Draw a labelled diagram of AC generator. Derive the expression for the instantaneous value of the emf induced in the coil.

Construction

Main parts of an ac generator:

1. Armature − Rectangular coil ABCD

2. Filed Magnets − Two pole pieces of a strong electromagnet

3. Slip Rings − The ends of coil ABCD are connected to two hollow metallic rings R₁ and R₂.

4. Brushes − B₁ and B₂ are two flexible metal plates or carbon rods. They are fixed and are kept in tight contact with R₁ and R₂ respectively.

Theory and Working − As the armature coil is rotated in the magnetic field, angle θ between the field and normal to the coil changes continuously. Therefore, magnetic flux linked with the coil changes. An emf is induced in the coil. According to Fleming’s right-hand rule, current induced in AB is from A to B and it is from C to D in CD. In the external circuit, current flows from B₂ to B₁.

To calculate the magnitude of emf induced:

Suppose

A → Area of each turn of the coil

N → Number of turns in the coil

→ Strength of magnetic field

θ → Angle which normal to the coil makes with at any instant t

∴ Magnetic flux linked with the coil in this position:

= NBA cosθ= NBA cosωt …(i)

Where, ‘ω’ is angular velocity of the coil

As the coil rotates, angle θchanges. Therefore, magnetic flux Φ linked with the coil changes and hence, an emf is induced in the coil. At this instant t, if e is the emf induced in the coil, then