Fundamental Engineering Concepts - Mathematics and Statistics for the Environment - page 289

Conductors parallel to lines
of force, EMF minimum

N

N

N

Rotation

N S

I

N S

S

(c) (d) (e)

S

(b)

S

Conductors cutting directly across
field, EMF is maximum negative

(a)

Conductors cutting directly across field
EMF is maximum positive

Direction of
current flow

EMF

One alternation

(180 - 360°)

(0-180°)

Zero

One cycle

One alternation

FIGURE 11.54 Basic AC sine wave and AC generator.

The loop has now been rotated through half a circle (one alternation, or 180°). The sine curve shown
in the lower part of Figure 11.54 shows the induced voltage at every instant of rotation of the loop.
Notice that this curve contains 360°, or two alternations. Two alternations represent one complete
circle of rotation.

Note: Two complete alternations in a period is called a cycle .

In Figure 11.54, if the loop is rotated at a steady rate and if the strength of the magnetic field is
uniform, the number of cycles per second (cps), or hertz, and the voltage will remain at fixed values.
Continuous rotation will produce a series of sine-wave voltage cycles, or, in other words, an AC
voltage. In this way, mechanical energy is converted into electrical energy.

11.7.11.3 Frequency, Period, and Wavelength
The frequency of an alternating voltage or current is the number of complete cycles occurring in
each second of time. It is indicated by the symbol f and is expressed in hertz (Hz). One cycle per
second equals 1 hertz; thus, 60 cycles per second (cps) equals 60 Hz. A frequency of 2 Hz (Figure
11.55A) is twice the frequency of 1 Hz (Figure 11.55B). The amount of time for the completion
of 1 cycle is the period . It is indicated by the symbol T for time and is expressed in seconds (sec).
Frequency and period are reciprocals of each other:

1 Hz 2 Hz

e or i e or i

+ +

Time, s

0 Time, s 0

1
4

1
2

3
4

1

1
4

1
2

3
4

1

(A) (B)

_ -

FIGURE 11.55 Comparison of frequencies.