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Generation of Alternating EMF's

A voltage can be developed in a coil of wire in one of the three ways:
1. By changing the flux through the coil.
2. By moving the coil through the magnetic field.
3. By altering the direction of the flux with respect to the coil.

The first one is that voltage is said to be induced emf and in accordance with Faraday's law, its magnitude at any instant of time is given by the formula as shown below:

e = N(dΦ/dt) x 10 -8 volts

where N is the number turns in a coil
dΦ/dt = rate at which the flux in maxwells changes through the coil

Please take note that in this method of developing an emf, there is no physical motion of coil or magnet; the current through the exciting coil that is responsible for the magnetism is altered to change the flux through the coil in which the voltage is induced. For the second and third method mentioned above, there is actual physical motion of coil or magnet, and in altered positions of coil or magnet flux through the coil changes. A voltage developed on these ways is called a generated emf and is given by the equation:

e = Blv x 10-8 volts

where B is the flux density in lines per square inch
l is the length of the wire, in., that is moved relative to the flux
v is the velocity of the wire, in.per sec., with respect to the flux

Two-pole single AC Generator
The figure above illustrates an elementary a-c generator. The single turn coil may be moved through the magnetic field created by two magnet poles N and S. As you can see, the ends of the coil are connected to two collectors upon which two stationary brushes rest on it. For the clockwise rotation as shown, the side of the coil on north pole N is moving vertically upward to cut the maximum flux under north pole N, while the other side of the coil on south pole S is moving vertically downward to cut the maximum flux under south pole S. After the coil is rotated one quarter of a revolution to the position as shown below:

Rotated 90 degree
the coil sides have no flux to be cut and no voltage is generated. As the coil proceeds to rotate, the side of the coil on south pole S will cut the maximum flux on north pole N. Then, the side of the coil previously on north pole N will cut the maximum flux on south pole S. With this change in the polarity that are cut by the conductors, reversal in brush potential will occur. There are two important points that would like to emphasize in connection with the rotation of the coil of wire through a fixed magnetic field:

1. The voltage changes from instant to instant.
2. The electrical polarity (+) and minus (-) changes with alternating positions under north and south poles.

In actual, ac generator rotate a set of poles that is placed concentrically within a cylindrical core containing many coils of wires. However, a moving coil inside a pair of stationary poles applies equally well to the rotating poles construction; in both arrangements there is a relative motion of one element with respect to the other.
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