Question

Explain with the help of a labelled diagram, the principle and working of an a.c. generator? Write the expression for the emf generated in the coil in terms of speed of rotation. Can the current produced by an a.c. generator be measured with the help of moving coil galvanometer?

Answer 1

Electric generator: A device which converts mechanical energy into electrical energy is called an electric generator or dynamo.

A.C. generator or A.C. dynamo

Principle: A.C generator is based upon the phenomenon of electromagnetic induction i.e., whenever magnetic flux linked with a coil changes, an e.m.f. is induced in the coil.

Construction: It consists of the following essential parts:

1. Armature: It acts as a rotor. It consists of a large number of turns of insulated wires wound over a laminated soft iron core.

2. Magnet. Armature coil is rotated between pole pieces of a permanent (these days electromagnet) magnet.

3. Slip rings: AB is connected to the ring R₁ and CD to ring R₂. These rings rotate with the coil.

4. Brushes: B₁ and B₂ are two brushes or carbon rods. They are kept fixed and touch R₁ and R₂ lightly. The brushes are used to pass the current from armature coil to external load R.

Working: As armature coil rotates, the magnetic flux linked with the coil changes, hence induced e.m.f. is produced in the armature coil.

Let the armature ABCD is rotating in such a way that the arm AB moving upward and CD downward. By Flemings Right Hand Rule, we see that the induced current flows in the armature as shown in Fig. (a).

By the time the armature turns through 180° (Fig. b) with arm AB moving downward and CD moving upward, again applying Fleming’s Right Hand Rule, we find that the induced current flows in the armature as shown in Fig. (b).

From Fig (a) and (b), we find that the directrion of induced e.m.f. and current in the external circuit is reversed after the armature has rotated through an angle 180°. Hence the current produced is alternating in nature

Theory: Let initially the coil is vertical i.e. θ = 0 at t = 0. Let at time t, if θ is angle through which it has rotated with angular velocity to ω (Fig.(c, d))

So θ = ωt.

The magnetic flux linked with the coil.

Φ = n BA cos θ

or Φ = n BA cos ωt 

Where n = number of turns of the coil

A = area enclosed‘by each turn of the coil

B = strength of magnetic field

θ = angle which the normal to the coil makes with \(\overrightarrow B\) at any time t.

∴ Induced e.m.f.

E = -\(\frac{d\phi}{dt} = -\frac{d}{dt}\) (nBA cos ωt)

or E = -nBA \(\frac{d}{dt}\) (cos ωt)

E = nBA ω sin ωt. .............(1)

E will be maximum if sin ωt = 1

If E₀ is the maximum value of E, then

E₀ = nBAω ............(2)

Putting Eq.(2) in (1), we get

E = E₀ sin ωt

or E = E₀ sin θ ...........(3)

At θ = 0°, E = E₀ sin 0 = 0

At θ = 90°, E = E₀ sin 90 = E₀

At θ = 180°, E = E₀ sin 180° = 0

At θ = 270°, E = E₀ sin 270° = -E₀

At θ = 360°, E = E₀ sin 360° = 0

If we plot a graph between θ and E, the graph is as shown in [Fig. (d)]

Current produced by an a.c. generator cannot be measured by moving coil galvanometer, because the average value of ac over full cycle is zero.