Magnetic Fields Tutorial 6 - Simple AC Generators

 

 

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 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


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.

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.