Frequency

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Frequency
The number of cycles per second made by voltage induced in
the armature is the frequency of the generator. If the armature
rotates at a speed of 60 revolutions per second, the generated
voltage will be 60 cycles per second. The accepted term for
cycles per second is hertz. The standard frequency in the United
States is 60 hertz. The following illustration shows 15 cycles in
1/4 second which is equivalent to 60 cycles in one second

Four-Pole AC Generator

The frequency is the same as the number of rotations per
second if the magnetic field is produced by only two poles.
An increase in the number of poles, would cause an increase
in the number of cycles completed in a revolution. A two-pole
generator would complete one cycle per revolution and a four pole
generator would complete two cycles per revolution. An
AC generator produces one cycle per revolution for each pair of
poles.

Voltage and Current

The sine wave illustrates how voltage and current in an AC
circuit rises and falls with time. The peak value of a sine wave
occurs twice each cycle, once at the positive maximum value
and once at the negative maximum value

The value of the voltage or current between the peak positive
and peak negative values is called the peak-to-peak value

The instantaneous value is the value at any one particular time.
It can be in the range of anywhere from zero to the peak value

The voltage waveform produced as the armature rotates
through 360 degrees rotation is called a sine wave because
instantaneous voltage is related to the trigonometric function
called sine (sin θ = sine of the angle). The sine curve represents
a graph of the following equation

e = Epeak x sin θ

Instantaneous voltage is equal to the peak voltage times the
sine of the angle of the generator armature. The sine value is
obtained from trigonometric tables. The following table reflects
a few angles and their sine value

The following example illustrates instantaneous values at 90,
150, and 240 degrees. The peak voltage is equal to 100 volts.
By substituting the sine at the instantaneous angle value, the
instantaneous voltage can be calculated

Any instantaneous value can be calculated. For example

240°
e = 100 x -0.866
e = -86.6 volts

Alternating voltage and current are constantly changing values.
A method of translating the varying values into an equivalent
constant value is needed. The effective value of voltage and
current is the common method of expressing the value of AC.
This is also known as the RMS (root-mean-square) value. If the
voltage in the average home is said to be 120 volts, this is the
RMS value. The effective value figures out to be 0.707 times
the peak value

 

The effective value of AC is defined in terms of an equivalent
heating effect when compared to DC. One RMS ampere of
current flowing through a resistance will produce heat at the
same rate as a DC ampere