2.1
11
The a.c. generator
By the end of this spread, you should be able to …
1 Describe the function of a simple a.c. generator.
Introduction
Alternating current has been mentioned many times throughout this course, but no
explanation has been given of how it differs from direct current or why it is used. Most of
the comments about a.c., for example when dealing with the domestic circuit, have
simply asked you to just assume it behaves like d.c. This spread will go some way to
correcting this simplification, but it will not attempt to cover a.c. theory completely,
because of its complexity, especially when other components are also in a circuit.
Alternating current (a.c.)
With a direct current (d.c.), the conduction electrons in a wire drift along the wire,
normally at a very slow speed. This was dealt with at AS level (AS book, spread 2.1.1).
Batteries always supply direct current. Any magnetic field produced by a constant d.c.
will itself be constant.
In contrast, with alternating current (a.c.), the conduction electrons oscillate about their
mean position and do not drift along the wire at all. Alternating current is used in all
countries for mains electrical distribution for the simple reason that it produces a variable
magnetic field. The changing magnetic field means that electromagnetic induction can be
used with a.c., in particular in transformers. These will be considered in the next spread.
One problem with a.c. concerns the value given to the current. If the electrons are merely
oscillating backwards and forwards, the average current is clearly zero. A graph of a.c.
plotted against time is shown in Figure 1. The current is shown starting at zero, rising to
a maximum of 10 A after a time of 0.005 seconds, reaching zero after 0.010 s and then
another half cycle in the opposite direction, when the current is then negative. The shape
of the graph has a sine wave pattern. One complete cycle takes 0.020 s, a frequency of
50 Hz. All European countries use 50 Hz. In the USA, 60 Hz is used.
Current/A
10
7.1
d.c.
a.c.
0
0
0.005
0.010
0.020
0.030
0.040
Time/s
10
Figure 1 The variation of current with time in an alternating current. The direct
current that provides the same heating effect is also shown
Axis of
rotation
The a.c. generator
Coil
Slip
rings
Brushes
Connections
to circuit
Figure 2 A simplified diagram of an a.c. generator
Not only is a.c. useful because it has a varying magnetic field, but
it is also easy to produce, using a rotating coil. If a rectangular coil
is rotated in a constant magnetic field at a rate of 50 rotations per
second it will produce an alternating current of 50 Hz in a sine
wave shape in any resistor to which it is connected. Figure 2
shows a simplified version of such a generator. The coil is free to
rotate on an axle and the coil is connected to the electrical circuit
via two slip rings against which brushes, usually made out of a
solid paste of carbon and copper, make contact. When the coil is
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Module 1
Electric and magnetic fields
The a.c. generator
STRETCH and CHALLENGE
On Figure 1 a line is also drawn showing a direct current. This has a value of 7.07 A.
If these two currents were passing, separately, through the same resistor, they would
both produce the same heating effect. For this reason an alternating current that varies
between –10 A and +10 A is said to be a 7.1 A r.m.s. current. The term r.m.s. stands for
root mean square. This may seem rather odd, but the average current is zero, and the
heating effect of a current, I2R, clearly depends on I2. The square root of the average
value of I2 is much more useful. All the values you are used to using with a.c. are the
r.m.s. values. A 13 A fuse, for example, can carry a current that varies between
+13√2 A and –13√2 A 50 times a second, that is between +18.4 A and –18.4 A.
Questions
Sketch a current/time graph of the 50 Hz alternating current I of peak value 5.0 A in a
resistor of resistance 8.07.
Sketch on the same time axis the values of I2. (Hint: it never becomes negative and it is
still a sine wave pattern.)
in the horizontal position shown it is cutting magnetic field at maximum rate. The e.m.f.
generated at this moment is therefore a maximum. When it is in the vertical position the
wires at the top are moving in the direction of the field and so no e.m.f. is generated. On
the way down, the e.m.f. is in the opposite direction, which will give rise to the reversal of
direction of any current the e.m.f. causes. All mains electricity is generated by this basic
system. Figure 3 shows the many coils in a large generator. In generators of this size the
situation in Figure 2 is reversed. The coils remain fixed in position and the magnet spins
inside the coils.
Figure 3 A large commercial generator
showing the coils that generate the
electrical power. In this instrument it is the
magnet that rotates, and the coils remain
stationary
Questions
1 A small generator coil is rotated at 60 revolutions per minute in the
uniform magnetic field between the poles of an electromagnet.
The coil is connected via slip-rings to a resistor and oscilloscope.
See Figure 4.
(a) At the instant shown, t = 0, in Figure 4, the oscilloscope
reading is +0.4 V. State the reading at
t = (i) 0.25 s, (ii) 0.50 s, (iii) 1.75 s and (iv) 3.0 s.
(b) Sketch a graph of the oscilloscope reading against time from
t = 0 to 3.0 s.
(c) How would the graph change if (i) the number of turns on the
Figure 4
coil were doubled, or (ii) the area of the coil were halved, or
(iii) the speed of rotation were increased to 90 revolutions per minute?
2 Figure 5 shows a cross-section through a simple a.c. generator.
(a) (i) Copy Figure 5 and sketch two complete flux loops which pass through the
poles of the rotor.
(ii) The core of the generator is made from iron. Give reasons why iron is used.
(b) Explain how rotating the magnet causes an e.m.f. in the coil.
(c) In which position is the magnet when the e.m.f. is (i) a maximum and (ii) zero?
(d) Suggest two modifications to the generator and explain how each of these would
increase the e.m.f. induced in the coil.
Oscilloscope
Coil
N
Rotor
S
Iron
core
Figure 5
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