Second, the field is weakened by the armature reaction. Con-
sider the diagram (Fig. 301) of the drum- wound bipolar machine.
With clockwise rotation, the brushes will be shifted from the
symmetrical plane to the positions A and D (Par. 570). In the
inductors in the semi-circumference A BCD, the current is flowing
ELEMENTS OF ELECTRICITY.
in; in the other semi-circumference it is flowing out. The effect
of the current in the inductors C to D and A to F is to produce a
field in the direction of the large arrow, that is, opposite to the
field of the magnets and consequently weakening that field, and
this effect increases as the current through the armature increases.
For this reason, the ampere turns between C and D and between
A and F, or in the double angle of lead, are named the demagnet-
The critical resistance for a shunt generator is that resistance
of the external circuit which if reduced will cause the machine
588. Compound Generator. The properties desired of a gener-
ator vary in accordance with the use to which the current is to
be put. In some circumstances constancy of current is required;
in others, constancy of potential. Of these, the more important,
notably in the case of electric lighting (Par. 511), is constancy of
potential. Neither the series nor the shunt generator afford this
desired constancy. However, we have shown above that the
voltage of a series generator rises as the current is increased,
while that of the shunt machine falls with this increase. The
, logical attempt to combine these windings in one machine so that
their effects counterbalance, has led to the development of the
compound generator. This compounding may be so carried out
that the voltage, even under wide fluctuations in the current,
remains nearly constant.
589. Overcompounding. If in a compound machine the series
coils be given a few more turns than are needed to preserve con-
stant potential, the voltage rises with increase of current, although
not so rapidly as in the case of the simple series machine. The
generator is then said to be over compounded. The object of over-
compounding will be understood from the following. Let G, Fig.
302, represent a compound generator supplying current to a dis-
l OHM c
B 1 OHM
tant group of lamps CD. Suppose each lamp to require one
ampere at 100 volts and suppose the resistance of the leads AC
and BD to be each one ohm. When one lamp is turned on, there
is a drop of one volt from A to C, and of one volt from D to B.
In order therefore that the voltage between C and D shall be 100,
the generator must develop between its brushes 102 volts. If all
five lamps be turned on, there will be a drop of five volts from
A to C, and of five from D to B; the generator must therefore
develop between its brushes 110 volts. We see then that a gener-
ator is overcompounded so that a constant difference of potential
may be maintained between two points at a distance from the
474 ELEMENTS OF ELECTRICITY.
DIRECT CURRENT MOTORS.
590. The Motor and the Generator Identical. An electric
generator, as we have already seen, is a machine to which
mechanical energy is applied and from which electrical energy
is drawn; on the other hand, an electric motor is a machine to
which electrical energy is applied and from which mechanical
energy is derived. Electrically, they are identical, and a machine
which if turned by mechanical power will produce a current,
will, if supplied with a current, develop mechanical power. The
truth of this statement may be shown by the following simple
illustration. Fig. 303 represents the arrangement, already de-
I I I "A
scribed several times, of a wire sliding on parallel conducting
rails which include between them a magnetic field. The wire AB
is a conductor in a magnetic field and if pushed in the direc-
tion C, there will be induced in it a current from A to B (Par.
422); it is therefore a generator in its simplest form. If instead
of pushing the wire, a current be passed through it from A to B,
it becomes a conductor carrying a current and placed in a magnetic
field and experiences a force (Par. 356) which will cause it to
move in the direction D (Par. 352); it is therefore also a motor.
591. Explanation of Motion. Let AB, Fig. 304, represent a
coil of wire placed in a magnetic field NS and free to revolve
about the axis CD. If a current be sent through this coil it will
start to rotate. The simplest explanation of this motion is that
each side of the coil is a conductor carrying a current and placed
in a magnetic field and is therefore acted upon by a force which
is at right angles to the field and whose strength is (Par. 356)
/=/. H.I dynes
In this expression I is the current in absolute units, H is the
strength of the field, or number of lines of force per square centi-
meter, and I is the length in centimeters of the wire at right angles
to the field. The direction of the current in one side of the coil
being opposite to that in the other, the force acting upon one side
is opposite to that acting upon the other; in other words, the two
forces constitute a couple and rotation will be produced. Its
direction may be determined by applying the left hand rule (Par.
The following additional explanation of this movement is given
as it involves certain conceptions which will be used in a discus-
sion later on.
The lines of force of the field run from N to S as shown by the
heavy arrow. If a current enters the coil by A and leaves by B,
there will be produced within the coil a field whose direction, as
shown by the broken arrow, is from above downward. In ac-
cordance with Maxwell's law (Par. 371), the coil will turn until
it embraces its own field and that of the magnet; it will therefore
take up a counter-clockwise rotation.' The turning effect of the
couple mentioned above becomes zero when the coil has revolved
until it lies in the vertical plane, and is reversed when the coil
passes through this plane. The coil would therefore come to rest
in this position. However, by means of a suitable commutator,
476 ELEMENTS OF ELECTRICITY.
as explained under generators (Par. 556), the current is reversed
as the coil passes through the vertical plane; its field is therefore
shifted 180 ahead and the rotation becomes continuous. More-
over, by using many coils upon the armature (Par. 558), it is
always possible to have the current flowing through those in
which the turning effect is at or near a maximum.
592. Power Developed by a Motor. Power is the rate at which
work is done (Par. 492), therefore
Power = -.
Work is force exerted over a path, hence
Power = frce X path
= force X IT
= force X velocity
Consider one of the inductors of the armature of a motor (Fig.
^ , 305). The force exerted upon it is (Par. 591)
f=I . H .1 dynes. The same force is exerted
upon the inductor diametrically opposite.
If r be the radius of the armature, in one
complete revolution the inductor travels a dis-
tance 2irr. In n revolutions it travels 2irrn.
If these n revolutions be made in time t, the
velocity with which the inductor travels is
big. 305. _ .
From above, power = forceX velocity, hence power developed
by the motor is
This may be written
P = IHlx2rX2>jm/t
But / HI X2r = armature moment = torque, and 2irn/t= angular
velocity of the armature, hence the power developed varies with
the torque and with the speed of rotation of the armature.
593. Counter Electro-Motive Force. Ignoring for the moment
the cause of the movement, consider a rectangular coil, as de-
scribed in Par. 591, rotating in a counter-clockwise direction in
a magnetic field. The sides of this coil are conductors moving in
a magnetic field. Application of the right hand rule (Fig. 306)
will show that there is induced in the coil an E. M. F. which acts
in at B and out at A. The more rapid the rotation, the greater
this E. M. F. (Par. 425). Comparing figures 306 and 304, we see
that this E. M. F. is opposed to that of the current which causes
the motor to rotate; in other words, the rotation of the motor sets
up an E. M. F. which opposes the current which produces the
rotation. This opposing E. M. F. is called the counter or back
E. M. F.
The first conspicuous effect of the counter electro-motive force
developed by a motor is to cut down the current supplied. If an
ammeter be connected in series with a motor and the circuit be
closed, it will be noted that before the motor begins to move, the
current is very large (indeed, without some special arrangement
to be described later [Par. 601] it may be excessive), but as the
motor speeds up, the current falls steadily.
If the E. M. F. applied to the brushes of a motor be E, and the
resistance of its armature be R, the current through the armature
before the motor moves is
and as R is small, I is great.
As the motor gains speed, the current becomes
j _ E EB
1 " ~R~
478 ELEMENTS OF ELECTRICITY.
or only so much as can be driven through the armature by the
difference of the impressed and the back E. M. F.
594. Relation Between Counter E. M. F. and Power Developed.
Since the power which a generator delivers to the brushes of a
motor is IE watts (Par. 494), and since, as shown above, 7 is cut
down by the back E. M. F. developed and hence the power re-
ceived by the motor is thereby diminished, it would seem that
back E. M. F. is a defect. However, consider the following:
From above, the current which a generator supplies to a running
motor is T E-E B
whence IR = EE B
whence PR = IE-IE B
whence IE = I 2 R + IE B
or IE-, the total
power delivered to the motor by the generator, is divided -into two-
parts, one of which, I 2 R, represents power lost in heating the
armature coils (Par. 494); the other, IE B , represents the useful
power of the motor. Hence, the useful power of a motor is direct-
ly proportional to the back E. M. F. which it develops.
From the foregoing, the useful power of a motor varies with the
product of the two factors / and E B . In Par. 592 it was shown
that this power also varies with the product of two other factors,
the torque and the speed of rotation. The torque, / . H . I X 2r,
if the field H be constant, varies directly with the current /, con-
sequently, the remaining factor, E B , the counter E. M. F., varies
directly with the speed of rotation. This might have been antici-
pated since we have shown above that the counter E. M. F. varies
with the rate at which the lines of force of the field are cut.
595. Reading of Voltmeter Across Seat of Counter E. M. F.
There is sometimes some confusion in the mind of a beginner as
to the reading of a voltmeter shunted around a seat of counter
E. M. F. The correct reading is always the sum of the counter
E. M. F. and of the regular IR drop over the resistance between
the two points. As an illustration, let G, Fig. 307, represent a
generator connected up in circuit with a motor M across whose
brushes a voltmeter is shunted, Let the E. M. F. of the generator
be 100 volts and suppose its resistance to be negligible. Let the
resistance of the leads be one ohm and that of the motor be one
ohm. Suppose that the generator is started but that the motor
is held fast and not allowed to rotate. The current is I = E/R =
100/2 = 50 amperes. The drop over the leads is 772 = 50 volts
and that across the motor is /r = 50 volts, which is the reading
of the voltmeter. Suppose now that the motor is released and
speeds up, producing a back E. M. F. of 90 volts. The current is
T E-E B 100-90 c
now / = o - = o = 5 amperes, or is reduced to one-tenth
of what it was originally. The IR drop over the leads is only 5
volts; the reading of the voltmeter therefore is 100 5=95 volts,
that is 90 for the back E. M. F. and 5 for the Ir drop across the
596. Efficiency of Motors. A generator delivers to the brushes
of a motor a current / of voltage E. The resistance across the
brushes is R. The motor rotates and by belts or gearing or other-
wise turns out mechanical power. The ratio of the power turned
out by the motor to the power delivered to its brushes by the
generator is the measure of the motor's efficiency. Thus, if the
generator supplies ten horse-power to the motor and the motor
turns out nine horse-power, its efficiency is 9/10 or 90 per cent.
The power delivered to the motor is IE watts (Par. 494) ; the
useful power turned out by the motor is IBs watts (Par. 594);
the efficiency of the motor is therefore measured by IE B /IE or
by EB/E; that is, the nearer the counter E. M. F. approaches the
applied E. M. F., the greater the efficiency of the motor.
The foregoing may be shown graphically as follows. The cur-
rent through the motor when the latter is running is (Par. 593)
jr = E - E B
Substituting this value of I in the above expressions, we obtain
for the power delivered to the motor
E(E - E B )
ELEMENTS OF ELECTRICITY.
and for the power turned out by the motor
E B (E -
whence the efficiency is
E(E - E B )
Upon rectangular axes (Fig. 308) lay off OA =OB propor-
J K tional to E B , and OD=OF propor-
tional to E. Complete the squares.
The area of the rectangle ADJG,
since it is proportional to E B (E-
EB), is proportional to the power
developed by the motor. The area
of the rectangle BJKF, since it is
proportional to E(EE B ), is pro-
portional to the power delivered to
the motor. The ratio of the first of
these rectangles to the second meas-
Fig. 308. ures the efficiency of the motor. The
rectangle BJKF is greater than ADJG by the area of the square
JGKH. The efficiency of the motor approaches unity as this
square diminishes, which it does as OA increases, that is, the
efficiency of the motor increases as the counter E. M. F. increases.
It must be noted, however, that as the counter E. M. F. OA =
OB, increases, the current through the motor decreases, and the
rectangles representing the power applied and the power turned
out both diminish, therefore, so long as the motor develops ap-
preciable power, its efficiency is never perfect.
597. Maximum Output of Power. Maximum efficiency must
not be confused with maximum output of power. From the pre-
ceding paragraph, the power turned out by the motor is
The first differential coefficient with respect to E B is
Placing this equal to zero and solving for EB
or the power turned out by a motor is a maximum when the
counter E. M. F. is equal to one-half the impressed E. M. F. In
this case the efficiency is only one-half; that is, there is a loss of
one-half of the power delivered to the motor.
Reference to the conclusion drawn in Par. 340 will show that
in a battery also when the power developed is a maximum, the
loss is one-half.
598. Classes of Direct-Current Motors. There are three classes
of direct-current motors, the series, the shunt and the compound.
The majority belong to the first two of these classes. In structure
they are, with a few minor changes, the same as the correspond-
ing generators. Thus, the requirement of being able to reverse
the direction of rotation at will involves the setting of the brushes
at right angles to the commutator surface instead of inclined there-
to. So also in the operation of a motor, the armature reaction
causes the brushes to be shifted backward from the neutral plane
instead of forward as in the case of the generators.
As a rule, motors are operated on constant potential circuits,
the voltage between the mains being constant.
599. Shunt Motors. The shunt motor possesses certain ad-
vantages over the other forms which render it by far the most
desirable for most mechanical purposes. Chief among these is
its ability, as shown below, to make automatic adjustment for
fluctuations in the load thrown upon it and in spite of these
fluctuations to vary but little in speed.
Fig. 309 represents in simplest diagrammatic form a shunt motor.
The difference of potential between A and B being constant, as
stated above, the current through the field coil AB is constant.
The force on the several inductors of the armature is (Par. 592)
/ = /. H .1 dynes
In this expression H and I are constant, hence the torque varies
directly with the current through the armature. In order there-
fore to vary the torque for different loads, this current must vary.
482 ELEMENTS OF ELECTRICITY.
The current through the armature is (Par. 593)
I = E-E B
From this we see that the current can be increased by increas-
ing E, decreasing EB, or decreasing R. Now E is the voltage
between the mains, which we have seen above is constant, and R
is the armature resistance, which is fixed when the machine is
built. The only remedy therefore is to decrease E B , the back
E. M. F. This back E. M. F. varies with the rate at which the
lines of force of the field are cut (Par. 594), that is, it varies
directly with the speed of rotation.
When the load upon a shunt motor is suddenly increased, the
speed will be observed to decrease slightly. This does not mean
that the machine is weakening. On the contrary, by slowing
down, the back E. M. F. is decreased, the current and hence the
A numerical example will bring this out clearly. If in the above
expression for the current we make 7 = 110, 7^ = 100 and R = l,
we get 7 = 10 amperes. If we make E B = 9Q, I becomes 20
amperes, hence a reduction of one-tenth in the speed of rotation
doubles the torque on the armature.
Since the power developed by the motor is IE B (Par. 594),
it may be asked whether the increase in / were counterbalanced
by the decrease in EB, for if they varied reciprocally, the power,
IE B , might remain constant and nothing would be gained.
However, I increases in a more rapid ratio than E B decreases.
In the numerical example above, with 5 = 100, the power is
1000 watts; with E B = 90, the power is 1800 watts.
The valuable characteristic of the shunt motor therefore is
that by slight variations in speed it adjusts itself automatically
for wide variations in the load. Even should the load be suddenly
entirely taken off, the motor will not "race," or speed up danger-
600. Control of Speed of Shunt Motors. The speed at which
a shunt motor runs under a certain load may be controlled in one
of two ways. The first and most frequently employed method is
by varying the strength of the field. There is inserted in the field
circuit a rheostat by which the current through the field coils may
be varied. By increasing the resistance in this circuit, the field
H is weakened. This causes E B to diminish and the current
through the armature consequently increases. The torque, IHlX
2r (Par. 592), is thus increased and the machine speeds up. It is
true that the torque depends also upon H, but we have shown in
the preceding paragraph that I increases more rapidly than H
decreases. This increase of speed also follows from the fact that
if the field be weakened, the armature must revolve faster in
order to cut the same number of lines of force in the same time
and thus develop the same power.
The second method is to insert between the motor and one of
the mains, as shown in Fig. 310, a rheostat R. The field H is not
affected by this, but the voltage applied to the armature is the
total voltage between A and B less the drop over the rheostat.
By varying the resistance in R, and hence the drop across the
rheostat, the voltage between C and B, and hence the current
through the armature, may be varied. Since the torque, IHlX
2r, H remaining constant, varies directly with /, a decrease in
the current decreases the speed of rotation,
From the foregoing it is seen that the speed of a shunt motor
may be increased (a) by decreasing the current through the field
coils, or (b) by increasing the current through the armature.
It should be remarked that control by rheostat is objectionable.
The power consumed in heating the coils of the rheostat repre-
sents pure waste which, where power is purchased, must be paid
for just as if it were doing useful work. The waste in the second
method above, since a larger current passes through the rheostat,
is much greater than that in the first method.
601. Starting-Box for Shunt Motors. It was stated above,
(Par. 593), that the full voltage can not without serious risk be
turned on a motor at rest. It is customary to use a starting-box,
a form of rheostat by which, as the back E. M. F. rises, the ap-
ELEMENTS OF ELECTRICITY.
plied E. M. F. may be gradually increased. The starting-box for
a series motor does not differ sufficiently from an ordinary rheostat
to warrant a special description. The starting-box for a shunt
motor possesses certain features which require explanation.
Although for these motors the full voltage can not be applied at
first to the armature, it can with perfect safety be applied to the
field coils. This enables the field to attain its full strength H at
once, and although the current / through the armature be small,
the torque is great enough to cause the machine to gather headway
Fig. 311 represents diagrammatically a form of starting-box
largely used. It is a box-shaped frame with lattice- work sides for
ventilation and contains a number of resistance coils in series
between a set of contacts arranged along the arc of a circle on
the marble cover of the box. The wire of the coils must be of
sufficient size to carry the current required by the motor, and
therefore to secure the necessary resistance they have to be long.
An iron arm, pivoted at P, can be swept along over the contacts.
At the pivot of this arm there is a spring which, when the arm is
released, throws it back to the safety position. When the arm is
placed on the first contact C, the current from the positive main
comes in by L, thence to P, thence up the arm to C where it
divides, a part passing through all the resistance coils to D, thence
to A, thence to the armature of the motor and thence to the
negative main, and the other part passing through the coil H,
thence to F, thence through the field coils to the negative main.
At starting, therefore, the current through the armature is cut
down by the entire resistance of the coils from C to D, while the
field is of full strength. As the armature begins to revolve it
generates a back E. M. F. and it becomes safe to apply more
voltage. The arm is therefore rotated to the right and gradually
cuts out the resistance in the armature circuit.
When the arm is hard over to the right, the entire resistance is
out of the armature circuit and the arm is held by the electro-
magnet H. The object of this magnet is the following. Should
the circuit be broken or the power be turned off while the motor
is in operation, the arm of the rheostat should be automatically
returned to the safety position, otherwise the break might be
repaired or the power be turned on again with the arm in its full
load position and the armature coils be overheated or even burned
out. When a break occurs, the magnet loses its power and the
spring at P throws the arm back to the safety position. This
arrangement is called a "no voltage release."
Again, should by any accident the current through the field
coils be greatly reduced or entirely cut off leaving only the residual
magnetism of the field magnets, the motor, from what has been
shown in the preceding paragraph, would speed up dangerously,
or, if this did not occur, would not generate sufficient back E. M.
F. to keep the current through the armature down to safe limits.
Therefore, in this case also the rheostat arm should be automati-
cally thrown back to the safety position.
It will be noted that with the arm hard over to the right, the
current which actuates the electro-magnet H is the field current
and is taken off by the upper one of the contacts at D. Should
a break occur in the field circuit, this magnet releases the arm
which is thrown back by the spring. This arrangement is called
a "no field release."
These starting-boxes frequently include an overload switch in
addition to the two releases described above.