alternating, instead of upon direct-current, circuits. In such cases the motors are essentially the same as direct-current series-wound motors; for since in such a machine the current must reverse in the field magnets at the same time that it reverses in the armature, it will be seen that

Trolley Wire or 3d Rail

Generator
at Power
Station

A

Track

FIG. 320. Street-car circuit

the armature is always impelled to rotate in one direction, whether it is supplied with a direct or with an alternating current. Other types of A.C. motors are not well adapted to starting with full load.

360. Back E.M.F. in motors. When an armature is set into rotation by sending a current from some outside source through it, its coils move through a magnetic field as truly as if the rotation were produced by a steam engine, as is the case in running a dynamo. An induced E.M.F. is therefore set up by this rotation. In other words, while the machine is acting as a motor it is also acting as a dynamo. The direction of the induced E.M.F. due to this dynamo effect will be seen, from Lenz's law or from a consideration of the dynamo and motor rules, to be opposite to the outside P.D., which is causing current to pass through the motor. The faster the motor rotates, the faster the lines of force are cut, and hence the greater the value of this so-called back E.M.F. If the motor were doing no work, the speed of rotation would increase until the back E.M.F. reduced the current to a value simply sufficient to overcome friction. It will be seen, therefore, that, in general, the faster the motor goes, the less the current which passes through its armature, for this current is always due to the difference between the P.D. applied at the brushes - 500 volts in the case of trolley cars - and the back E.M.F. When the

motor is starting, the back E.M.F. is zero; and hence, if the full 500 volts were applied to the brushes, the current sent through would be so large as to ruin the armature through overheating. To prevent this motors are furnished with a starting box, consisting of resistance coils which are thrown into series with the motor on starting, and thrown out again gradually as the speed increases and the back E.M.F. rises.* Trolley cars are usually run by two motors which, on starting, work in series, so that each supplies a part of the starting resistance for the other. After speed is acquired, they work in parallel.

361. The recording watt-hour meter. The recording watthour meter (Fig. 321) is the instrument which fixes our electric-light bills. It is essentially an electric motor containing no iron, so that the current through the armature A is proportional to the P.D. between the mains, while the current through the field magnets F is the current flowing into the house. Therefore the force acting between 4 and F, or the turning power on A (torque), is proportional to the product of volts by amperes; that is, it is proportional to the watts consumed. The rate of rotation is made slow by the magnetic drag due to the reaction between the magnets M and the current induced in the rotating aluminium disk D which rotates between the poles of the magnets. The recording dials have therefore a speed which is proportional to the watts used, and their total rotation is proportional to the total energy, or watt hours, consumed.

*This discussion should be followed by a laboratory experiment on the study of a small electric motor or dynamo. See, for example, Experiment No. 37 of the authors' Manual.

QUESTIONS AND PROBLEMS

1. What is the function (use) of the field magnet of a dynamo? Wood is cheaper than iron; why are not the field cores made of wood? 2. How would it affect the voltage of a dynamo to increase the speed of rotation of its armature? Why? to increase the number of turns of wire in the armature coils? Why? to increase the strength of the magnetic field? Why?

3. When a wire is cutting lines of force at the rate of 100,000,000 per second, there is induced in it an E.M.F. of one volt. A certain dynamo armature has 50 coils of 5 loops each and makes 600 revolutions per minute. Each wire cuts 2,000,000 lines of force twice in a revolution. What is the E.M.F. developed?

4. What does the commutator of a dynamo do? What is the purpose of the commutator of a motor?

5. Explain the process of "building up in a dynamo.

6. Explain how an alternating current in the armature is transformed into a unidirectional current in the external circuit.

7. Explain why a series-wound motor can run on either a direct or an alternating circuit.

8. If a current is sent into the armature of Fig. 313 at ', and taken out at b, which way will the armature revolve?

9. Will it take more work to rotate a dynamo armature when the circuit is closed than when it is open? Why?

10. Single dynamos often operate as many as 10,000 incandescent lamps at 110 volts. If these lamps are all arranged in parallel and each requires a current of .5 ampere, what is the total current furnished by the dynamo? What is the activity of the machine in kilowatts and in horse power?

11. How many 110-volt lamps like those of Problem 10 can be lighted by a 12,000-kilowatt generator?

12. Why does it take twice as much work to keep a dynamo running when 1000 lights are on the circuit as when only 500 are turned on?

PRINCIPLE OF THE INDUCTION COIL AND TRANSFORMER

362. Currents induced by varying the strength of a magnetic field. Let about 500 turns of No. 28 copper wire be wound around one end of an iron core, as in Fig. 322, and connected to the circuit of a galvanometer G. Let about 500 more turns be wrapped about another portion of the core and connected into the circuit of two dry cells. When the key K is closed, the deflection of the galvanometer will indicate that

a temporary current has been induced in one direction through the coil ́s; and when it is opened, an equal but opposite deflection will indicate an equal current flow

K

FIG. 322. Induction of current by magnetizing

and demagnetizing an iron core

ciple of the induction coil and the transformer. The coil p, which is connected to the source of the current, is called the primary coil, and the coil s, in which the currents are induced, is called the secondary coil. Causing lines of force to spring into existence inside of s (in other words, magnetizing the space inside of 8) has caused an induced current to flow in s; and demagnetizing the space inside of s has also induced a current in s in accordance with the general principle stated in § 348, that any change in the number of magnetic lines of force which thread through a coil induces a current in the coil. We may think of the lines as always existing as closed loops (see Fig. 258, p. 255) which collapse upon demagnetization to mere double lines at the axis of the coil. Upon magnetization one of these two lines springs out, cutting the encircling conductors and inducing a current.

363. Direction of the induced current. Lenz's law, which, it will be remembered, followed from the principle of conservation of energy, enables us to predict at once the direction of the induced currents in the above experiments; and an observation of the deflections of the galvanometer enables us to verify the correctness of the predictions. Consider first the case in which the primary circuit is made and the core thus magnetized. According to Lenz's law the current induced in the secondary circuit must be in such a direction as to oppose the change which is being produced by the primary current, that is, in such a direction as to tend to magnetize the core oppositely to the direction in which it is being magnetized by the primary. This

means, of course, that the induced current in the secondary must encircle the core in a direction opposite to the direction in which the primary current encircles it. We learn, therefore, that on making the current in the primary the current induced in the secondary is opposite in direction to that in the primary.

When the current in the primary is broken, the magnetic field created by the primary tends to die out. Hence, by Lenz's law, the current induced in the secondary must be in such a direction as to tend to oppose this process of demagnetization, that is, in such a direction as to magnetize the core in the same direction in which it is magnetized by the decaying current in the primary. Therefore, at break the current induced in the secondary is in the same direction as that in the primary.

364. E.M.F. of the secondary. If half of the 500 turns of the secondary s (Fig. 322) are unwrapped, the deflection will be found to be just half as great as before. Since the resistance of the circuit has not been changed, we learn from this that the E.M.F. of the secondary is proportional to the number of turns of wire upon it, a result which followed also from § 351. If, then, we wish to develop a very high E.M.F. in the secondary, we have only to make it of a very large number of turns of fine wire.

365. Self-induction. If, in the experiment illustrated in Fig. 322, the coil s had been made a part of the same circuit as p, the E.M.F.'s induced in it by the changes in the magnetism of the core would of course have been just the same as above. In other words, when a current starts in a coil, the magnetic field which it itself produces tends to induce a current opposite in direction to that of the starting current, that is, tends to oppose the starting of the current; and when a current in a coil stops, the collapse of its own magnetic field tends to induce a current in the same direction as that of the stopping current, that is, tends to oppose the stopping of the current. This means merely that a current in a coil acts as though it had