Question

State the working of a.c. generator with the help of a labeled diagram.

The coil of an a.c. generator having N turns, each of area A, is rotated with a constant angular velocity ω. Deduce the expression for the alternating e.m.f. generated in the coil.

What is the source of energy generation in this device?

Answer 1

AC Generator: 

Principle − Based on the phenomenon of electromagnetic induction

Construction:

Main parts of an ac generator:

• Armature − Rectangular coil ABCD

• Filed Magnets − Two pole pieces of a strong electromagnet

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

• 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

`vecB`→ 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:

 `phi = N(vecB *vecA)`= NBA cos θ = NBA cos ωt …(i)

Where, ‘ω’ is angular velocity of the coil

As the coil rotates, angle θ changes. 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

`e =-(d theta)/dt = -d/dt(NAB cos omegat)`

` =-NAB d/dt (cos omegat)`

`=-NAB (-sin omegat)omega`

∴e = NAB ω sin ωt 

The generator converts the mechanical energy into electrical energy. The mechanical energy may be obtained from the rotation of the turbine associated with the generator. The turbine in turn, may be working by the kinetic energy of running water, wind or steam.