Download Nature of the Induced E

Nature of the Induced E.M.F.
Next consider what is happening" at the instant the coil
is perpendicular to the lines of force, the coil having made
one-quarter of a complete revolutio n fro m the positio n
indicated in Fig. 16. I ts po sitio n will then b e as in Fig.
18 , fro m which we see that each coil side is, at that instant,
moving along the direction of the lines of force. The
magnitude of the ind uced e.m.f. will thus be zero. Now,
whatever the position of the coil may be, the magnitude of
the induced e.m.f. is proportional to the rate at which the
coil sides cut the lines of force, and if the angular velocity
of the coil is uniform, this rate will be the greatest when
the coil sides are moving across the lines in a direction
perpendicular to them. This is illustrated b y Fig. 19. In the first diagram a
conductor moves a distance d from P to Q perpendicular to the lines of
force, and in its passage it cuts ten of these lines. In the second diagram the
conductor moves the same distance d, but this time the direction of motion is
oblique to the lines of force with the result that fewer of the lines are cut;
five in the figure. Hence in the case of our rectangular coil rotating in a two -pole
field, we see that the induced e.m.f. will have its maximum value when the coil
sides are directly opposite the pole centres as in Fig. 16, and that the e.m.f. will
gradually diminish as the coil rotates, becoming zero by the time the coil has
rotated one-quarter of a revolution from the position of maximum e.m.f.
When the coil has made still another quarter-revolution, that is, half a revolution
altogether from the position of Fig. 16, the coil side AB will be directly opposite
the south pole, while CD will be directly opposite the north pole. The
direction of the induced e .m.f. in the side AB will now be from В to A, while
that in side CD will be from С to D. Therefore, while the coil has made half a
revolution the e.m.f. induced in it has reversed in direction, and if the coil has
been connected all the time to an external circuit, the current in this circuit will
also have reversed in direction, the end F now being the positive terminal, and
E the negative terminal. Also in this position the induced e.m.f. will have its
maximum numerical value because the coil's sides will, at the instant, be
moving in a direction perpeadicular to the lines of force. After a third quarter revolution the coil will be again horizontal, the coil sides will at the instant be
moving along, instead of across, the lines of force, and therefore the
magnitude of the induced e.m.f. will be zero. Finally, when the coil has made
a complete revolution, it will be back in the position of Fig. 16, and the
e.m.f. in it will have its maximum value in the original direction. The changes
that will have taken place are best represented by a graph, as in Fig. 20 which
illustrates the following facts.
(a) The e.m.f. induced in the coil is an alternating one, since it is
alternately positive and negative in direction.
(b) The e.m.f. undergoes one complete "cycle" of changes in the time taken by
the coil to make one complete revolution. This is shown by the fact that the
graph begins to repeat itself after one revolution, as indicated by the dotted
continuation. There will be, in fact, as many of these repeats as there are
complete revolutions of the coil.
(c) When the e.m.f. has zero magnitude, e.g. when it has made one-quarter or
three-quarters of a revolution, it is either on the point of changing from
positive to negative direction, or vice versa.
It can be said generally of all heteropolar electrical machines, that is,
machines having alternate north and south polarity, that the e.m.f. induced in the
armature is an alternating one. This applies both to direct- and to alternatingcurrent machinery.
Magnitude of the Induced E.M.F.— The magnitude of the induced e.m.f.
depends upon the linear velocity of the conductor measured in a direction
perpendicular to the lines of force, the length of the con ductor, and the strength
of the magnetic field. It will be remembered that the strength of a magnetic
field is measured by the number of lines which cross each square inch, or
square centimetre, of normal cross section.
Let B=field strength in lines per sq. cm.
l= length of conductor in cms.
v — velocity of conductor in cms. per sec. in a direction perpendicular to the
lines of force.
E = e.m.f. in volts induced in one conductor i.e. one -half turn of a singleturn coil.
Then E = Blv X 10 -8 volts.
If the length is exp ressed in inches, then, since 1 in, is eq ual to 2.54
cms., a length of 1 in. will be equal to 2.54 X 1 cms. Also, if the field
strength is in lines of force per square inch, then since there are (2*54) 2 =
6*45 sq. cms. to 1 sq. in., a field strength of B lines per sq. in. corresponds
to B/6*45 lines per sq. cm. Again, a velo cit y o f v ft. p er sec. is eq u al to a
velo cit y o f 1 2 X 2 *5 4 X v = = 30*5 v cms. per. sec. Hence, if B is
expressed in lines per sq. in., l in inches, and v in ft. per sec, the expression
for E is —
B
E
 2  54l  30  5v  10  8
6  45
 E  12 Blv  10  8 volts
М.А. Беляева и др. «Сборник технических текстов на англ. языке»