Download Motion Along a Straight Line at Constant Acceleration

Book Reference : Pages 127-129
1.
To understand how we generate alternating
current (A.C.)
2.
To begin to appreciate some of the
advantages of A.C.
A simple A.C. generator consists of a spinning
rectangular coil in a uniform magnetic field.
A slip ring / brush
arrangement is used to
allow electrical
connections to be
maintained as the coil
spins
As the coil spins the flux
linkage changes
continuously
When the normal to the plane of the coil is at an
angle  to the field lines the flux linkage is given
by:
N = BAN cos 
If the coil is spinning with a steady frequency f
then at time t after =0, =2ft so
N = BAN cos 2ft
+BAN
The flux linkage changes
T/2 (1/2f)
T (1/f)
with time as shown :
-BAN
The gradient of the flux linkage (cosine) curve is
the change in flux linkage per second N/t
which as we have seen before represents the
induced EMF.
Mathematically the gradient of the curve is the
first differential and so the alternating induced
EMF is given by
= 0 sin 2ft
[acsin.swf]
Where 0 is the peak EMF. Note this can be rewritten using an angular frequency = 0 sin t
The diagram below shows how the induced emf changes
with time
The induced EMF is
zero when the sides
of the coil are
parallel to the field
lines
The EMF is a
maximum when the
sides of the coil cut
at right angles across
the field lines
When the induced EMF is at a maximum, the
induced EMF in each wire on each side is given by
Blv. Where B is the magnetic flux density, l is the
length of the wire and v is the speed.
The coil has 2 sides & N turns and so the maximum
induced EMF is given by :
0 = 2N Blv
This shows that the maximum induced EMF will
increase with the strength of the magnetic field,
the number of turns, the size of the coil & the
speed (frequency) of rotation
D.C. generators can be made by using a split ring
commutator (much like the electric motor)
The induced EMF does
not reverse direction
each half cycle because
the connection
arrangement for the
split commutator also
reverses each half cycle
EMF
1 cycle
Note this DC is very
“lumpy” and typically
smoothing capacitors
will be used to reduce
the bumps
While the underlying principles are the same, power
stations actually generate electricity slightly differently.
Firstly, they generate what is
called “three phase” electricity.
Three sets of coils are offset by
120 & generate 3 separate
EMFs which are 120 out of
phase with each other
Secondly, to remove the need for slip rings, the 3 sets of
coils are kept stationary (they are called stators).
In this case the magnetic
field must move to cause a
change in flux linkage. An
electromagnet, (called the
rotor) is driven from a DC
source and spins insides the
stators.
The electricity leaving the power station is “stepped up”
to a very high voltage (lower current) by a transformer.
The three phases are distributed to factories and local
substations where it is “stepped down” by a further
transformer.
It is common for the local substation to supply different
streets with one each of the different phases
In contrast industry will use all three phases together for
high powered machinery
The coil of an AC generator has 80 turns, a length of
65mm & a width of 38mm. It spins at 50Hz in a magnetic
field with a flux density of 130mT
Calculate the maximum flux linkage through the coil
[26 mWb]
Show that each side of the coil moves at a speed of 6 m/s
Show that the peak voltage is 8.1V
A rectangular coil of N turns, with an area A spins at a constant
frequency f in a uniform magnetic field which has a flux density of
B. Complete the table
Time
0
Orientation of the
coil
Flux linkage
Parallel to field
1/4f
Perpendicular to field
1/3f
Parallel to field
3/4f
Perpendicular to field
Flux linkage 0, 0, -BAN
EMF : 0 -0, 0
Induced EMF
+0
+BAN