CHAPTER XXIV.

DYNAMOS AND MOTORS.

§ 1. Magnetos, or Separately-Excited Machines, as Motors. Let us consider what will happen if a current from an external source be run through the armature of any machine in which the magnetic field is constant, i.e. through the armature of a magneto or of a separately-excited machine.

A reference to the figures of Chapter XXIII. §§ 3, 5, 8, and 9, shows us that action will take place between the field-magnets on the one hand, and the armatures (mainly the iron cores of these) on the other; this reaction causing rotation of the armatures, since they only are moveable.

Either by tracing carefully the direction of polarity given in each case to the armature by the external current, or by the application of the arguments given in Chapter XXI. § 6, and summed up in Lenz's law, we can see that the rotation will be of such a nature that an E.M. F. is induced in the armature opposed to the E.M.F. of the external current. If the armature move with little friction, and be not constrained to do any work in turning, it will move faster and faster as the action continues. The faster it rotates the greater will be the induced E. M. F. opposed to the exciting current, and the smaller will this current consequently bccome. The limit of velocity possible is reached when the induced E.M. F. equals that of the exciting current, so that this is reduced to zero; this limit can never be reached in practice owing to friction. If the exciting current be reversed in direction, So will the rotation. A dynamo thus caused to turn by the passage of an external current through its armature is called an electro-motor. Any dynamo can be employed as a motor, but as a rule the best form for a motor is not the same as the best form for a driver of current.

Two magnetos' coupled.—If we connect the terminals of two

magnetos, such as the Grammes drawn in § 8, and if one machine be worked, the other will turn also in consequence of the current driven through its armature. The two machines will act, at least as regards direction of rotation, as would two wheels connected by an endless strap passing round them. A galvanometer in the circuit will indicate the changes in the current that ensue when that machine which is for the time acting as motor is held fast, allowed to turn slowly against friction, or allowed to run freely, respectively. [Compare with § 4.]

Magneto and secondary cell.-If we connect a Gramme, or other magneto, with a Faure's 'accumulator' or 'storage cell' an interesting experiment may be tried. Let us charge the cell by means of the machine, and let us then leave off turning this latter. The Faure's cell will now drive a current reverse in direction to that by which it was charged. This will pass through the Gramme, and will cause it to turn as a motor; the direction of rotation being, of course, such as to oppose the current from the Faure's cell. Now such a direction of rotation must be the same as that in which the Gramme turned when it was charging the cell. Or we shall see the Gramme, acting now as a motor, continuing to turn in the same direction as that in which it was turned when it acted as a driver of current.

§ 2. Series-Dynamos as Motors.-Inasmuch as the magnetic field in the series-dynamo changes sign when the current through the armature does so [for the field-magnets are here in one circuit with the armature]-it follows that a series-dynamo when driven as a motor will turn in one direction only. We can readily determine whether this direction will be with the brushes-i.e. in the direction in which the machine is intended to turn, that in which the segments on the axis do not meet the points of the collecting brushes; or whether the direction will be against the brushes-i.e. such that the segments on the axis meet the points of the brushes. Imagine the machine to be turning with the brushes as a driver of current, and now imagine an external current to be driven through the machine contrary in direction to that which was driven by the machine. Were the field constant in direction, the machine would turn in the same direction as before, since such rotation would oppose the external exciting current. But the field is reversed by this reverse exciting current.

Hence the dynamo, acting now as a motor, will be driven in a reverse direction against the brushes. If we reverse the exciting current, we reverse the current in the armature and also the field; and hence the machine runs still in the same direction, i.e. against the brushes.

Similar remarks apply to the shunt-dynamo when used as a

motor.

$3. General Remarks on Dynamos and Motors. In what follows we shall speak of that machine which is driving the current as the dynamo, and that which is being driven by the current as the electro-motor or motor. This latter is generally of a different construction from the former, though not differing in principle. We shall use the following symbols. E= = the E.M.F. of the dynamo ; e = the reverse E.M.F. induced in the motor when this is turned; C = the current in the circuit; R the resistance of this whole circuit, including the armatures of both dynamo and inotor; C, the current that runs when the motor is not allowed to turn, or when e is zero.

By Ohm's law it follows that C. =

E
R'

while C =

E-e
R

To give the above symbols a clear meaning, and to simplify the reasoning that will follow in §§ 4 and 5, we shall, unless the contrary be stated, assume

(i.) That the dynamo and motor are both either magnetos or separately-excited machines, so that in both of them the E.M.F. depends solely on the velocity of rotation of the armatures.

(ii.) That in the simple (i.e. not branched nor shunted) circuit composed of the two armatures and the external connecting wires, R is constant; the speed of rotation not affecting appreciably the resistance occurring where the brushes make contact with the segments on the axes.

(iii.) That the speed of rotation of the driving dynamo, and therefore (since we have assumed its field to be constant) the driving E.M.F. E, is constant.

When the driver is a series-dynamo, matters are not so simple. As the reverse E.M.F. of the motor increases in magnitude the current falls off, and, therefore, so will the field and E.M.F. of the driver. Any accidental retardation in the dynamo may now

so lower E that it becomes less than e. The current will in such a case be reversed, and so will the field and E.M.F. E of the dynamo. Thus, when a series-dynamo is used as driver, not only are calculations less simple on account of the variability of E, but also we may have to encounter sudden reversals of action.

In practice such reversals can be obviated by means of pieces of apparatus that interfere automatically to set matters right whenever the current begins to be reversed.

With a shunt-dynamo matters are still more complex. For here we have to consider not only the changes in E, but also the complex nature of R due to the branched circuit that is open to the current.

Hence, as stated above, we shall keep to the simple case where dynamos and motors both have constant fields.

Referring to Chapter XV. § 9, mutatis mutandis, it is plain that the following statements are true.

(EC work per second, or activity, expended on the dynamo.

=

Je C work per second, or activity, expended against the reverse E.M.F. of the motor.

(Ee) C=C2 R= work per second, or activity, expended in developing heat in the circuit.

§ 4. Formulæ for Activity, &c. Maximum Activity.-Let us suppose that a dynamo of a constant E.M.F. E is driving a motor, and let the symbols have the same meaning as in § 3. Instead of work per second we shall use the proper expression, activity. If E and e be given in volts, and R in ohms, then the activity is given in watts. We refer the reader to Chapter XV. §§ 2 and 3 for the relations between watts, ergs per second, and English horse-power.

The steam-engine expends a certain activity on the dynamo. In practice a small portion of this has its equivalent in heat evolved per second owing to friction. We shall, however, disregard this at present, and shall assume that it has its equivalent entirely in the electrical activity E C.

We may, as we did before in the case of a voltaic battery, think of our dynamo as a machine in which the electricity is pumped up through a certain AV measured by E, and thus acquires potential energy. In the voltaic cell we expended chemical energy in order to gain this

electrical energy; in the case of the dynamo it is mechanical energy that is so expended.

to

This activity EC is again transformed; it appears as (a) heatE -e activity measured by (Ee) C, or C2R, since C = R gether with (6) the activity e C expended against the reverse E. M.F. of the motor.

This division of the expended activity E C is the only one which would agree with Joule's law, and with the fact that to drive a current C against an E.M.F. e must require activity to the amount of e C; conservation of energy being also satisfied.

From the nature of an electro-motor it is clear that the activity e C can only appear as mechanical activity; either kinetic energy gained per second, or work done per second against some force. We here neglect friction in the motor.

Now let us consider what will happen if we start with the motor at rest, and let it gradually increase in velocity until e comes to be as nearly equal to E as possible.

(1) Motor at rest, e is zero.—We now have C。

E

= or the R' current is at a maximum. Hence the activity E C. expended on the dynamo is at a maximum. But it all appears as heat-activity evolved in the circuit; it gives us E Co, or C.2 R, heat-activity (measured in watts).

(2) Motor moving slowly, e is small.-Now we have C=

E

R

e

or CC. The activity expended on the dynamo is also less than before, being now E C, which is <EC.. Of this we expend e C on the motor, while (Ee) C appears as heat-activity.

(3) Motor moving rapidly, e nearly equal to E.-In this case C

E
R

e

is very small, since it equals The activity EC expended

on the dynamo is also very small, or the dynamo is 'easy to turn.' Of this activity the part e C spent on the motor is the greater, and the part (Ee) C wasted in heat is the smaller.

Thus by letting the motor run very fast, which would be effected by giving it very little work per second to do, we can convert into useful activity a very large percentage of that expended upon the dynamo, and waste in heat a relatively small amount; but at the