Three-phase motors are usually multipolar, each principal pole being subdivided into three parts. The figure shows a P P P FIG. 451.-Connections of three-phase generator to the poles P of the field magnet of the motor. field having twelve small poles which are so wound as to form. a rotary field with two north poles and two south poles. How this is done may be understood from the diagram in which the field ring is supposed to be cut at one point and bent out flat so that we look directly at the faces of the twelve poles. A For simplicity the wire is represented as carried only once through each groove. It will be seen that when the current in 1 is a maximum in the direction of the arrow the poles will be situated as shown in the upper row of letters. A third of a period later the current in 2 will be a maximum in the same direction, and the poles will then be as indicated in the second Then after another one-third of a period current 3 will row. FIG. 452. S S NN N S S S N N N S N S S S N N N S S S N N have reached its maximum and the poles will have shifted to the positions indicated in the third row of letters. There is thus produced a steady movement of the poles around the ring, moving over the distance between two similar poles in the time of one complete period of alternation of the current. In the above case, if the current has a frequency of sixty periods per second, the field will make thirty revolutions per second. cm. Problems. 1. The core of a Gramme ring armature has a cross-section of 6x10 How many turns of wire must it have that it may give an electromotive force of 20 volts when making 800 revolutions per minute in a magnetic field so strong that where the lines of force in the ring are most concentrated there are 6000 per square centimeter? 2. A certain dynamo armature when making 1000 revolutions per minute is supplying a current of 50 ampères at 100 volts. Find the horse-power required to drive it and thence the moment of force or torque in pound-feet required to turn the armature at the given speed. 3. When the armature of a certain motor is held fixed a current of 10 ampères through it causes a difference in potential between its brushes of 5 volts. When the armature is permitted to run at 600 revolutions per minute the current is 4 ampères and difference of potentials at the brushes is 30 volts. Determine the back electromotive force of the motor. 4. The core of a drum armature is a cylinder of iron 30 cm. long and 15 cm. in diameter, the induction through its middle longitudinal section is 6000 lines of force per square centimeter. If there are 50 complete turns of wire on the armature, or 100 longitudinal wires in grooves on its surface, what is its electromotive force when making 1200 revolutions per minute? 5. A transformer has a coil of 250 turns; what must be the size of the iron core in order that an average electromotive force of 100 volts may be developed in this coil while the number of lines of force in the core changes from +6000 to -6000 per sq. cm., the current alternating at the rate of 60 complete periods or cycles per second? 6. A certain transmission line has a resistance of 20 ohms. How much power will be lost in the line when 100 kilowatts are transmitted at 2000 volts? How much when the same power is transmitted at 20000 volts? ELECTRIC OSCILLATIONS AND WAVES. 762. Oscillatory Discharge of a Leyden Jar.-It has been already stated (§586) that when the resistance of the discharge circuit is sufficiently small the discharge of a Leyden jar is oscillatory. This was discovered by the American physicist Joseph Henry, who, as early as 1842, found that when a Leyden jar was discharged through a wire wound around a needle the latter was magnetized, but sometimes one end was made the north pole and sometimes the other, although the jar was always charged the same way. He believed that this was caused by the oscillation of the discharge current which kept reversing the magnetism of the needle back and forth until the current became too small to have a further effect. This opinion was confirmed by eating off the surface layer. of the needle with acid, when the interior was found magnetized opposite to the outer layer. Lord Kelvin, in 1855, quite unaware of Henry's discovery, showed by the principle of energy that the discharge must oscillate back and forth until all the original energy of charge is expended in sound, heat, light, and radiation, and that when the resistance of the circuit is very small the period of oscillation is given by the formula P=2VLC where L is the coefficient of self-induction of the circuit and C is the capacity of the jar. In case of an ordinary gallon jar discharged by a short discharging rod, the period of oscillation may be as small as two ten-millionths of a second, while Lodge, by using a battery of large capacity and discharging it through a very long circuit having large self-induction, was able to make the alternations so slow as to give out a distinct musical note. Feddersen, in 1859, first analyzed the spark by a rotating mirror, as already related ($586). 763. Electric Resonance.-When a Leyden jar is discharged not only may there be oscillations in the discharge circuit itself, but in consequence of induction there are set up electric oscillations or surgings in neighboring conductors. In general these are but feeble, but if the free period of the surging happens to be the same as that of the oscillations in the discharge circuit, quite energetic surgings may result, just as a tuning-fork will excite strong vibrations in a resonator which is in tune with it. The circuits are then said to be in resonance. -e A 764. A Case of Electrical Resonance. The influence of electrical resonance is well shown in the following experiment due to Lodge. Two Leyden jars of nearly equal capacities are chosen. One which can be charged by an electrical machine or induction coil is provided with a short circuit of thick wire which is attached to the outer coating and terminates in a knob separated by a short spark gap from the knob of the jar. The second jar has a strip of tinfoil reaching from the inner coating over the edge and terminating in a point at e near the upper edge of the outer coating; its inner and outer coatings are connected by a wire circuit, part of which, marked AB in the figure, can be slid along changing the length of the path. When the two jars are placed, say, a foot apart with the two circuits parallel, a position for the slider AB may be found by trial, such that whenever the first jar discharges across between the knobs, a spark leaps the gap between the tinfoil strip and the outer coating of the second jar. If the slider is moved a short distance away from this position in either direction, the sparks at e cease. Lodge calls the sparks at e the "slopping over" of the powerful surgings due to the two circuits being in resonance. FIG. 454.-Sir Oliver Lodge's resonance experiment. 765. Electric Waves in Wires.-When one end of a long straight wire is given a charge or touched to a battery pole, a wave of electric pressure or potential runs along the wire with a velocity which depends on the insulating medium immediately surrounding the wire. In case of a bare wire in air the wave has the velocity of light. On reaching the end of the wire the wave is reflected back, just as a sound wave is reflected at the end of a stopped organ pipe. If, instead of a single impulse, a series of alternate positive and negative charges are given to the end of the wire in exactly the right frequency, it may be set in strong electrical resonance just as a stopped pipe vibrates powerfully when a tuning-fork of the proper frequency is sounded at its mouth. Resonance will occur when the period of the electrical impulses is four times. as long as it takes a wave to run the length of the wire, exactly as in case of a stopped organ pipe. The resonance of waves in wires may be beautifully shown by the following experiment due to the German electrician Seibt: A large Leyden jar has its coatings connected by a circuit having a spark gap at S with zinc knobs. By moving the slider L nearer to the jar or farther away, the length and self-induction of the discharge circuit may be varied and consequently the period of the oscillatory discharge can be adjusted. L FIG. 455.-Resonance experiment. Two long helical coils of wire A and B are mounted on insulating stands. They are both connected at the bottom to one of the coatings of the Leyden jar while each terminates above in a point. One helix is wound with a much greater length of wire than the other. If by means of a powerful induction coil the Leyden jar is caused to discharge across the gap S, each discharge will be oscillatory and consequently a series of impulses is communicated to the lower ends of the helices A and B, and when the slider is in such a position that the period of oscillation of the discharge is the same as the period of oscillation in the wire on A, a strong brush discharge will be observed from the upper point of that helix; while by moving the slider until the jar circuit is in resonance with B, the discharge will take place from the top of B instead of from A. |