Describle the construction and working of an AC generator ( an alternator).

Explanation

Principle : AC generator works on principle of electromagnetic induction.
As the coil rotates in a magnetic field B, the effective area of the loop (the face perpendicular to the field) Acos`theta` is also get changed, where `theta` is the angle between `vecA` and `vecB`.
This method of producing a flux change is the principle of operation of a simple AC generator. An AC generator converts mechanical energy into electrical energy.

The basic elements of an AC generator are shown in figure. It consists of a coil mounted on a rotor shaft. The axis of rotation of the coil is perpendicular to the direction of the magnetic field. The coil (called armature) is mechanically rotated in the uniform magnetic field by some external means. The rotation of the coil causes the magnetic flux through it to change, so an emf is induced in the coil. The ends of the coil are connected to an external circuit by means of slip rings and brushes.
Derivation of Equation for emf:
When the coil is rotated with a constant angular speed `omega` , the angle `theta` between the magnetic field vector B and the area vector A of the coil at any instant t is `theta = omegat` (assuming `theta = 0^@` at t = 0). As a result, the effective area of the coil exposed to the magnetic field lines changes with time, and from equation, the flux at any time t is,
`phi_B=BA cos theta = BA cos omegat`
From Faraday.s law, the induced emf for the rotating coil of N turns is then,
`epsilon=-N(dPhi_B)/(dt)=-NBAd/(dt)(cos omegat)`
Thus, the instantaneous value of emf is,
`epsilon=NBAomegasinomegat`...(1)
where `NBAomega` is the maximum value of the emf, which occurs when `sinomegat = +1`. If we denote `NBAomega` as `epsilon_0` , then
`epsilon=epsilon_0sin omegat`...(2)
Since the value of the sine function varies between + 1 and - 1, the sign or polarity of the emf changes with time. The direction of the current changes periodically and therefore the current is called alternating current (AC).
Since `omega=2piv`, equation (2) can be written as
`epsilon=epsilon_0 sin 2pivt`..(3)
Where v is the frequency of revolution of the generator.s coil.