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33
equal intervals is said to be periodic, and the minimum time interval elapsing before
the same instantaneous value recurs is called the periodic time or the period.
Frequency.– The number of complete cycles per second through which a voltage or
current passes is called the frequency. It is always expressed in cycles per second, the
reciprocal of this number being the periodic time.
Frequencies are now standardized for power purposes in the principal countries of the
world, the standard for Great Britain being 50 cycles per second, while the U.S.A. has
adopted 60 cycles per second.
Wave Form. – The shape of the graph of the voltage or current, when plotted against
time as a base, is called the wave form or wave shape. The ideal aimed at is that of
the sine wave*, i.e. the graph has the same shape as the graph of a sine function in
mathematics. The sine goes through 360° in a complete cycle, and so the time scale
on the wave form of a voltage or current is usually represented in degrees, 360° being
considered the equivalent of the time corresponding to 1 cycle, or the periodic time.
Since these degrees may not always coincide with the geometrical degrees through
which the rotating member of a machine has been rotated, they are called electrical
degrees, in order to distinguish them from geometrical degrees.
One cycle is thus regarded as the equivalent of 360°, and 180° is considered as a half-
cycle, i.e. the duration of the voltage or current in one direction only.
Fig. 2(a) shows the ideal wave form, which is that
of the sine wave, while Fig. 2(b) shows a non-
sinusoidal wave form. The possible
number of non-sinusoidal wave forms is infinity, some
being close approximations to the ideal sine shape, while
others are widely dissimilar.
Phase and Phase Difference. – During the interval of
time necessary for a current to pass through one complete
cycle, it passes through many phases. In fact it has a
different phase for each different interval of time.
Consider the analogous case of
the phases of the moon. Starting from the time of new
moon the, moon passes through its various phases,
measured by its age from the time of the new moon, up
to full moon, and then onwards through the various
stages of the waning moon. Similarly an alternating
current goes through various phases, starting from zero,
rising up to maximum, and dying down again to zero.
In the A.C. case, however, this comprises only half a
cycle, for the whole series
of values are then repeated in the opposite (negative) direction. Other electrical
quantities, such as voltage, power, etc., in addition to current go through various
phases from 0° to 360°; indeed all quantities which vary in a periodic manner do so.
When two voltages or two currents are considered together, however, or when a
voltage and current are considered simultaneously, the frequency being the same,
Fig. 2. Examples of
Wave Form.
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