**
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:

E_{0}
= BANw

A coil of 10 turns and area 6 cm^{2}
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? |

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