Magnetic Fields Tutorial 6 - Simple AC Generators

A generator converts kinetic energy to electrical energy.  It is called an energy transducer.  A simple DC electric motor will generate DC when it is turned.  A pick-up cartridge in a vinyl record deck is a generator .

 

 

This is a generator that gives off a tiny voltage (100 mV). It is the pick up cartridge on a record deck that plays old-fashioned vinyl LPs (not so old fashioned - HMV report that vinyl record sales are up by 31 % as I write this).   The stylus waggles a tiny magnet between four coils. The current is amplified by the amplifier.

 

The picture below is of an alternator that is found on a car engine.  Its shaft is driven by a pulley from the crankshaft of the engine

 

 

Image by Christopher Ziemnowicz, Wikimedia Commons 
 

The alternator in a car generates 12 volts at up to 70 amps.  The AC is converted to DC by diodes to charge up the battery and run the electrical components in a car.  Without it, the battery will run down very quickly.  Once the battery fades, petrol cars will stop.  A similar device is found on light aeroplanes.  However ignition is provided by a separate system of magnetos.  Should the battery fail, the plane will not fall out of the sky.

 

Simple AC Generator
 

 

The diagram above is a simple alternating current generator.  It consists of a coil of N turns, radius r and length l spinning in a magnetic field of flux density B.  Its angular velocity is w radians per second.  The motion is, of course, circular.

 

We can make a simple AC generator using the components from the Westminster Motor Kits that are found in many schools and colleges:

 

 

 

We can show how the output varies as the generator is turned.  The set up is like this:

 

 

We will start the generator from the coil being vertical.  The red spot allows us to trace the motion of the coil:

 

 

A quarter of a turn later:

 

Half a turn later:

 

Now at three quarters of a turn:

 

And now a full turn:

 

The trace shows a sine wave.

 

Explaining the sine wave

We can use the fact that circular motion and simple harmonic motion are closely linked.  So we can use the equation for displacement:

 

x = A cos wt

 

Here the x term refers to the displacement from a fixed point.  We can make the point at which the coil is vertical the “rest position”. The maximum amplitude is r as in the diagram.

 

 

So our equation becomes x = r cos wt

 


 

Since the coil is rotating at a constant angular velocity, w, the speed of the edge of the coil is given as v = wr.  From SHM we can say:

 

v = -rw sin wt

 

We can now bring in our EMF and linear speed equation:

 

We can combine the two equations above to give:

 

 

The minus signs disappear and we can also say that A = rl.

 

Therefore:

 

This explains why the output of an AC generator is sinusoidal. The output of an AC generator is a sine wave.

 

The maximum value of the e.m.f. is when sin wt = 1.  Therefore:

E0 = BANw

 

Question 1

A coil of 10 turns and area 6 cm2 is turning at a rate of 500 r.p.m. between the poles of a magnet of magnetic field strength 0.45 T.  What is the peak voltage? What is the r.m.s voltage? 

Answer


Alternators

The AC generator here is inefficient, but could be made more efficient by changing the shape of the magnet, and wrapping the coil around soft iron.  Practical AC generators have a rotating magnet (rotor) which passes between stationary coils (stator).  The alternating e.m.f is induced in these coils.  The machine is called an alternator.

 

Here is a generator that generates single phase alternating current.

 

 

A 7 PS (pferdstärke or horse-power) petrol engine drives this generator which provides power to a house when there is a power cut.  It also can be used to drive electric garden machinery.  The generator can be seen just below the front panel.  As well as a 230 V output, there is a 12 V output from the exciter.  This is a separate low voltage DC generator that generates electrical energy for the electromagnet in the rotor.  The rotor turns between stationary coils.  These produce the 230 V output.  The stationary coils are referred to as the stator.

 

Question 2

The maximum power that can given out by this generator is 3 kW.  If the engine output is 7 PS, calculate the efficiency of the generator.

(1 PS = 750 W)

Answer

 

Power station generators are massive.  They have a rotor that is connected to its own generator, called an exciter.  The stator coils are placed at 120 degrees to each other to allow 3-phase AC to be generated.  The voltage is 25 000 V, while currents of 15 000 A are common.  The whole machine is cooled by hydrogen gas, which has a particularly high specific heat capacity.  The picture below shows a power station alternator.

 

 

The generator is actually in the rectangular box on the right.  To the left is the low-pressure turbine.

 

Turbines and generators are so big that when the machine is off, the shaft has to be rotated slowly, otherwise it would sag and go out of shape (which is not a good idea).  It is driven by a barring motor.

 

 

Power station alternators generate electricity using 3-phase.  This means that there are three separate live wires that carry the electrical energy away from the machine.  There is a common neutral wire.  The study of three-phase is not part of any A-level syllabus, but you can find out more on my sister website HERE.