Question 7: What is AC generator? Explain how alternating emf is generated by a loop of wire rotating in a magnetic field?

## AC Generator

It is a device that converts mechanical energy into alternating current.

### Principle of AC generator

An AC generator works on the principle of motional emf. It makes use of the principle of electromagnetic induction. A coil rotates in the magnetic field, experiences a change of flux and hence an emf is induced in it.

### Construction of AC generator

In the adjoining figure, parts of a simple AC generator are shown.

#### Armature

It consists of a rectangular coil of N turns wound on a cylindrical iron core and placed between the poles of a magnet. It can rotate about an axis perpendicular to a uniform magnetic field of density B. With the rotation of the armature, the flux linking it also changes, resulting an induced emf.

#### Field Magnets

The field magnet represented by N and S provides a uniform magnetic field.

#### Slip rings

Both the free terminals of the armature are connected with the Slip rings. These are concentric with the axis and rotate along with the armature.

#### Carbon brushes

Carbon brushes slide along the rings and connected to the load resistor.

The resistor or the useful instrument through which the generated alternating current passes is called Load.

### Working

As the armature rotates between the poles of the magnet, the flux linked with it changes from maximum to minimum and vice versa. When the plane of the coil is parallel to the field, the flux is minimum and when it is perpendicular to the field the flux is maximum. As the coil rotates, the flux continuously changes, thereby, producing and induced emf in it. The induced current also changes its direction from maximum to minimum with the emf. For a rotation of 1800 of the coil, the current changes its direction continuously.

## Expression for induced emf

We find the change of flux through the coil. Let ω be the constant angular velocity of the coil then, time period and frequency are given by,

Suppose at a particular instant of time, θ be the angle between B and n̂, the unit normal vector to the area of the coil A. Now we know that the flux through the coil of N turns is,

Also we know that, θ = ωt so we can write the above equation as,

φ = NAB cos ω t

This is the equation which describes the electromotive force in the AC generator in sufficient details. This shows the sinusoidal nature of the emf.

A schematic diagram is shown in the following figure which explains the waveform thus produced.

#### Expression for current

As the emf varies between its maximum and minimum values, it has its maximum value V0 = NABω and instantaneous value V= NABωsinωt. The instantaneous emf (voltage) can be expressed in terms of maximum voltage, V = V0sinωt = V0 sin 2πft (as ω = 2πf) Since V = IR by Ohm’s Law, therefore, the current produced is,

This also indicates that the current is sinusoidal alternating current.

#### Uses

AC generator is a very useful invention. At Tarbela and Mangla, huge AC generators convert the kinetic energy of water falls to electrical energy which is used throughout the country. In case of petrol or diesel use, the AC generator transforms chemical energy into electrical energy.
As most of the appliances run with alternating current, therefore, AC generator is an important source of energy in our daily life. It supplies electric power to all these appliances like light bulbs, fans and air conditioners etc.
Due to its transportable nature, it can be used in any outdoor activity like camping in remote areas.