wave. The number of harmonics present in an alternating non-
sinusoidal quantity will depend upon the complexity of the wave shape. A
symmetrical wave is the one whose positive half is identical to its negative

half. Whether a wave is symmetrical or not can be tested by lifting the
negative half and shifting it to the positive half axis and placing it just over

the positive half. If both the half waves match each other, the wave shape is
symmetrical. When generators are built physically symmetrical, the EMF

wave shape induced in the coils in such machines are symmetrical in nature.
A symmetrical wave will contain fundamental and odd harmonics only. The

presence of even harmonics, i.e., 2nd harmonic, 4th harmonic, etc. will be
there in non-symmetrical, non-sinusoidal ac waves.

3.1.5 Concept of Average Value and Root Mean Square (RMS) Value of an

Alternating Quantity

For a symmetrical alternating voltage or current wave, the positive half is

identical to the negative half, and hence the average value of the quantity for
a complete cycle is zero. In earlier days the usefulness of such ac was
questioned and only dc was considered effective. However, it was observed

that when ac is allowed to pass through a resistance element, heat is
produced. The question that arose was that if the average value of an

alternating quantity is zero, why then was it producing heat. The concept of
effective value was then brought in from the point of view of heat
equivalence.

Average value

The average value of an alternating quantity is the sum of all its values

divided by the total number of values. A waveform has continuous variable
values with repeat to time, t or angle θ where θ = ωt. The pattern of wave
repeats after every cycle. The sum of all the values in a cycle is determined

by the integration of its values over a period of time. A full cycle is formed in
2π radians or in T seconds where T is the time period. A symmetrical wave is

one where the positive half cycle is exactly the same as the negative half