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An electric generator converts mechanical energy into electrical energy in the form of voltage and current in a conducting circuit.

A generator contains mainly a stator, a rotor, load (resistance or the consumers network).  In the stator, there is a strong permanent magnet with a cylindrical vacant space between the two poles North and South.

There is a rotor in the air space between the two poles. It is in the shape of a cylinder.  Around it there is a rectangular coil wound (in many turns).  This is made of conducting wire closely wound from end to end of the cylinder.  Across the ends of the coil, the consumer load is connected outside the rotor.

Using an external mechanical force and energy, the rotor is rotated at a constant angular speed between the poles.  The magnetic flux through the area enclosed by the coil changes continuously and periodically.  This is due to the change of the angle between the normal to the coil and the direction of magnetic field.  Due to electromagnetic  induction principle, we get an electromotive force between the ends of the coil and so current flows through it.

     ε = emf generated = -  dФ / dt
     here  Φ = B * A Cos ω t 
       B = magnetic field between the poles
       A = area of the rectangular coil
       N = number of turns.
        ω = angular speed of the rotor
         t = time

   ε = ABN Sin ωt

This is the single phase generator.  For multiple phases, there more more number of south and north poles equally spaced in a circle.  Then the induced voltage gets multiplied by the number of pole pairs Z.

The frequency of the generated current is ω/2π in Hz.

In a DC generator, a commutator ring is used to make the direction of the current in the coil to be the same in the two half cycles of the one time period.  The direction of the current flow is reversed by the use of the commutator exactly at half cycle point.

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