Hawkins Electrical Guide, Vol 5

Figs. 1,206 to 1,212.—Apparatus which operates successfully on a direct current circuit. The direct current will operate incandescent lamps, arc lamps, electric heating apparatus, electro-plating and typing bath, direct current motors; charge storage batteries, produce electro-chemical action. It will flow through a straight wire or just as freely through the same wire when wound over an iron bar.

Figs. 1,213 to 1,217.—Apparatus which operates successfully on an alternating circuit. The alternating current will operate incandescent lamps, arc lamps, electric heating apparatus, alternating current motors. It will flow through a straight wire with slightly increased retarding effect, but if the wire be wound on an iron bar its strength is greatly reduced.

Fig. 1,218.—Application and construction of the sine curve. The sine curve is a wavelike curve used to represent the changes in strength and direction of an alternating current. At the left of the figure is shown an elementary alternator, consisting of a loop of wire ABCD, whose ends are attached to the ring F, and shaft G, being arranged to revolve in a uniform magnetic field, as indicated by the vertical arrows representing magnetic lines at equidistances. The alternating current induced in the loop is carried to the external circuit through the brushes M and S. The loop, as shown, is in its horizontal position at right angles to the magnetic field. The dotted circle indicates the circular path described by AB or CD during the revolution of the loop. Now, as the loop rotates, the induced electric pressure will vary in such a manner that its intensity at any point of the rotation is proportional to the sine of the angle corresponding to that point. Hence, on the horizontal line which passes through the center of the dotted circle, take any length as 08, and divide into any number of equal parts representing fractions of a revolution, as 0°, 90°, 180°, etc. Erect perpendiculars at these points, and from the corresponding points on the dotted circle project lines (parallel to 08) to the perpendiculars; these intersections give points, on the sine curve, for instance, through 2 at the 90° point of the revolution of the loop, and projecting over to the corresponding perpendicular gives 2'2, whose length is proportional to the electric pressure at that point. In like manner other points are obtained, and the curved line through them will represent the variation in the electric pressure for all points of the revolution. At 90° the pressure is at a maximum, hence by using a pressure scale such that the length of the perpendicular 2'2 for 90° will measure the maximum pressure, the length of the perpendicular at any other point will represent the actual pressure at that point. The curve lies above the horizontal axis during the first half of the revolution and below it during the second half, which indicates that the current flows in one direction for a half revolution, and in the opposite direction during the remainder of the revolution.

Fig. 1,219—Diagram illustrating the sine of an angle. In order to understand the sine curve, it is necessary to know the meaning of the sine of an angle. This is defined as the ratio of the perpendicular let fall from any point in one side of the angle to the other side divided by the hypotenuse of the triangle thus formed. For instance, in the diagram, let AD and AE be the two sides of the angle φ, and DE a perpendicular let fall from any point D of the side AD to the other side AE. Then, the sine of the angle (written sin φ) = DE ÷ AD.
It is evident that if the perpendicular be let fall at a unit's distance from the
apex A, as at B,

This line BC is called the natural sine of the angle, and its values for different angles are given in the table on page 451.

Fig. 1,220.—Diagram illustrating the equation of the sine curve: y = sin φ. y is any ordinate, and φ, the angle which the coil makes with the horizontal line, corresponding to the particular value of y taken.

Fig. 1,221.—Diagram showing one alternation of the current in which the latter varies from zero to maximum and back to zero while the generating loop ABCD makes one half revolution.

Fig. 1,222.—Diagram illustrating amplitude of the current. The current reaches its amplitude or maximum value in one quarter period from its point of zero value, as, for instance, while the generating loop moves from position ABCD to A'B'C'D'. At three-quarter revolution, the current reaches its maximum value in the opposite direction.

Fig. 1,223.—Diagram of alternator and engine, illustrating frequency. The frequency or cycles per second is equal to the revolution of armature per second multiplied by one-half the number of poles per phase. In the figure the armature makes 6 revolutions to one of the engine; one-half the number of poles = 8 ÷ 2 = 4, hence frequency = (150 × 4 × 6) ÷ 60 = 60. The expression in the parenthesis gives the cycles per minute, and dividing by 60, the cycles per second.

Fig. 1,224—Diagram answering the question: Why are alternators always built multipolar? They are made multipolar because it is desirable that the frequency be high. It is evident from the figure that to obtain high frequency would require too many revolutions of the armature of a bipolar machine for mechanical safety—especially in large alternators. Moreover a double reduction gear in most cases would be necessary, adding complication to the drive. Comparing the above illustration with fig. 1,223, shows plainly the reason for multipolar construction.

Fig. 1,225.—Diagram illustrating "phase." In wave, vibratory, and simple harmonic motion, phase may be defined as: the portion of one complete vibration, measured either in angle or in time, that any moving point has executed.

Figs. 1,226 and 1,227.—Diagram and sine curves illustrating synchronism. If two alternators, with coils in parallel planes, be made to rotate at the same speed by connecting them with chain drive or equivalent means, they will then be "in synchronism" that is, the alternating pressure or current in one will vary in step with that in the other. In other words, the cycles of one take place with the same frequency and at the same time as the cycles of the other as indicated by the curves, fig. 1,226. It should be noted that the maximum values are not necessarily the same but the maximum and zero values must occur at the same time in both machines, and the maximum value must be of the same sign. If the waves be distorted the maximum values may not occur simultaneously. See fig. 1,348.

Fig. 1,228—Pressure and current curves illustrating the term "in phase." The current is said to be in phase with the pressure when it neither lags nor leads.

Fig. 1,229—Pressure and current curves illustrating the term "out of phase." The current is said to be out of phase with the pressure when it either lags or leads, that is when the current is not in synchronism with the pressure. In practice the current and pressure are nearly always out of phase.

Figs. 1,230 to 1,233.—Curves showing some phase relations between current and pressure. Fig. 1,230, synchronism of current and pressure, expressed by the term "in phase," meaning simultaneous zero values, and simultaneous maximum values of the same sign; fig. 1,231, in quadrature, current leading 90°; fig. 1,232 in quadrature, current lagging 90°; fig. 1,233, in opposition, meaning that the phase different between current and pressure is 180°.

Fig. 1,234.—Elementary alternator developing one average volt. If the loop make one revolution per second, and the maximum number of lines of force embraced by the loop in the position shown (the zero position) be denoted by N, then each limb will cut 2N lines per second, because it cuts every line during the right sweep and again during the left sweep. Hence each limb develops an average pressure of 2N units (C.G.S. units), and as both limbs are connected in series, the total pressure is 4N units per revolution. Now, if the loop make f revolutions per second instead of only one, then f times as many lines will be cut per second, and the average pressure will be 4N f units. Since the C.G.S. unit of pressure is so extremely small, a much greater practical unit called the volt is used, which is equal to 100,000,000, or 10⁸ C.G.S. units is employed. Hence average voltage = 4Nf ÷ 10⁸. The value of N in actual machines is very high, being several million lines of force. The illustration shows one set of conditions necessary to generate one average volt. The maximum pressure developed is 1 ÷ .637 = 1.57 volts; virtual pressure = 1.57 × .707 = 1.11 volts.

Fig. 1,235.—Maximum and average values of the sine curve. The average value of the sine curve is represented by an ordinate MS of such length that when multiplied by the base line FG, will give a rectangle MFSG whose area is equal to that included between the curve and base line FDGS.

Fig. 1,236.—Diagram illustrating "virtual" volts and amperes. The word virtual is defined as: Being in essence or effect, not in fact; not actual, but equivalent, so far as effect is concerned. As applied to the alternating current, it denotes an imaginary direct current of such value as will produce an effect equivalent to that of the alternating current. Thus, a virtual pressure of 1,000 volts is one that would produce the same deflection in an electrostatic voltmeter as a direct pressure of 1,000 volts: a virtual current of 10 amperes is that current which would produce the same heating effect as a direct current of 10 amperes. Both pressure and current vary continually above and below the virtual values in alternating current circuits. Distinction should be made between the virtual and "effective" values of an alternating current. See fig. 1,237. The word effective is commonly used erroneously for virtual. See note page 1,011.

Fig. 1,237.—Diagram illustrating virtual and effective pressure. If the coil be short circuited by the switch and a constant virtual pressure be impressed on the circuit, the whole of the impressed pressure will be effective in causing current to flow around the circuit. In this case the virtual and effective pressures will be equal. If the coil be switched into circuit, the reverse pressure due to self induction will oppose the virtual pressure; hence, the effective pressure (which is the difference between the virtual and reverse pressures) will be reduced, the virtual or impressed pressure remaining constant all the time. A virtual current is that indicated by an ammeter regardless of the phase relation between current and pressure. An effective current is that indicated by an ammeter when the current is in phase with the pressure. In practice, the current is hardly ever in phase with the pressure, usually lagging, though sometimes leading in phase. Now the greater this phase difference, either way, the less is the power of a given virtual current to do work. With respect to this feature, effective current may be defined as: that proportion of a given virtual current which can do useful work. If there be no phase difference, then effective current is equal to virtual current.

Fig. 1,238.—Current or pressure curve illustrating form factor. It is simply the virtual value divided by the average value. For a sine wave the virtual value is 1 / √2 times the maximum, and the average is 2 / π times the maximum, so that the form factor is π/2√2 or 1.11. The induction wave which generates an alternating pressure wave has a maximum value proportional to the area, that is, to the average value of the pressure wave. Hence the induction values corresponding to two pressure waves whose virtual values are equal, will be inversely proportional to their form factors. This is illustrated by the fact that a peaked wave causes less hysteresis loss in a transformer core than a flat topped wave, owing to the higher form factor of the peaked wave. See wave forms, figs. 1,245 to 1,248.

Figs. 1,239 and 1,240.—Relative heating effects of alternating and direct currents. If it takes say five minutes to produce a certain heating effect with alternating current at say 63.7 average volts, it will take 33 seconds longer with direct current at the same pressure, that is, the alternating current has about 11 per cent. more heating power than the direct current of the same average pressure. The reader should be careful not to get a wrong conception of the above; it does not mean that there is a saving by using alternating current. When both voltmeters read the same, that is, when the virtual pressure of the alternating current is the same as the direct current pressure, the heating effect is of course the same.

Figs. 1,241 to 1,244.—Various forms of pressure or current waves. Figs. 1,241 to 1,243 show the general shape of the waves produced by some alternators used largely for lighting work and having toothed armatures. The effect of the slots and shape of pole pieces is here very marked. Fig. 1,244 shows a wave characteristic of large alternators designed for power transmission and having multi-slot or distributed windings.

Figs. 1,245 and 1,246.—Resolution of complex curves into sine curves. The heavy curve can be resolved into the simpler curves A and B shown in No. 1, the component curves A and B have in the ratio of three to one; that is, curve B has three times as many periods per second as curve A. All the curves, however, cross the zero line at the same time, and the resultant curve, though curiously unlike either of them, has a certain symmetry. In No. 2 the component curves, besides having periods in the ratio of three to one, cross the zero line at different points. The resultant curve produced is still less similar to its components, and is curiously and unsymmetrically humped. At first sight it is difficult to believe that such a curious curve could be resolved into two such simple and symmetrical ones. In both figures the component curves are sine curves, and as the curves for sine and cosine functions are exactly similar in form, the simplest supposition that can be made for the variation of pressure or of current is that both follow a sine law.

Fig. 1,247.—Reproduction of oscillograph record of wave form of alternator with one coil per phase per pole. Here the so-called "super-imposed harmonic" is clearly indicated.

Fig. 1,248.—Reproduction of oscillograph record of Wagner alternator having three coils per phase per pole.

Fig. 1,249.—Elementary one loop alternator and sine curve illustrating single phase alternating current. There are three points during the revolution at which there is no current: at 0° the position shown, 180°, and 360°; in other words, at the beginning, middle point and end of the cycle. The current reaches a maximum at 90°, reverses at 180°, and reaches a maximum in the reverse direction at 270°.

Figs. 1,250 to 1,252.—Hydraulic analogy illustrating the difference between direct (continuous) and alternating current. In fig. 1,250 a centrifugal pump C forces water to the upper pipe, from which it falls by gravity to the lower pipe B and re-enters the pump. The current is continuous, always flowing in one direction, that is, it does not reverse its direction. Similarly a direct electric current is constant in direction (does not reverse); though not necessarily constant in value. A direct current, constant in both value and direction as a result of constant pressure, is called "continuous" current. Similarly in the figure the flow is constant, and a gauge D placed at any point will register a constant pressure, hence the current may be called, in the electrical sense, "continuous." The conditions in fig. 1,251 are quite different. The illustration represents a double acting cylinder with the ends connected by a pipe A, and the piston driven by crank and Scotch yoke as shown. In operation, if the cylinder and pipe be full of water, a current of water will begin to flow through the pipe in the direction indicated as the piston begins its stroke, increasing to maximum velocity at one-quarter revolution of the crank, decreasing and coming to rest at one-half revolution, then reversing and reaching maximum velocity in the reverse direction at three-quarter revolution, and coming to rest again at the end of the return stroke. A pressure gauge at G will register a pressure which varies with the current. Since the alternating electric current undergoes similar changes, the sine curve will apply equally as well to the pump cycle as to the alternating current cycle.

Fig. 1,253.—Elementary two loop alternator and sine curves, illustrating two phase alternating current. If the loops be placed on the alternator armature at 90 magnetic degrees, a single phase current will be generated in each of the windings, the current in one winding being at its maximum value when the other is at zero. In this case four transmission conductors are generally used, two for each separate circuit, and the motors to which the current is led have a double winding corresponding to that on the alternator armature.

Figs. 1,254 and 1,255.—Hydraulic analogy illustrating two phase alternating current. In the figure two cylinders, similar to the one in fig. 1,251, are shown, operated from one shaft by crank and Scotch yoke drive. The cranks are at 90° as shown, and the cylinders and connecting pipes full of water. In operation, the same cycle of water flow takes place as in fig. 1,251. Since the cranks are at 90°, the second piston is one-half stroke behind the first; the flow of water in No. 1 (phase A) is at a maximum when the flow in No. 2 (phase B) comes to rest, the current conditions in both pipes for the entire cycle being represented by the two sine curves whose phase difference is 90°. Comparing these curves with fig. 1,253, it will be seen that the water and electric current act in a similar manner.

Figs. 1,254 and 1,255.—Hydraulic analogy illustrating two phase alternating current. In the figure two cylinders, similar to the one in fig. 1,251, are shown, operated from one shaft by crank and Scotch yoke drive. The cranks are at 90° as shown, and the cylinders and connecting pipes full of water. In operation, the same cycle of water flow takes place as in fig. 1,251. Since the cranks are at 90°, the second piston is one-half stroke behind the first; the flow of water in No. 1 (phase A) is at a maximum when the flow in No. 2 (phase B) comes to rest, the current conditions in both pipes for the entire cycle being represented by the two sine curves whose phase difference is 90°. Comparing these curves with fig. 1,253, it will be seen that the water and electric current act in a similar manner.

Fig. 1,256.—Diagram of three wire two phase current distribution. In order to save one wire it is possible to use a common return conductor for both circuits, as shown, the dotted portion of one wire 4 being eliminated by connecting across to 1 at M and S. For long lines this is economical, but the interconnection of the circuits increases the chance of trouble from grounds or short circuits. The current in the conductor will be the resultant of the two currents, differing by 90° in phase.

Figs. 1,257 to 1,259.—Various two phase armature connections. Fig. 1,257, two separate circuit four collector ring arrangement; fig. 1,258, common middle connection, four collector rings; fig. 1,259, circuit connected in armature for three collector rings. In the figures the black winding represents phase A, and the light winding, phase B.

Fig. 1,260.—Elementary three loop alternator and sine curves, illustrating three phase alternating current. If the loops be placed on the alternator armature at 120 magnetic degrees from one another, the current in each will attain its maximum at a point one-third of a cycle distant from the other two. The arrangement here shown gives three independent single phase currents and requires six wires for their transmission. A better arrangement and the one generally used is shown in fig. 1,261.

Fig. 1,261.—Elementary three wire three phase alternator. For the transmission of three phase current, it is not customary to use six wires, as in fig. 1,260, instead, three ends (one end of each of the loops) are brought together to a common connection as shown, and the other ends, connected to the collector rings, giving only three wires for the transmission of the current.

Figs. 1,262 and 1,263.—Hydraulic analogy illustrating three phase alternating current. Three cylinders are here shown with pistons connected through Scotch yokes to cranks placed 120° apart. The same action takes place in each cylinder as in the preceding cases, the only difference being the additional cylinder, and difference in phase relation.

Fig. 1,264.—Experiment illustrating self-induction in an alternating current circuit. If an incandescent lamp be connected in series with a coil made of one pound of No. 20 magnet wire, and connected to the circuit, the current through the lamp will be decreased due to the self-induction of the coil. If now an iron core be gradually pushed into the coil, the self-induction will be greatly increased and the lamp will go out, thus showing the great importance which self-induction plays in alternating current work.

Fig. 1,265.—Non-inductive and inductive resistances. Two currents are shown joined in parallel, one containing a lamp and non-inductive resistance, and the other a lamp and inductive resistance. The two resistances being the same, a sufficient direct pressure applied at T, T' will cause the lamps to light up equally. If, however, an alternating pressure be applied, M will burn brightly, while S will give very little or no light because of the effect of the inductance of the inductive resistance.

Fig. 1,266.—Inductance test, illustrating the self-induction of a coil which is gradually increased by moving an iron wire core inch by inch into the coil. The current is kept constant with the adjustable resistance throughout the test and readings taken, first without the iron core, and again when the core is put in the coil and moved to the 1, 2, 3, 4, etc., inch marks. By plotting the voltmeter readings and the position of the iron core on section paper, a curve is obtained showing graphically the effect of the self-induction. A curve of this kind is shown in fig. 1,302.

Fig. 1,267.—Diagram illustrating the henry. By definition: A circuit has an inductance of one henry when a rate of change of current of one ampere per second induces a pressure of one volt. In the diagram it is assumed that the internal resistance of the cell and resistance of the connecting wires are zero.

Figs. 1,268 to 1,270.—Various coils. The inductance effect, though perceptible in an air core coil, fig. 1,268, may be greatly intensified by inserting a core made of numerous pieces of iron wire, as in fig. 1,269. Fig. 1,270 shows a non-inductive coil. When wound in this manner, a coil will have little or no inductance because each half of the coil neutralizes the magnetic effect of the other. This coil, though non-inductive, will have "capacity." It would be useless for solenoids or electromagnets, as it would have no magnetic field.

Fig. 1,271.—Hydraulic-mechanical analogy illustrating inductance in an alternating current circuit. The two cylinders are connected at their ends by the vertical pipes, each being provided with a piston and the system filled with water. Reciprocating motion is imparted to the lower pulley by Scotch yoke connection with the drive pulley. The upper piston is connected by rack and pinion gear with a fly wheel. In operation, the to and fro movement of the lower piston produces an alternating flow of water in the upper cylinder which causes the upper piston to move back and forth. The rack and pinion connection with the fly wheel causes the latter to revolve first in one direction, then in the other, in step with the upper piston. The inertia of the fly wheel causes it to resist any change in its state, whether it be at rest or in motion, which is transmitted to the upper piston, causing it to offer resistance to any change in its rate or direction of motion. Inductance in the alternating current circuit has precisely the same effect, that is, it opposes any change in the strength or direction of the current.

Fig. 1,272.—Experiment showing effect of inductive and non-inductive coils in alternating current circuit. The apparatus is connected up as shown; by means of the switch, the lamp may be placed in parallel with either the inductive or non-inductive coil. These coils should have the same resistance. Pass an alternating current through the lamp and non-inductive coil, of such strength that the lamp will be dimly lighted. Now turn the switch so as to put the lamp and inductive coil in parallel and the lamp will burn with increased brilliancy. The reason for this is because of the opposition offered by the inductive coil to the current, less current is shunted from the lamp when the inductive coil is in the circuit than when the non-inductive coil is in the circuit. That is, each coil has the same ohmic resistance, but the inductive coil has in addition the spurious resistance due to inductance, hence it shunts less current from the lamp than does the non-inductive coil.

Figs. 1,273 to 1,275.—General Electric choke coils. Fig. 1,273, hour glass coil, 35,000 volts; fig. 1,274, 4,600 volt coil; fig. 1,275, 6,600 volt coil. A choke coil is a coil with large inductance and small resistance, used to impede alternating currents. The choke coil is used extensively as an auxiliary to the lightning arrester. In this connection the primary objects of the choke coil should be: 1, to hold back the lightning disturbance from the transformer or generator until the lightning arrester discharges to earth. If there be no lightning arrester the choke coil evidently cannot perform this function. 2, to lower the frequency of the oscillation so that whatever charge gets through the choke coil will be of a frequency too low to cause a serious drop of pressure around the first turns of the end coil in either generator or transformer. Another way of expressing this is from the standpoint of wave front: a steep wave front piles up the pressure when it meets an inductance. The second function of the choke coil is, then, to smooth out the wave front of the surge. The principal electrical condition to be avoided is that of resonance. The coil should be so arranged that if continual surges be set up in the circuit, a resonant voltage due to the presence of the choke coil cannot build up at the transformer or generator terminals. In the types shown above, the hour glass coil has the following advantages on high voltages: 1, should there be any arcing between adjacent turns the coils will re-insulate themselves, 2, they are mechanically strong, and sagging is prevented by tapering the coils toward the center turns, 3, the insulating supports can be best designed for the strains which they have to withstand. Choke coils should not be used in connection with cable systems.

Fig. 1,276.—Inductance experiment with intermittent direct current. A lamp S is connected in parallel with a coil of fairly fine wire having a removable iron core, and the terminals T, T' connected to a source of direct current, a switch M being provided to interrupt the current. The voltage of the current and resistance of the coil are of such values that when a steady current is flowing, the lamp filament is just perceptibly red. At the instant of making the circuit, the lamp will momentarily glow more brightly than when the current is steady; on breaking the circuit the lamp will momentarily flash with great brightness. In the first case, the reverse pressure, due to inductance, as indicated by arrow b, will momentarily oppose the normal pressure in the coil, so that the voltage at the lamp will be momentarily increased, and will consequently send a momentarily stronger current through the lamp. On breaking the main circuit at M, the field of the coil will collapse, generating a momentary much greater voltage than in the first instance, in the direction of arrow a, the lamp will flash up brightly in consequence.

FIG. 1,277.—Diagram showing alternating circuit containing inductance. Formula for calculating the ohmic value of inductance or "inductance reactance," is X_i = 2πfL in which X_i = inductance reactance; π = 3.1416; f = frequency; L = inductance in henrys (not milli-henrys). L = 15 milli-henrys = 15 ÷ 1000 = .015 henrys. Substituting, X_i = 2 × 3.1416 × 100 × .015 = 9.42 ohms.

Fig. 1,278.—- Diagram illustrating effect of capacity in an alternating circuit. Considering its action during one cycle of the current, the alternator first "pumps," say from M to S; electricity will be heaped up, so to speak, on S, and a deficit left on M, that is, S will be + and M-. If the alternator be now suddenly stopped, there would be a momentary return flow of electricity from S to M through the alternator. If the alternator go on working, however, it is obvious that the electricity heaped up on S helps or increases the flow when the alternator begins to pump from S to M in the second half of the cycle, and when the alternator again reverses its pressure, the + charge on M flows round to S, and helps the ordinary current. The above circuit is not strictly analogous to the insulated plates of a condenser, but, as is verified in practice, that with a rapidly alternating pressure, the condenser action is not perceptibly affected if the cables be connected across by some non-inductive resistance as for instance incandescent lamps.

Fig. 1,279.—Mechanical analogy illustrating effect of capacity in an alternating circuit. If an alternating twisting force be applied to the top R of the spring S, the action of the latter may be taken to represent capacity, and the rotation of the wheel W, alternating current. The twisting force (impressed pressure) must first be applied before the rotation of W (current) will begin. The resiliency or rebounding effect of the spring will, in time, cause the wheel W to move (amperes) in advance of the twisting force (voltage) thus representing the current leading in phase.

Fig. 1,280.—Hydraulic analogy illustrating capacity in an alternating current circuit. A chamber containing a rubber diaphragm is connected to a double acting cylinder and the system filled with water. In operation, as the piston moves, say to the left from the center, the diaphragm is displaced from its neutral position N, and stretched to some position M, in so doing offering increasing resistance to the flow of water. On the return stroke the flow is reversed and is assisted by the diaphragm during the first half of the stroke, and opposed during the second half. The diaphragm thus acts with the flow of water one-half of the time and in opposition to it one-half of the time. This corresponds to the electrical pressure at the terminals of a condenser connected in an alternating current circuit, and it has a maximum value when the current is zero and a zero value when the current is a maximum.

Fig. 1,281—Diagram illustrating a farad. A condenser is said to have a capacity of one farad if it will absorb one coulomb of electricity when subjected to a pressure of one volt. The farad is a very large unit, and accordingly the microfarad or one millionth of a farad is often used, though this must be reduced to farads before substituting in formulæ.

Fig. 1,282.—Condenser of one microfarad capacity. It is subdivided into five sections of .5, .2, .2, .05 and .05 microfarad. The plates are mounted between and carried by lateral brass bars which are fastened to a hard rubber top. Each pair of condenser terminals is fastened to small binding posts mounted on hard rubber insulated posts.

Fig. 1,283.—Parallel connection of condensers. Like terminals are joined together. The joint capacity of such arrangement is equal to the sum of the respective capacities, that is C = c + c' + c".

Fig. 1,284.—Series or cascade connection of condensers. Unlike terminals are joined together as shown. The total capacity of such connection is equal to the reciprocal of the sum of the reciprocals of the several capacities, that is, C = 1 ÷ (1 / c + 1 / c' + 1 / c")

Figs. 1,285 and 1,286.—Diagrams showing effect of condenser in direct and alternating current circuits. Each circuit contains an incandescent lamp and a condenser, one circuit connected to a dynamo and the other to an alternator. Since the condenser interposes a gap in the circuit, evidently in fig. 1,285 no current will flow. In the case of alternating current, fig. 1,286, the condenser gap does not hinder the flow of current in the metallic portion of the circuit. In fact the alternator produces a continual surging of electricity backwards and forwards from the plates of the condenser around the metallic portion of the circuit, similar to the surging of waves against a bulkhead which projects into the ocean. It should be understood that the electric current ceases at the condenser, there being no flow between the plates.

Fig. 1,287.—Diagram showing alternating circuit containing capacity. Formula for calculating the ohmic value of capacity or "capacity reactance" is X_c = 1 ÷ 2πfC, in which X_c = capacity reactance; π = 3.1416; f = frequency; C = capacity in farads (not microfarads). 22 microfarads = 22 ÷ 1,000,000 = .000022 farad. Substituting, X_c = 1 ÷ (2 × 3.1416 × 100 × .000022) = 72.4 ohms.

Fig. 1,288.—Pressure and current curves, illustrating lag. The effect of inductance in a circuit is to retard the current cycle, that is to say, if the current and pressure be in phase, the introduction of inductance will cause a phase difference, the current wave "lagging" behind the pressure wave as shown. In other words, inductance causes the current wave, indicated in the diagram by the solid curve, to lag behind the pressure wave, indicated by the dotted curve. Following the curves starting from the left end of the horizontal line, it will be noted that the current starts after the pressure starts and reverses after the pressure reverses; that is, the current lags in phase behind the pressure, although the frequency of both is the same.

Fig. 1,289.—Pressure and current curves illustrating lead. The effect of capacity in a circuit is to cause the current to rise to its maximum value sooner than it would otherwise do; capacity produces an effect exactly the opposite of inductance. The phase relation between current and pressure with current leading is shown graphically by the two armature positions in full and dotted lines, corresponding respectively to current and pressure at the beginning of the cycle.

Fig. 1,290.—Mechanical analogy of lag. If at one end force be applied to turn a very long shaft, having a loaded pulley at the other, the torsion thus produced in the shaft will cause it to twist an appreciable amount which will cause the movement of the pulley to lag behind that of the crank. This may be indicated by a rod attached to the pulley and terminating in a pointer at the crank end, the rod being so placed that the pointer registers with the crank when there is no torsion in the shaft. The angle made by the pointer and crank when the load is thrown on, indicates the amount of lag which is measured in degrees.

Fig. 1,291.—Diagram of circuit for example I.

Fig. 1,292.—Diagram of circuit for example II.

Fig. 1,293.—Steam engine analogy of current flow at zero pressure (see questions below). When the engine has reached the dead center point the full steam pressure is acting on the piston, the valve having opened an amount equal to its lead. The force applied at this instant, indicated by the arrow is perpendicular to the crank pin circle, that is, the tangential or turning component is equal to zero, hence there is no pressure tending to turn the crank. The latter continues in motion past the dead center because of the momentum previously acquired. Similarly, the electric current, which is here analogous to the moving crank, continues in motion, though the pressure at some instants be zero, because it acts as though it had weight, that is, it cannot be stopped or started instantly.

Fig. 1,294.—Diagram of the circuit for example I. Here the resistance is taken at zero, but this would not be possible in practice, as all circuits contain more or less resistance though it may be, in some cases, negligibly small.

Fig. 1,295.—Diagram of circuit for example II. As in example I, resistance is disregarded.

Fig. 1,296.—Diagram of circuit for example III.

Fig. 1,297.—Diagram showing alternating circuit containing resistance, inductance, and capacity. Formula for calculating the impedance of this circuit is Z = √(R² + (X_i - X_c)²) in which, Z = impedance; R = resistance; X_i = inductance reactance; X_c = capacity reactance. Example: What is the impedance when R = 4, X_i = 94.2, and X_c = 72.4? Substituting Z = √(4² + (94.2 - 72.4)²) = 22.2 ohms. Where the ohmic values of inductance and capacity are given as in this example, the calculation of impedance is very simple, but when inductance and capacity are given in milli-henrys and microfarads respectively, it is necessary to first calculate their ohmic values as in figs. 1,295 and 1,296.

Fig. 1,298.—Diagram of circuit for example II.

Fig. 1,299.—Diagram of circuit for example III.

Fig. 1,300.—Diagram of circuit for example IV.

Fig. 1,301.—Simple choking coil. There is an important difference in the obstruction offered to an alternating current by ordinary resistance and by reactance. Resistance obstructs the current by dissipating its energy, which is converted into heat. Reactance obstructs the current by setting up a reverse pressure, and so reduces the current in the circuit, without wasting much energy, except by hysteresis in any iron magnetized. This may be regarded as one of the advantages of alternating over direct current, for, by introducing reactance into a circuit, the current may be cut down with comparatively little loss of energy. This is generally done by increasing the inductance in a circuit, by means of a device called variously a reactance coil, impedance coil, choking coil, or "choker." In the figure is a coil of thick wire provided with a laminated iron core, which may be either fixed or movable. In the first case, the inductance, and therefore also the reactance of the coil, is invariable, with a given frequency. In the second case, the inductance and consequent reactance may be respectively increased or diminished by inserting the core farther within the coil or by withdrawing it, as was done in fig. 1,266, the results of which are shown in fig. 1,302.

Fig. 1,302.—Impedance curve for coil with variable iron core. The impedance of an inductive coil may be increased by moving an iron wire core into the coil. In making a test of this kind, the current should be kept constant with an adjustable resistance, and voltmeter readings taken, first without the iron core, and again with 1, 2, 3, 4, etc., inches of core inserted in the coil. By plotting the voltmeter readings and the positions of the iron core on section paper as above, the effect of inductance is clearly shown.

Fig. 1,303.—Diagram of a resonant circuit. A circuit is said to be resonant when the inductance and capacity are in such proportion that the one neutralizes the other, the circuit then acting as though it contained only resistance. In the above circuit X_i = 2πfL = 2 × 3.1416 × 100 × .01 = 6.28 ohms; X_c = 1 ÷ (2 × 3.1416 × 100 × .000253) = 6.28 ohms whence the resultant reactance = X_i - X_c = 6.28 - 6.28 = 0 ohms. Z = √(R² + (X_i - X_c)²) = √(7² + 0²) = 7 ohms.

Fig. 1,304.—Application of a choking coil to a lighting circuit. The coil is divided into sections with leads running to contacts similar to a rheostat. Each lamp is provided with an automatic short-circuiting cutout, and should one, two, or more of them fail, a corresponding number of sections of the choking apparatus is put in circuit to take the place of the broken lamp or lamps, and thus keep the current constant. It must not be supposed that this arrangement of lamps, etc. is a general one; it being adopted to suit certain special conditions.

Fig. 1,305.—Curve showing variation of current by increasing the frequency in a circuit having inductance and capacity. The curve serves to illustrate the "critical frequency" or frequency producing the maximum current. The curve is obtained by plotting current values corresponding to different frequencies, the pressure being kept constant.

Fig. 1,306.—Section of conductor illustrating "skin effect" or tendency of the alternating current to distribute itself unequally through the cross section of the conductor as shown by the varied shading flowing most strongly in the outer portions of the conductor. For this reason it has been proposed to use hollow or flat conductors instead of solid round wires. However with frequency not exceeding 100 the skin effect is negligibly small in copper conductors of the sizes usually employed. Where the conductor is large or the frequency high the effect may be judged by the following examples calculated by Professor J. J. Thomson: In the case of a copper conductor exposed to an electromotive force making 100 periods per second at 1 centimetre from the surface, the maximum current would be only .208 times that at the surface; at a depth of 2 centimetres it would be only .043; and at a depth of 4 centimetres less than .002 part of the value at the surface. If the frequency be a million per second the current at a depth of 1 millimetre is less than one six-millionth part of its surface value. The case of an iron conductor is even more remarkable. Taking the permeability at 100 and the frequency at 100 per second the current at a depth of 1 millimetre is only .13 times the surface value; while at a depth of 5 millimetres it is less than one twenty-thousandth part of its surface value. The disturbance of current density may be looked upon as a self-induced eddy current in the conductor. It necessarily results in an increase of ohmic loss; as compared with a steady current: proportional to the square of the total current flowing and consequently gives rise to an apparent increase of ohmic resistance. The coefficient of increase of resistance depends upon the dimensions and the shape of the cross section, the frequency and the specific resistance. A similar but distinct effect is experienced in conductors due to the neighborhood of similar parallel currents. For example in a heavy multicore cable the non-uniformity of current density in any core may be considered as partly due to eddy currents induced by the currents in the neighboring cores and partly to the self-induced eddy current. It is only the latter effect which should rightly be considered as comprised under the term skin effect.

Fig. 1,307.—Sine curve showing that the rate of change in the strength of an alternating current is greatest when the current is least, and zero when the current is at a maximum. This is evident from the diagram, since during say the first 10° as OA, the current increases 4 amperes; during BC, 2½ amperes; during DE it rises and falls ½ ampere. The reverse pressure of self-induction being proportional to the rate of change of the current, is a maximum when the current is zero, and zero when the current is a maximum, giving a phase difference of 90° between reverse pressure of self-induction and current.

Fig. 1,308.—Sine curves showing phase relation between current and reverse pressure of self-induction. This reverse pressure, being proportional to the rate of change in the current strength, is greatest when the current is at zero value, and zero when the current is maximum, and in phase is 90° behind the current.

Fig. 1,309.—In a right angle triangle the square on the hypothenuse is equal to the sum of the squares on the other two sides. That is: hypothenuse² = base² + altitude². Draw AB, 4 inches long, and BC, 3 inches long and at right angles to AB. Join AC, which will be found to be 5 inches long. From the diagram, it must be clear that the square on AC = sum of squares on AB and BC; that is, 5² = 4² + 3². Further, 4² = 5² - 3²; 3² = 5² - 4²; 5 = √(4² + 3²); 4 = √(5² - 3²); 3 = √(5² - 4²).

Fig. 1,310.—Diagram illustrating the representation of forces by straight lines. If 80 lbs. of steam be applied to a piston of 4 square inches area, the total pressure acting on the piston is 4 × 80 = 320 lbs. This may be balanced by an equal and opposite force. To represent the latter by a line, select any convenient scale whose divisions represent any convenient number of pounds—1, 3, 5 or, as here taken, 25 lbs. If the scale selected be divided into inches with ¼-inch divisions, then each ¼ inch represents a force of 25 lbs.; or, as usually stated, 1" = 100 lbs. Strictly speaking 1" is equivalent to 100 lbs. Draw the line f = 3.2 ins., then its length represents the magnitude of the force or 320 lbs., that is, 3.2 × 100 = 320 lbs.

Fig. 1,311.—Parallelogram of forces for boat acted upon by both wind and tide.

Fig. 1,312.—Parallelogram of forces; method of obtaining the resultant of two components acting at right angles.

Fig. 1,313.—Diagram illustrating the active, and self-induction pressures, or the two components of the impressed pressure in circuits containing resistance and inductance. The active pressure is the volts required to overcome the resistance of the circuit. In the figure only the portion from A to C is considered as having resistance (the rest being negligibly small) except at R, a resistance equivalent to that of the inductive coil is inserted next to the non-inductive coil, so P_a will give the total "ohmic drop" or active pressure, that is, the pressure necessary to force any equivalent direct current from A to C. This active pressure P_a or component of the impressed pressure is in phase with the current. The other component or self-induction pressure P_i that is the reactance drop necessary to overcome the reverse pressure of self-induction and is at right angles to the current and 90° ahead of the current in phase. It is registered by a voltmeter between B and C, less the pressure due to ohmic resistance of the inductive coil. The impressed pressure P_im then or total pressure required to force electricity around the circuit not including the resistance R, (which is removed from the circuit when the reading of the impressed pressure is taken), is equal to the square root of the sum of the squares of the two components, that is, P_im = √(P_{a}² + P_{i}²).

Fig. 1,314.—Graphical method of obtaining the impressed pressure in circuits containing resistance and inductance, having given the ohmic drop, and reactance drop due to inductance. With any convenient scale lay off AB = ohmic drop and erect the perpendicular BC = reactance drop (using same scale). Join AC, whose length (measured with same scale) will give the impressed pressure. Constructing a parallelogram with dotted lines AD and CD, it is evident that AC is the resultant of the two components AB and BC, or its equal AD.

Fig. 1,315.—Diagram for impressed pressure on circuit containing 5 volts ohmic drop and 15 volts reactance drop.

Fig. 1,316.—Diagram of circuit containing 5 volts ohmic drop, and 15 volts reactance drop.

Fig. 1,317.—Diagram for obtaining reactance drop in circuit containing 5 volts ohmic drop, and 15.8 volts impressed pressure.

Fig. 1,320.—Diagram of circuit containing 5 ohms resistance, 15 milli-henrys inductance, with 3 ampere 60 frequency current.

Fig. 1,321.—Diagram for impressed pressure on circuit containing 5 ohms resistance and inductance of 15 milli-henrys, the current being 10 amperes with frequency of 60.

Fig. 1,322.—Graphical method of obtaining the impedance in circuits containing resistance and inductance, having given the resistance and reactance, that is, the ohmic resistance and spurious resistance. With any convenient scale lay off AB = resistance, and erect the perpendicular BC = reactance (using the same scale); join AC, whose length (measured with the same scale) will give the impedance.

Fig. 1,323.—Diagram for obtaining the impedance of a circuit containing 4 ohms resistance and 3 ohms reactance.

Fig. 1,324.—Diagram for impedance of circuit containing 20 ohms resistance, and inductance of 15 milli-henrys, when the frequency is 100.

Fig. 1,325.—Diagram showing angle of lag for current containing 4 ohms resistance and 3 ohms reactance.

Fig. 1,326,—Circuit diagram illustrating the distinction between capacity in series and capacity in parallel. The condition for capacity in series is that the circuit must be discontinuous as at M; for capacity in parallel the main circuit must be continuous; this means that the capacity must be inserted in a branch of the main circuit as at A. In the figure the capacity S is connected in series with respect to the branch, that is, the branch is discontinuous, but it is in parallel with respect to the main circuit, when the latter is continuous, that is, when the switch W is closed. If W be opened, the main circuit becomes discontinuous and S is changed from in parallel to in series connection.

Fig. 1,327.—Current and pressure curves showing that the condenser pressure is 90° ahead of the current. A current flowing into a condenser encounters a gradually increasing pressure which opposes it, beginning from zero pressure when the current enters at maximum flow and increasing to the same value as the current pressure, at which time the current ceases to flow. Hence, since the current varies from zero to maximum in one quarter period, or 90°, the phase difference between current and condenser pressure is 90°. The condenser pressure reaching a positive maximum when the current starts from zero on the positive wave, is 90° ahead of the current.

Fig. 1,328.—Current and pressure curves, showing phase relation between the current, condenser pressure, and impressed or capacity pressure necessary to overcome the condenser pressure. The capacity pressure, since it must overcome the condenser pressure, is equal and opposite to the condenser pressure, that is, the phase difference is 180°. The condenser pressure being 90° ahead of the current, the impressed pressure is 90° behind the current.

Fig. 1,329.—Graphical method of obtaining the impressed pressure in circuits containing resistance and capacity, having given the ohmic drop and reactance drop due to capacity. With any convenient scale, lay off AB = ohmic drop, and at right angles to AB draw BC = reactance drop (using the same scale). Join AC, whose length (measured with the same scale) will give the impressed pressure. The mathematical expressions for the three quantities are given inside the triangle, and explained in the text.

Fig. 1,330.—Diagram of circuit containing a resistance of 30 ohms and capacity of 125 microfarads. The calculation for impressed pressure, ohmic drop, and reactance drop for a current of 8 amperes at frequency 60 is given in the example on page 1,089, the diagram for impressed pressure being given in fig. 1,331.

Fig. 1,331.—Diagram for obtaining the impressed pressure of the circuit shown in fig. 1,330.

Figs. 1,332 and 1,333.—Diagrams for circuits containing inductance and capacity. Since inductance and capacity act 180° apart, their reactances, or their ohmic drops may be represented by oppositely directed lines. These may be drawn above and below a reference line, as in fig. 1,332, and their algebraic sum taken, or both may be drawn on the same side of the reference line and their difference in lengths, as CD, fig. 1,333, measured. Recourse to a diagram for obtaining the resultant reactance in circuits containing inductance and capacity is unnecessary as it is simply a matter of taking the difference of two quantities.

Fig. 1,334.—Diagram of circuit containing 30 milli-henrys inductance and 125 microfarads capacity, with current of 20 amperes, 100 frequency.

Fig. 1,335.—Impedance diagram for circuit (of above example) containing inductance and capacity. With any convenient scale, erect a perpendicular AB = 18.25 ohms, and CD = 12.76 ohms. Continue CD by dotted line to D' so that CD' = AB, then DD' = AB - CD = inductance reactance - capacity reactance, which is equal to the impedance. Expressed by letters Z = X_i - X_c = DD', which by measurement = 5.49 ohms.

Fig. 1,336.—Impedance diagram for circuit containing resistance, inductance and capacity. The symbols correspond to those used in equation (1) below. In constructing the diagram from the given values, lay off AB = resistance; at B, draw a line at right angles, on which lay off above the resistance line, BC = inductive reactance, and below, BD = capacity reactance, then the resultant reactance = BC - BD = BD'. Join A and D', then AD' = impedance.

Fig. 1,337.—Impedance diagram of a circuit containing 25 ohms resistance, 30 ohms inductance, and 40 ohms capacity. The resultant reactance being due to excess of capacity, the impedance line AC' falls below the horizontal line AB, indicating that the current leads pressure.

Fig. 1,338.—EXAMPLE: A resistance of 20 ohms and an inductance of .02 henry are connected in parallel as in the diagram. What is the impedance, and how many volts are required for 50 amperes, when the frequency is 78.6? SOLUTION: The time constants are not alike, hence the geometric sum of the reciprocals must be taken as the reciprocal of the required impedance. That is, the combined conductivity will be the hypothenuse of the right triangle, of which the ohmic conductivity and the reactive conductivity are the two sides, respectively. Accordingly: 1 / R = 1 / 20 = .05, and 1 / (2πfL) = 1 / 10 = .1, from which, 1 / R = √((1 / R₁)² + (1 / (2πfL))²) = .111. Whence Z = 1 / .111 = 9 ohms.

Fig. 1,339.—Diagram of circuit containing 23 ohms resistance, 41 milli-henrys inductance, and 51 microfarads capacity, with current supplied at a frequency of 150.

Fig. 1,340.—Impedance diagram for the circuit shown in fig. 1,339. Note that the resultant reactance being due to excess of inductance, the impedance line AC' falls above the horizontal line AB. This indicates that the current lags behind the pressure.

Fig. 1,341.—Diagram of circuit containing 25 ohms resistance, .15 henry inductance, and 125 microfarads capacity, with current of 8 amperes at 60 frequency.

Fig. 1,342.—Diagram for finding the pressure necessary to be impressed on the circuit shown in fig. 1,341, to produce a current of 8 amperes.

Fig. 1,343.—Marine analogy of power factor. A ferry boat in crossing a river to a slip C would head for some point B up stream from C to allow for the effect of the tide. Under such conditions the actual motion (referred to the water) would be from A to B, and the apparent motion, from A to C. Accordingly, the energy expended in propelling the boat from A to B in still water, will propel it from A to C when the tide is running in the direction of the arrow. The effect of the tide is the same as that of inductance or capacity in an alternating circuit, that is, it puts the applied force or thrust (impressed volts) out of phase with the motion of the boat (amperes), this phase difference being indicated by the angle BAC or φ. Now, work (watts) is the product of two factors, pressure (volts) and distance (amperes); accordingly, the apparent work done in propelling the boat from A to C is the product of the thrust of the paddle wheels multiplied by AC, which in analogy corresponds to the product of voltmeter and ammeter readings at the alternator, called "kva." Actually, however, the power is only applied from A to B, the boat being carried sidewise by the tide, as it crosses, a distance BC which represents no energy expended by the paddle wheels. In analogy, the actual power, expended in propelling boat from A to B corresponds to the wattmeter reading in an alternating current power circuit. To obtain the actual work done on the boat, the product of its apparent motion × thrust must be multiplied by a coefficient or power factor because the thrust is applied at an angle to the apparent motion, the power factor being equal to the cosine of this angle, (φ) or AB ÷ AC. Similarly, when there is phase difference between pressure and alternating current, the voltmeter and ammeter readings must be multiplied by the power factor or cos φ to give the output of an alternator available for external work, the excess power indicated by ammeter and voltmeter readings, performing no external work, but causing objectionable heating of the alternator.

Fig. 1,344.—Method of drawing the power curve from the pressure and current curves. As shown, the same scale is used for all curves. This as a rule, makes the power curve inconveniently high, hence it is usually drawn to smaller scale as in fig. 1,345.

Fig. 1,345.—Usual method of drawing power curve from the pressure and current curves. A smaller scale is employed for the power curve in order to reduce its height.

Fig. 1,346.—Synchronism of current and pressure. Power curve showing that the power factor is unity. This is indicated by the fact that the power curve does not project below the base or zero line.

Fig. 1,347.—Diagram of circuit containing only resistance; in such a circuit the power factor is unity.

Fig. 1,348.—Case of synchronism of current and pressure with power factor less than unity. Suppose the waves of current and voltage to be in phase, but distorted in form, and not symmetrical, so that they do not run uniformly together, as shown in the figure. Then the real power factor may not be unity, although indicated as such by the power factor meter. However, the switchboard instruments are made to show the angle of lag as the power factor, because the error due to wave distortion is generally too small to be considered.

Fig. 1,349.—Effect of lag on the power factor. When the current lags behind the pressure the power factor becomes less than unity. It will be seen that the power curve projects below the zero line giving the shaded area which represents negative power which must be subtracted from the + areas above the zero line to get the net power. In the figure the line WW' is drawn at a height corresponding to the average power, and HN at a height corresponding to the average power that would be developed if the current were in phase with the pressure. The power factor then is represented by M ÷ S, and by inspection of the figure it is seen that this is less than unity.

Fig. 1,350.—Effect of lead on the power factor. When the current is in advance of the pressure the power factor becomes less than unity. The curve, as shown, projects below the zero line, giving the shaded area which represents negative power which must be subtracted from the + areas above the zero line to get the net power. As in fig. 1,349, the line WW' at a height M represents the average power, and HN the average power for synchronism of current and pressure. The power factor then is M ÷ S which is less than unity.

Fig. 1,351.—Steam engine analogy of power factor. The figure represents an indicator card of an engine in which the steam distribution is such that the steam is expanded below the back pressure line, that is below the pressure of the exhaust. This results in negative work which must be overcome by the momentum or kinetic energy previously stored in the fly wheel, and which is represented on the diagram by the shaded loop S. If the exhaust valve had opened at G, the amount of work done during the revolution would be represented by the area M, but continuing the expansion below the back pressure line, the work done is M - S. This latter case as compared with the first when expansion does not continue below the back pressure line gives an efficiency (power factor) of (M - S) ÷ M, the shaded area representing so much loss.

Fig. 1,352.—Power curve illustrating the so-called wattless current in which case the power factor is zero. By noting that the curve projects equally on each side of the zero line, the + power areas equal the negative power areas, hence the summation of these areas for the period is zero, that is, the two + areas minus the two shaded areas equal zero. It should be noted that the line of average power WW', which is visible in the other figures, here coincides with the zero line, and the average power then is zero, since the positive part above the zero line is equal to and offsets the negative (shaded) part below the line. This is the case of "wattless" current and (considering a circuit with resistance so small that it may be considered as zero) shows plainly the possibility of having full load current and voltage on a circuit yet delivering no power, the current simply surging to and fro without an actual transfer of power.

Fig. 1,353.—Example of wattless current showing that the power factor is zero when the phase difference between current and pressure is 90°. For zero power factor the current may lead 90° as in fig. 1,352, or lag 90° as here shown. Since the shaded or negative areas = the plus areas, the average power (indicated by WW' which coincides with the zero line) is zero, that is the circuit is carrying current under pressure yet delivering no power, hence, the power factor is zero.

Fig. 1,354.—Performance curves of General Electric single phase repulsion induction motor.

Figs. 1,355 to 1,357.—Mechanical analogy of wattless current. If a man lift a weight any distance, as from the position of fig. 1,355 to position of fig. 1,356, he does a certain amount of work on the weight giving it potential energy. When he lowers it to its original position, as in fig. 1,357, the weight loses the potential energy previously acquired, that is, it is given back to the man, the "system" (man and weight) having returned to its original condition as in fig. 1,355. During such a cycle, the work done by the man on the weight is equal to the work done by the weight on the man and no useful external work has been accomplished.

Fig. 1,358.—Method of obtaining the active component of the current; diagram illustrating why the power factor is equal to cos φ. If AB and AC be respectively the given current and pressure, or readings of the ammeter and voltmeter, and φ the angle of phase difference between current and pressure, then drawing from B, BD perpendicular to AC will give AD the active component. Now, true power = AC × AD, but AD = AB cos φ, hence true power = AC × AB cos φ. Again, apparent power = AC × AB, and since true power = apparent power × power factor, the power factor = cos φ.

Fig. 1,359.—Diagram for obtaining the active component of the current in a circuit having a current of 200 amperes and angle of lag of 30°.

Fig. 1,360.—Diagram for obtaining the power factor for example II. With convenient scale, lay off AB = 20 amperes. From A draw AC at 45° to AB, and from B, draw BD perpendicular to AC. Then, the power factor which is equal to cosine of angle of lag, = AD ÷ AB = (by measurement) 14.15 ÷ 20 = .707.

Figs. 1,361 to 1,365.—Diagrams illustrating why the power factor is unity or one when there is no resultant reactance in the circuit, that is, when the circuit is resonant or has only resistance. The power factor is equal to the cosine of the angle of lag (or lead). In the figures this angle is BAC or φ and the value of the natural cosine AC gives the power factor. By inspection of the figures, it is evident that decreasing the reactance decreases the angle φ and increases cos φ or the power factor. The circular arc in each figure being at unity distance from the center A, the power factor with decreasing reactance evidently approaches unity as its limit, this limit being shown in fig. 1,365 where the reactance B'C' = 0.

Fig. 1,366.—Diagram illustrating power factor test, when on non-inductive and inductive circuits. The instruments are connected as shown and by means of the double throw switch can be put on either the non-inductive or inductive circuit. First turn switch to left so that current passes through the lamps; for illustration, the following readings are assumed: ammeter 10, voltmeter 110, and wattmeter 1,100. The power factor then is wattmeter reading ÷ volts × amperes = 1,100 actual watts ÷ 1,100 apparent watts = 1, that is, on non-inductive circuit the power factor is unity. Now throwing the switch to the right connecting instruments with the inductive circuits, then for illustration the following readings may be assumed: ammeter 8, voltmeter 110, and wattmeter 684. Now, as before, power factor = wattmeter reading ÷ volts × amperes = 684 ÷ (8 × 110) = 684 ÷ 880 = .78.

Fig. 1,367.—Ayrton and Sumpner method of alternating current power measurement. Three voltmeters are required, and accordingly the method is sometimes called the three voltmeter method. It is a good method where the voltage can be regulated to suit the load. In the figure, let the non-inductive resistance R be placed in series with the load AB. Measure the following voltages: V across the terminals of R, V₁ across the load AB, and V₂ across both, that is from A to C. Then, true watts = (V₂² - V₁² - V²) ÷ 2R. The best conditions are when V = V₁, and, if R = ½ ohm, then W = V₂² - V₁² - V².

Fig. 1,368—Curves illustrating power factor. In a circuit having no capacity or inductance, the power is given by the product of the respective readings of the voltmeter and ammeter, as in the case of a direct current. In the case of a circuit having capacity or inductance, this product is higher than the true value as found by a wattmeter, and is known as the apparent watts. The ratio true watts ÷ apparent watts is known as the power factor. The current flowing in an inductive circuit, such as the primary of a transformer, is really made up of two components, as already explained, one of which (the load or active component), is in phase with the pressure, while the other the magnetizing component, is at right angles to it, that is, it attains its crest value when the other is at zero, and vice versa. To illustrate, take a complete cycle divided into 360 degrees and lay out on it the current required to correspond to a given load on the secondary of a transformer, say a crest value of 100 amperes, and at right angles to this lay out the current required for exciting the magnetic circuit of the transformer, giving A, merely for purposes of illustration, a crest value of 25 amperes. Combining these curves, the dotted curve in the figure is obtained and which represents the resultant current that would be indicated by an ammeter placed in the primary circuit of the transformer. It will be noted that this current attains its maximum at a point 14° 2´ later than the load current, giving the angle of lag. Multiplying the apparent watts by the cosine of the angle of lag gives the true watts. Now assuming the diagram to show the full load condition of the transformer, the angle of lag being 14° 2´, the power factor at full load is .97 (.97 being the value of the natural cosine of 14° 2´ as obtained from table, such as on page 451). With no external load on the transformer, the load component of the current is that necessary to make up the core losses. For instance, at 5 amperes, while the magnetizing current remains as before at 25 amperes, the angle of lag becomes 78° 41´ and the power factor .196. It is thus seen that in transformers, induction motors, etc., the power factor is a function of the load.

Fig. 1,368.—Fleming's combined voltmeter and ammeter method of measuring power in alternating current circuits. It is quite accurate and enables instruments in use to be checked. In the figure, R is a non-inductive resistance connected in shunt to the inductive load. The voltmeter V measures the pressure across the resistance XY. A and A₁ are ammeters connected as shown. Then, true watts = (A₁² - A² - (V/R)²) × R / 2. If the volt meter V take an appreciable amount of current, it may be tested as follows: disconnect R and V at Y, and see that A and A₁ are alike; then connect R and V at Y again, and disconnect the load. A₁ will equal current taken by R and V in parallel.

Fig. 1,369.—Wattmeter method of three phase power measurement. Two wattmeters are required in unbalanced systems as shown in the illustration. The total power transmitted is then the algebraic sum of the readings of the two wattmeters. If the power factor be greater than .5, the power is the arithmetical sum, and if it be less than .5, the power is the arithmetical difference of the readings.

Fig. 1,370.—Elementary four pole single phase alternator. It has four "inductors" whose pitch is the same as the pole pitch. They are connected in series and terminate at the two collector rings as shown. The poles being alternate N and S, it is evident that there will be two cycles of the current per revolution of the armature. For any number of poles then the number of cycles equals the number of poles divided by two. Applying Fleming's rule for induced currents, the direction of the current induced in the inductors is easily found as indicated by the arrows. The field magnets are excited by coils supplied with direct current, usually furnished from an external source; for simplicity this is not shown. The magnets may be considered as of the permanent type.

Fig. 1,371.—Developed view of elementary single phase four pole alternator and sine curve showing the alternating current or pressure generated during one revolution. The armature is here shown as a flat surface upon which a complete view of the winding is seen. If M be any position of an inductor, by projecting up to the curve gives N, the corresponding value of the current or pressure. Magnetic lines are shown at the poles representing a field decreasing in intensity from a maximum at the center to zero at points half way between the poles, this being the field condition corresponding to the sine form of wave. In actual machines the variation from the sine curve is considerable in some alternators. See figs. 1,247 and 1,248.

Fig. 1,372.—Elementary four pole two phase alternator. The winding consists of one inductor per phase per pole, that is, four inductors per phase, the inductors of each phase being connected in series by the "connectors" and terminating at the collector rings. This arrangement requires four collector rings, giving two independent circuits. The pitch of the inductors of each phase is equal to the pole pitch, and the phase difference is equal to one-half the pole pitch, that is, phase B winding begins at B, a point half-way between inductors A and A' of phase A winding. Hence when the current or pressure in phase A is at a maximum, in the ideal case, when inductor A for instance is under the center of a pole, the current or pressure in B is zero, because B is then half-way between the poles.

Fig. 1,373.—Developed view of elementary two phase four pole alternator and sine curves, showing the alternating current or pressure generated during one revolution of the armature. The complete winding for the three phases are here visible, the field magnets being represented as transparent so that all of the inductors may be seen. By applying Fleming's rule, as the inductors progress under the poles, the directions and reversals of current are easily determined, as indicated by the sine curves. It will be seen from the curves that four poles give two cycles per revolution. Inductors A, and B are lettered to correspond with fig. 1,372, with which they should be compared.

Fig. 1,374.—Elementary four pole three phase alternator. There are three sets of inductors, each set connected in series and spaced on the drum with respect to each other two-thirds pole pitch apart. As shown, six collector rings are used, but on actual three phase machines only three rings are employed, as previously explained. The inductors have distinctive coverings for the different phases. The arrows indicate the direction in which the induced pressures tend to cause currents.

Fig. 1,375.—Elementary four pole three-phase alternator and sine curves showing current or pressure conditions for one revolution. Six collector rings are shown giving three independent circuits. The pitch of the inductors for each phase is the same as the pole pitch, and the phase difference is equal to two-thirds of the pole pitch, giving the sequence of current or pressure waves as indicated by the sine curves. The waves follow each other at ⅓ period, that is, the phase difference is 120 degrees. Inductors A, B, and C, the beginning of each phase winding, are lettered to correspond with fig. 1,374, with which they should be compared.

Fig. 1,376.—Diagram of six phase winding with star grouping, being equivalent to a three phase winding in which the three phases are disconnected from each other and their middle points united at a common junction.

Fig. 1,377.—Diagram of six phase winding with mesh grouping.

Fig. 1,378.—Diagram of twelve phase winding star grouping.

Fig. 1,379.—Diagram of six phase winding consisting of combination of mesh and star grouping.

Fig. 1,380.—Belt-driven alternator. By use of a belt, any desired speed ratio is obtained, enabling the use of a high speed alternator which, being smaller than one of slow speed, is cheaper. It affords means of drive for line shaft and has other advantages, but requires considerable space and is not a "positive" drive. Belting exerts a side pull which results in friction and wear of bearings. Means for tightening the belt as shown in fig. 1,381, or equivalent, must be provided.

Fig. 1,381.—Sub-base and ratchet device for moving alternator to tighten belt. A ratchet A, operated by lever B, works the block C by screw connection, causing it to move the block. The latter, engaging with the frame, causes it to move, thus providing adjustment for belt. After tightening belt, the bolts D, which pass through the slots in the sub-base, are tightened, thus securing the machine firmly in position.

Fig. 1,382.—Allis-Chalmers pedestal type, belted alternator. The bearings are of the ring oiling form with large oil reservoirs. The bearings have spherical seats and are self aligning.

Fig. 1,383.—Diagram illustrating rule for horse power transmitted by belts. A single belt travelling at a speed of 1,000 feet per minute will transmit one horse power; a double belt will transmit twice that amount, assuming that the thickness of a double belt is twice that of a single belt. This is conservative practice, and a belt so proportioned will do the work in practically all cases. The above rule corresponds to a pull of 33 lbs. per inch of width. Many designers proportion single belts for a pull of 45 lbs. For double belts of average thickness, some writers say that the transmitting efficiency is to that of single belts as 10 is to 7. This should not be applied to the above rule for single belts, as it will give an unnecessarily large belt.

Fig. 1,384.—Fort Wayne revolving field belt driven alternator. It is designed for belted exciter, having a shaft extension at the collector ring end for exciter driving pulley.

Figs. 1,385 and 1,386.—Diagram showing the distinction between direct connected and direct coupled units. In a direct connected unit, fig. 1,385, the engine and generator are permanently connected on one shaft, there being one bed plate upon which both are mounted. An engine and generator are said to be direct coupled when each is independent, as in fig. 1,386 being connected solely by a jaw or friction clutch or equivalent at times when it is desired to run the generator. At other times the generator may be disconnected and the engine run to supply power for other purposes.

Fig. 1,387.—Engberg direct connected, or "engine type" alternator. In many places direct connected units are used, owing to the great saving in floor space, convenience of operation, and absence of belts.

Fig. 1,388.—Crocker-Wheeler 2,000 kva. 2,400 volt coupled type alternator. The coupled type of alternator is desirable for use with steam, gas, and oil engines, and water wheels where it is inconvenient to mount the alternator on the engine shaft or to extend the engine base to accommodate a bearing. This type consists of alternator complete with shaft and bearings similar to belt type machines, but with bearings not necessary designed for the side pull of belts.

Fig. 1,389.—Revolving armature alternator. Revolving armatures are suitable for machines generating current at comparatively low pressure, as no difficulty is experienced in collecting such current. Revolving armature alternators are also suitable for small power plants, isolated lighting plants, where medium or small size machines are required.

Fig. 1,390.—Ring wound dynamo arranged as alternator by replacing commutator with collector rings connected to the winding at points 180° apart.

Fig. 1,391.—Engberg alternating current generating set; shown also in cross section in fig. 1,387. The set comprises a vertical engine and alternator, direct connected and placed on one base. The lubrication system comprises an oil pump situated in the base of the engine, pumping the oil from an oil reservoir up into a sight feed oil cup which leads to a distributing oil trough on the inside of the engine frame, from here oil pipes lead to all movable bearings, which are grooved to insure proper distribution of oil. The oil is drained from bearings into the base, filtered and re-pumped. A water shed partition is provided in the engine frame, preventing any water passing from the cylinder down into the engine base and mixing with the oil, consequently leaving good, clean oil in the oil reservoir at all times. The details of the lubrication system are shown in fig. 1,387.

Fig. 1,392.—Allis-Chalmers revolving field self-contained belted type alternator.

Fig. 1,393.—Marine view, showing that motion is purely a relative matter. In order that there may be motion something must be regarded as being stationary. In the above illustration a catboat is shown at anchor in a stream which is flowing at a rate of four miles per hour in the direction of the arrow. The small dory running at a speed of four miles per hour against the current is moving at that velocity relative to the current, yet is at a standstill relative to the catboat. In this instance both catboat and dory are moving with respect to the water if the latter be regarded as stationary. Again if the earth be regarded as being stationary, the two boats are at rest and the water is moving relative to the earth.

Fig. 1,394.—Diagram showing essential parts of a revolving field alternator and method of joining the parts in assembling.

Fig. 1,395.—Western Electric stationary armature and frame of engine driven alternator. It is of cast iron and surrounds the laminated iron core in which the armature windings are embedded. Heavy steel clamping fingers hold the core punchings in place and numerous ventilating ducts are provided in the core at frequent intervals to allow free circulation of cool air. The armature coils are form wound, insulated, and retained in the core slots by means of wedges.

Figs. 1,396 and 1,397.—Elementary inductor alternator; diagram showing principle of operation. It consists of a field magnet, at the polar extremities of which is an armature winding both being stationary as shown. Inductors consisting of iron discs are arranged on a shaft to rotate through the air gap of the magnet poles. Now in the rotation of the inductors, when any one of them passes through the air gap as in fig. 1,396, the reluctance or magnetic resistance of the air gap is greatly reduced, which causes a corresponding increase in the number of magnetic lines passing through the armature winding. Again as an inductor passes out of the air gap as in fig. 1,397, the number of magnetic lines is greatly reduced; that is, when an inductor is in the air gap, the magnetic field is dense, and when no inductor is in the gap, the field is weak; a variable flux is thus made to pass through the armature winding, inducing current therein. The essential feature of the inductor alternator is that iron only is revolving, and as the design is usually homopolar, the magnetic flux in its field coils is not alternating, but undulating in character. Thus, with a given maximum flux through each polar mass, the total number of armature turns required to produce a given voltage is just twice that which is required in an alternator having an alternating instead of an undulating flux through its field windings. The above and the one shown in figs. 1,398 and 1,399 are examples of real inductor alternators, those shown in the other cuts are simply so called inductor alternators, the distinction being that, as above, the inductor constitutes no part of the field magnet.

Figs. 1,398 and 1,399.—A low tension ignition system with an inductor magneto of the oscillating type. The inductor E is rotated to and fro by means of a link R, one end of which is attached to the inductor crank, and the other to the igniter cam C. Two views are shown: immediately before and after sparking. S is the grounded electrode of the igniter; T an adjustable hammer which is secured in position by a lock nut N.

Figs. 1,400 and 1,401.—One form of inductor alternator. As shown, the frame carries the stationary armature, which is of the slotted type. Inside of the armature is the revolving inductor, provided with the projections built up of wrought iron or steel laminations. The circular exciting coil is also stationary and encircles the inductor, thus setting up a magnetic flux around the path indicated by the dotted line, fig. 1,401. The projecting poles are all, therefore, of the same polarity, and as they revolve, the magnetic flux sweeps over the coils. Although this arrangement does away with collector rings, the machines are not so easily constructed as other types, especially in the large sizes. The magnetizing coil becomes large and difficult to support in place, and would be hard to repair in case of breakdown. Inductor alternators have become practically obsolete, except in special cases, as inductor magnetos used for ignition and other purposes requiring a very small size machine. The reasons for the type being displaced by other forms of alternator are chiefly because only half as great a pressure is obtained by a flux of given amount, as would be obtained in the ordinary type of machine. It is also more expensive to build two armatures, to give the same power, than to build one armature. This type has still other grave defects, among which may be mentioned enormous magnetic leakage, heavy eddy current losses, inferior heat emissivity, and bad regulation.

Figs. 1,402 and 1,403.—Homopolar and heteropolar "inductors". Homopolar inductors have their N and S poles opposite each other, while in the heteropolar type, they are "staggered" as shown.

Fig. 1,404.—Revolving field of Fort Wayne alternator equipped with amortisseur winding. The object of this winding is to check any tendency toward hunting when the alternator is to be run as a synchronous motor, either for rotary condenser or power service. The amortisseur winding consists of heavy copper bars, placed around and through the pole faces and short circuited at the ends by heavy copper rings; it serves as a starting winding to bring the rotor up to speed as an induction motor, and also serves as a damping device to neutralize any tendency toward "hunting" caused by variation in speed of the generator supplying the current.

Fig. 1,405.—Westinghouse field with amortisseur or "damper" winding for 75 kva. and larger belted alternators, which prevents hunting and reduces eddy currents in the pole pieces. The copper bars of the amortisseur cage winding are arranged in partially closed slots in the pole pieces.

Fig. 1,406.—Diagram of monocyclic system, showing monocyclic armature and transformer connections. The monocyclic system is a single phase system primarily intended for the distribution of lights with an incidental load of motors. The lighting load is entirely connected to one single phase circuit, and the motors are started and operated from this circuit with the assistance of the teazer wire. The long coil indicates the main winding of the armature, which is similar in its arrangement and size to the ordinary armature winding of a single phase alternator. The short coil which connects at one end to the middle point of the coil above mentioned, and at the other to a third collector ring is called the "teazer" coil. Its use is to generate a pressure in quadrature with that of the main coil. This pressure is combined with the main pressure of the alternator by transformers, so as to give suitable phase relations for operating induction motors. In the diagram the voltage has been assumed to be 2,080 volts, and the voltages marked to correspond with the generated pressure. The coils of the alternator armature are connected, as shown, to two main leads and to a teazer wire. Between each end of the main coil and the end of the teazer coils, a resultant pressure is generated. These resultants are about 12 per cent. larger than half the main pressure. They also have a phase difference.

Fig. 1,407.—Monocyclic system diagram showing transformer connections.

Fig. 1,408.—Diagram showing section of monocyclic alternator armature illustrating the armature winding. The main coils are wound on every other tooth, and the teazer coils are placed in quadrature with them, as shown.

Fig. 1,409.—Diagram showing connections of General Electric Monocyclic alternator. For 2,300 volt machine, connect as shown by solid lines. For 1,150 volt machine, omit connections A to B, C to D, E to F, and G to H, and connect as shown by dotted lines. The armature of a standard monocyclic alternator rotates in a counter clockwise direction facing the commutator. When the alternator is loaded, the voltage between the teazer coil and the two terminals of the main coil may be different; therefore, it is necessary to have the commutator connected in corresponding ends of the main coil. If the machine has not been arranged for clockwise rotation, the following change in the connections on the commutator-collector must be made if the machine is to be run in parallel with another. Fig. 1,410 shows the connections of monocyclic alternators. In fig. 1,409, the studs on the commutator-collector marked 1 and 6 are the terminals of the main coil. These should be reversed. The numbers are stamped on the ends of the stud and may be seen with the assistance of a mirror. By reference to this diagram it is a simple matter to trace out the connections with a magneto, after the armature leads are disconnected and the brushes raised.

Fig. 1,410.—Diagram showing connections of General Electric monocyclic alternator. The solid lines show standard connections for counter-clockwise rotation; the broken lines show connection changed for clockwise rotation.

Figs. 1,411 and 1,412.—Section of armature and field showing distorting effect of armature reaction on the field. When a coil is opposite a pole as in fig. 1,411, no current is flowing (assuming no self induction) and the field is undisturbed, but, as the inductors pass under a pole face as in fig. 1,412, current is induced in them, and lines of force are set up as indicated by the dotted lines. This distorts the main field so that the lines of force are crowded toward the forward part of the pole face as shown.

Fig. 1,413.—Section of armature and field showing weakening effect of armature reaction in the field. Self-induction being present (as it almost always is), the current lags more or less behind the pressure, so that when the coil is in the position of zero induction, as shown, the current has not yet come to rest. Accordingly, lines of force (indicated by the dotted lines) are set up by the current flowing through the coils which are in opposition to the field, thus weakening the latter. The dots and crosses in inductor sections, have their usual significance in defining the direction of current, representing respectively the heads and tails of arrows.

Fig. 1,414.—Section of armature and field showing strengthening effect of armature reaction when the current leads the pressure. If the circuit contain an excess of capacity the current will lead the pressure, so that when the coil is in the position of zero induction, as shown, the current will have come to rest and reversed. Accordingly, lines of force (indicated by the dotted lines) are set up by the current flowing through the coil and which are in the same direction as the lines of force of the field, thus strengthening the latter.

Fig. 1,415.—Fort Wayne separately excited belt driven alternator, a form adapted for installation in small plants where low power factor is to be encountered. This condition exists in a line where power is supplied to induction motors, transformers or other inductive apparatus. The type here shown is built in sizes from 37½ kw. to 200 kw., 60 cycles, two or three phases and voltages of 240, 480, 600, 1,150 or 2,300 volts. They may be operated as single phase alternators by using two of the phases and may then be rated at 70 per cent. of the polyphase rating. The field is excited by direct current at a pressure of 125 volts. These alternators may be used as synchronous motors and for this duty are fitted with amortisseur winding in the pole faces which does not interfere with their use as alternators.

Figs. 1,416 to 1,425.—Diagrams illustrating superposition of fields. In the figures magnetic curves representing the effect of the armature currents in several different cases are superposed upon the magnetic curves assumed to be due to the field magnet. The uppermost line shows the primary field due to the exciting coils on the magnet poles. They are shown passing into the armature teeth in two principal positions, where the middle of a pole is: 1, opposite a tooth, and 2, opposite a slot. In the second line is shown the field due to the armature currents assuming no lag, and that the magnets are not excited. If there be no lag, the places of strongest current will be opposite the poles. As shown in the right hand figure when the current in one phase C, is at its maximum, those in the other phases A and B will be of half strength. In the left hand figure when the current in one phase B, is at its zero value, those in the other phases will be of equal value, or 87 per cent. of the maximum. In the third line is shown the effect of superposing these fields due to the current upon those due to the magnets as depicted in the first line. Inspection of this resultant field shows how the armature current distorts the field without altering the total number of lines per pole. In the fourth and fifth lines are shown the effects of a lagging current. A lag of 90° is assumed; and in that case the maximum current occurs in any inductor one quarter period after the pole has passed, or at a distance of half a pole pitch behind the middle point of the pole, as in the fourth line. When these armature fields are superposed on those of the magnets in the first line the resultant fields are those depicted in the fifth line. On inspection it will be seen that in this case there is no distortion, but a diminution of the flux from each pole, as the lines due to the armature currents, tending to pass through the pole cores in the sense opposite to those of the primary magnetism, must be deducted from the total. The twelve lines per pole are correspondingly reduced to eight; and, of these eight, four go astray constituting a leakage field. This illustrates the effect of a lagging current in demagnetizing the field magnets and in increasing the dispersion.

Fig. 1,426.—Diagram showing lateral field between adjacent poles.

Figs. 1,427 and 1,428.—Diagram showing respectively the character of stray field between adjacent straight poles, and between adjacent poles with shoes. Across the slightly V-shaped spaces the stray field passes in lines that, save near the outer part, are nearly straight. Quite straight they would not be, even were the sides parallel, because the difference of magnetic pressure increases from the roots towards the pole ends. At the roots, where the cores are attached to the yoke, the magnetic pressure difference is almost zero. It would be exactly zero if there were not a perceptible reluctance offered by the joints and by the metal of the yoke. The reluctance of the joint causes a few of the lines to take paths through the air by a leakage which adds to the useful flux. At the tops of the cores there is a difference of magnetic pressure equal to the sum of the ampere turns on the two cores, tending to drive magnetic lines across. This difference of magnetic pressure increases regularly all the way up the cores from root to top; hence, the average value may be taken as equal to the ampere turns on one core. The stray field, therefore, will steadily increase in density from the bottom upwards. In addition to this stray field between the pole cores there is also a stray field between the projecting tips or edges of the pole shoes, as shown in fig. 1,428. In some machines the dispersion due to the pole shoes is greater than that between the flanks of the cores.

Fig. 1,429.—Lincoln revolving field alternator. The frame has openings for ventilation, the fanning action of the pole pieces causing a current of air to pass not only over the end of the windings, as is usual with other designs, but also through ventilating slots in the windings themselves. The armature core laminations are annealed after punching and before assembling to guard against the crystalizing effect of the punching. The armature coils are form wound and insulated before being placed in the slot. There is also slot insulation which is put in the slot previous to inserting the coil. When the winding is completed, it is tested with a pressure of 4 to 10 times the normal voltage of the machine. The bearings are self-aligning. The machine is normally designed to operate at a power factor of approximately 70 per cent., which means that at that power factor, the armature and fields at full load will heat equally. If it have a higher power factor than 70 per cent. it means that the field windings will run considerably cooler than the armature windings with full load. If the power factor be lower than this, it will mean that the field windings will run hotter than the armature on full load; however, the machine is designed so that harmful heating does not occur on full load with greater power factor than 40 per cent.

Fig. 1,430.—Western Electric armature for self-excited alternator. The main winding is placed at the bottom of the slots, each coil being surrounded by an armour of horn fibre. The exciter winding occupies a very small portion of the slot, being placed on top of the main winding, and connected to the commutator immediately in front of the core and between core and collector rings as shown.

Fig. 1,431.—Frame, bed plate and armature winding for Westinghouse bracket bearing polyphase alternator.

Fig. 1,432.—General Electric alternator with direct connected exciter mounted on shaft between field hub and bearing. In the smaller sizes, the magnet frame is bolted to the bearing bracket, but in the larger sizes special construction is used depending upon the conditions to be met. The exciters are capable of furnishing the desired excitation for low power factors.

Fig. 1,433.—Fort Wayne alternator with direct connected exciter mounted on the field shaft at such distance as to permit a pedestal and bearing to be mounted between the exciter and revolving field. In the view, the bearing is hidden by the exciter, only the foot of the pedestal being visible.

Fig. 1,434.—Diagram showing a Westinghouse 50 kva., 2,400 volt, three phase, 60 cycle revolving field separately excited alternator direct connected to a steam engine. The exciter is belted to the alternator shaft, the driving pulley being located outside the main bearing. The small pulley on the exciter gives an indication of its high speed as compared with that of the alternator.

Fig. 1,435.—Crocker-Wheeler 350 kva., slow speed alternator direct connected to a Corliss engine. In front is seen a belted exciter driven from a pulley on the main shaft between the alternator and the large band wheel. The latter serves to give the additional fly wheel effect needed for close speed regulation.

Fig. 1,436.—Three Crocker-Wheeler 75 kva., slow speed alternators direct connected to high speed engines. The alternator is styled slow speed although connected to a high speed engine, because what is considered high engine speed is slow speed for alternator operation. The alternators have direct connected exciters which are plainly seen in the illustration placed on an extension of bearing pedestal. Direct connected exciters on units of this kind do not, as a rule, assume too bulky proportions, because of the high engine speed.

Fig. 1,437.—General Electric 48 pole 750 kw., three phase fly wheel type alternator. It runs at a speed of 150 revolutions per minute, giving a frequency of 60 cycles per second and a full load pressure of 2,300 volts. The slip rings and leads to the field winding are clearly shown in the figure. The field magnets are mounted directly on the rim of the spider, which resembles very closely a fly wheel, and which in fact it is—hence the name "fly wheel alternator."

Fig. 1,438.—Allis-Chalmers high speed belted type alternator. The small pulley at the right and the angle of the belt suggest the high speed at which such alternators are run, a 50 kva. machine turning 1,200 revolutions per minute.

Fig. 1,439.—Allis-Chalmers 5,000 kva., 450 R. P. M., 6,600 volt, 60 cycle, 3 phase, horizontal water wheel alternator. The shaft is extended for the reception of a flange coupling for direct connection to water wheel. Owing to the wide range in output of the generating units and also in the speed at which they must operate to suit varying conditions of head, types of wheels used, and other features pertaining to water power developments, it has been necessary to design a very complete line of machines for this work. The bearings are of the ring oiling type with large oil reservoirs.

Fig. 1,440.—Stator of 500 k.w. Allis-Chalmers alternator for direct connection to vertical shaft hydraulic turbine.

Fig. 1,441.—Allis-Chalmers revolving field for water wheel alternator. In this type of alternator it is essential that the rotating part be designed to have a liberal factor of safety not only at the ordinary operating speed, but also at speeds much in excess of normal. Frequently machines are required to operate safely at a speed 50 to 75 per cent. in excess of normal, so that there may be no danger in case the water wheel races. In most machines the field spider is of steel cast in a single piece for the smaller alternators and in two or more parts for the larger sizes. For alternators running at high peripheral speed, the rim is built up of steel laminations supported by a cast steel spider; the latter serves merely to rotate the rim, which is in itself able to withstand all stresses due to the high speed. The field poles are laminated, being built up of steel punchings held between malleable iron or bronze end plates, the latter being used on high speed machines. With but very few exceptions the poles are attached by dovetail projections that fit into corresponding slots. Steel tapered keys are driven in alongside the dovetails, and the pole pieces cannot become loose. All field coils, except on a few of the smallest machines, are of edgewise wound copper strip. This style of coil is essential for revolving field alternators where the pressure on the insulation, due to centrifugal force, is so great that cotton insulation on round wire will not stand. Current is led into the rings by means of carbon brushes, the number of brushes being such that the current density at the rubbing contact is kept within conservative limits. At least two brushes per ring are always provided so that one can be removed for inspection without interrupting the exciting current. In large machines the brush holder studs are mounted on a stand supported from the base; in small alternators they are usually fastened to the cap of one of the bearing pedestals.

Figs. 1,442 to 1,444.—Diagram of turbine alternator windings for revolving armature. Fig. 1,442 illustrates a two pole design in which all overlapping is avoided. It has 72 slots of which only 48 are filled, giving 8 slots per phase. The projecting claws from the brass end shield which hold the coils in position are shown in section. Fig. 1,443 shows a four pole design having 48 slots or 4 slots per phase per pole, the coils being made up of 8 inductors per slot taped together, the end bends forming two ranges. Fig. 1,444 shows a two pole design for a two phase armature with 18 slots per pole per phase. The core discs are spaced out as for 108 slots, but of these, 4 lots of 7 each are not stamped out, and 8 of those stamped are left empty, so that there are 72 slots filled.

Fig. 1,445.—5,000 kw. Curtis turbine alternators installed for the New York Central R. R. at Yonkers, N. Y. The illustration shows also the auxiliary apparatus consisting of condensers, vacuum augmenters, circulating pumps, air pumps, etc. The augmenter of the first machine is plainly seen between the condenser and centrifugal circulating pump.

Fig. 1446.—Diagram of constant pressure image current alternator connections. The image or reproduced currents are characteristic of all types of asynchronous machines, and are called image currents because they are actually the reflection from the load currents delivered by the armature circuit. The principle of operation is explained in the accompanying text.

Fig. 1,447.—Diagram of connections of self-exciting image current alternator.

Figs. 1,448 and 1,449.—Westinghouse laminated hub and laminated pole piece for revolving field having squirrel cage winding. Thin steel is used for the laminations of both hub and pole piece; these are assembled and firmly riveted together under hydraulic pressure. The laminations are of the same thickness in both hub and spider.

Figs. 1,450 to 1,452.—Views of Triumph pole pieces. These consist of laminated punchings securely clamped between two cast steel end plates. The laminations are shaped with polar horns or shoes as shown, and which serve to keep the field coils securely wedged in position. In some designs the horns are separate. The two holes in each pole piece are for through bolts which secure the pole piece and coil to the spider run. Dovetail joints are sometimes used instead of through bolts, as in figs. 1,448 and 1,449.

Fig. 1,453.—Fort Wayne armature for self-excited alternator. There are two independent windings, one for the main current, and one for the exciting current. The winding for the latter current occupies a very small amount of space, and is placed in the slots on top the main winding. The commutator to which the exciter winding is connected, is located between the collector rings and the core. It is of standard construction with end clamps holding the bars in place on the insulated commutator drum. The armature coils are form wound and the core is built of sheet steel laminations, annealed and japanned to prevent hysteresis and eddy current losses. Ventilated openings are provided to allow a free circulation of air both around the ends of the windings and through ducts in the laminated core. The core is clamped by bolts between the flanges of the armature spider which is keyed to the shaft. These flanges have cylindrical extensions with ribbed surfaces, which form a support for the ends of the armature coils. The ribbed surfaces form air passages from the core outward around the ends of the coils, thus ventilating both core and coils.

Fig. 1,454.—Allis-Chalmers three bearing type alternator with exciter direct connected. The bearing pedestals are bolted to a substantial cast iron base having, in the large sizes, sufficient length to permit shifting frame sideways along the base to give access to the field and armature coils. The field coils are designed for 120 volt excitation, and are wound edgewise with copper strip. There is a liberal margin of field excitation to take care of overloads or for operation on loads of low power factor. The regulating qualities are as good as can be obtained without making the machine unnecessarily large and expensive. By regulation is meant the percentage rise in voltage when full load is thrown off, field excitation and speed being held constant; the percentage is referred to normal full load voltage. An alternator with poor regulation will show large variations in voltage with changes in load, the pressure falling whenever a load is thrown on and rising when it is thrown off. These changes will be especially pronounced if the load be inductive. A badly designed alternator might show very fair regulation on non-inductive load and yet be unable to give full voltage on inductive load.

Fig. 1,455.—Diagram of separately excited alternator. The field winding is supplied with direct current, usually at 125 volts pressure by a small dynamo called the "exciter." The latter may be driven by independent power, or by belt connection with the main shaft, and in some cases the exciter is directly connected to the alternator shaft.

Fig. 1,456.—Diagram of compositely excited alternator. The current for exciting the field magnets is obtained, partly from an exciter and partly from the windings of the alternator, being transformed into direct current by the rectifier. The connections are as shown. One end of the armature winding is connected to one of the collector rings; the other end, to the light part of the rectifier, as shown, the solid black part of the rectifier being connected to the other collector ring. Two brushes bear on adjacent teeth of the rectifier and are connected to the compensating winding circuit across which is a shunt. These connections are shown more clearly in fig. 1,457. In operation the separately excited coils set up the magnetism necessary for the generation of the voltage at no load. The main current coming from the armature is shunted, part going through the shunts and the remainder around the compensating winding, furnishing the additional magnetism necessary to supply the voltage to overcome the armature impedance. This composite method of field excitation is very similar to that used on a compound wound dynamo. As shown, both field windings encircle every pole, but in some machines the rectified current will traverse a few poles only, the current from the exciter traversing the remainder.

Fig. 1,457.—Diagram showing construction of rectifier and connections of compositely excited alternator. The rectifier consists of two castings M and S with teeth which fit together as shown, being insulated so they do not come in contact with each other. Every alternate tooth being of the same casting is connected together, the same as though joined by a conducting wire. There are as many teeth as there are poles. One end of the armature winding is connected direct to one of the collector rings, while the other is connected to M of the rectifier, the circuit being through brushes P and Q, the shunt, and compensating winding to the other collector ring. The brushes P and Q contact with adjacent teeth, when one is in contact with the solid black casting the other touches the light casting. The principle of action is the same as a commutator, briefly: to reverse the connections terminating at the brushes P and Q in synchronism with the reversals of the alternating current induced in the armature winding, thus obtaining direct current for the compensating field winding. The shunt resistance placed across the compensating winding circuit permits adjusting the compounding of the machine to the circuit on which it is to work, since by varying the resistance the percentage of the total current passing through the compensating winding can be changed. It will be seen by tracing the path of the current for each direction in the armature winding that while the rectifier causes the current to flow in the same direction in the compensating field winding, it still remains alternating in the external circuit.

Fig. 1,458.—Connecticut magneto; view showing permanent magnets in dotted lines. It consists of three permanent U shape magnets, between the poles of which is a shuttle type armature. The latter is geared to a hand crank in sufficient velocity ratio to give the desired speed without too rapid turning of the crank. This type of magneto is used to generate current for operation of telephone call bells.

Figs. 1,459 to 1,461.—Diagram illustrating the operation of a magneto. The shuttle shaped armature is wound from end to end with insulated wire, so that when rotated, a powerful alternating current is produced in the windings by cutting the magnetic lines, whose varying strength is shown by the shaded portions in the two views. When in the position shown in the first diagram, the lines of force mostly converge at the top and bottom, finding a direct path through the metal end flanges of the shuttle. When in the position shown in the second diagram, the lines are converged so as to pass through the armature core. Fig. 1,460 shows detail of the armature core.

Fig. 1,462.—Stationary field of Fort Wayne multiphase revolving armature alternator; view showing brass girds on pole pieces for synchronous motor operation. When designed for this use the machine is provided with amortisseur winding on the poles. As shown in the illustration this winding consists of a brass collar around the pole tip with a cross rib integral with the collar, fitting in a slot in the pole face parallel to the shaft. This construction assists in bringing the machine up to synchronous speed as an induction motor, ordinarily checks any tendency toward hunting and does not in any way affect the operation of the machine as an alternator. The main field winding should be connected through switches on the field frame in order that the field circuit may be broken up to eliminate any danger that might arise from induced voltage. It is not advisable to throw on a full rated voltage and a compensator should, therefore, be provided to reduce the pressure.

Fig. 1,463.—Triumph 36 pole fly wheel type revolving field. The spider has the form of a fly wheel having spokes and rim to which the field magnets are attached by through bolts. The field coils are of copper strap bent on end, the kind generally used on large machines. The series connection of the coils is plainly shown, also the two cables leading via one of the spokes to the slip rings.

Fig. 1,464.—Wagner cast steel hub with dovetail grooves for attaching the revolving field magnets. Such construction is generally used on machines of small and medium size.

Fig. 1,465.—Wagner laminated pole piece with horns stamped in one piece. The laminations are held together between two end pieces by through rivets, as shown.

Fig. 1,466.—Wagner revolving field of 300 kilowatt alternator during construction, illustrating the method of attaching the field magnets to the hub by dovetail joints. After the notched ends of the pole pieces are slid into the grooves in the hub, tapered keys, which are plainly seen, are driven in, thus making a tight joint which will not shake loose.

Fig. 1,467.—General Electric field coil, showing one method of winding. In the smaller machines the wire is wound on spools which are slipped over the pole pieces, which are built of sheet iron, spreading at the pole face so as to secure not only a wide polar arc for the proper distribution of the magnetic flux, but also to hold the field windings in place.

Fig. 1,468.—General Electric field coil showing another method of winding. The field coils on the larger machines consist of a single strip of flat copper, wound on edge as shown, so that the surface of every turn is exposed to the air for cooling. The flat sides of the copper strip rest against each other and the entire coil forms a structure of great solidity which can be easily removed for inspection and repair.

Fig. 1,469.—Allis-Chalmers 60 kva. belted two bearing alternator on base arranged so the armature can be shifted sideways as shown, to give access to the field and armature coils.

Fig. 1,470.—Revolving field of Fort Wayne 10 pole alternator. In construction, the cores of the field poles are built up from punchings of laminated steel, and assembled under considerable pressure between malleable iron or steel end plates and riveted together. Substantial insulation is placed on the pole cores and over this is wound the field coils of cotton covered wire. After the wire is in place, the completed poles are baked to expel any moisture and are then treated with insulating varnish. They are then assembled on a laminated spider, being held in place by dovetail joints made tight by the use of taper keys. Special casting plates are finally fastened in place over the dove tails effectually closing them. The assembly of the field is completed by the insertion of the shaft into the field spider under heavy hydraulic pressure. All the coils are connected in series, cable leads connecting them to slip rings placed on the shaft. Each slip ring is provided with a double type brush holder, making it possible to clean brushes while the alternator is in service, by simply removing one brush at a time.

Fig. 1,471.—General Electric slip rings; view showing construction and attachment of cable leads to field winding. They are so designed that all surfaces of the rings have easy access to the air, in order to obtain good ventilation. Slip rings, through which current is transmitted to a revolving field, are to be distinguished from collector rings whose function it is to "collect" or transmit the alternating currents induced in the armature to the brushes.

Fig. 1,472.—Allis-Chalmers brush holder and slip rings. The latter are made of cast copper, which the builders claim to be more satisfactory than cast iron. On some of the large low speed machines the collector rings are split, but on the majority of alternators they are in one piece. Current is led into the rings by means of carbon brushes, the number of brushes being such that the current density at the rubbing contact is kept within conservative limits. At least two brushes per ring are provided, so that one can be removed for inspection without interrupting the exciting current. In large machines the brush holder studs are mounted on a stand supported from the base; on small alternators they are usually fastened to the cap of one of the bearing pedestals.

Fig. 1,473.—Fort Wayne multiphase revolving armature alternator, designed for use in small power plants and isolated lighting plants where inductive loads are encountered. Built for pressures of 120, 240, 480, and 600 volts. These voltages have been recommended by the American Institute of Electrical Engineers, and will cover the needs of any set of conditions ordinarily met with. These standard voltages not only permit economical distribution, but they are such that no transformers are necessary to reduce the line pressure for ordinary cases. For transmitting power relatively long distances, 600 volts is usually employed. Where there is a demand for 480 volt service, a 480 volt alternator should be selected and if lower voltages are also desired an auto-transformer may be furnished by means of which 240 volts can be obtained. When 120 volt circuits are necessary for lighting, etc., the 240 volt pressure can be still further reduced to 120 volts by means of another auto-transformer. However, this double reduction will rarely be found necessary.

Fig. 1,474.—Western Electric stationary armature. In this type of armature, the core upon which the winding is placed, is built into the frame as shown, the core teeth projecting inwardly like internal gear teeth, forming a cylindrical chamber for the revolving field. The core is built up of iron, laminated and japanned to prevent eddy currents and hysteresis losses. The laminations are rigidly bolted between two heavy end plates. The armature coils are of copper bar impregnated with insulating compound. They are held in the slots by wedges which allow their ready removal for inspection or repairs.

Figs. 1,474 to 1,477.—Various types of armature; fig. 1,474 ring armature; fig. 1,475 disc armature; fig. 1,476 drum armature. The latter type is now almost universally used, the others being practically obsolete. A Gramme ring wound and connected to collector rings as in fig. 1,474, will yield an alternating current. In a multipolar field, the ring will need multipolar connections alternated at points corresponding to the pitch of the poles. Fig. 1,475 illustrates the so-called "Siemens" disc armature. The armature coils are arranged around the periphery of a thin disc. The field magnets consist of two crowns of fixed coils, with iron cores arranged so that their free poles are opposite one another. This type was created in 1878 by Herr von Hefner, engineer to Messrs. Siemens and Halske. Fig, 1,476 shows a modern drum armature of a three phase machine. It is similar in appearance to a direct current armature except for the absence of the commutator and its connections. The drum armature is the prevailing type.

Fig. 1,478.—A style of disc largely used for armature cores. The teeth are provided with dovetail grooves near the circumference. After the coil is inserted in a groove, a wooden wedge is driven in the groove which encloses the coil and secures it firmly in position. This obviates the necessity of bands to resist the centrifugal force acting on the inductors.

Fig. 1,479.—Large revolving armature construction with segmental discs dovetailed to spider spokes.

Fig. 1,480.—Construction of large stationary armature; view showing section of core and frame. The core discs are in segments and are attached to the frame by dovetail joints as shown. The joints are staggered in building up the core, that is, they are overlapped so as not to unduly increase the reluctance of the magnetic circuit. Dovetail joints obviate the use of through bolts which, if not insulated, are liable to give rise to eddy currents by short circuiting the discs.

Fig. 1,481.—General Electric revolving field and exciter armature. This is an example of direct connected exciter construction. In this arrangement the armature of the exciter is carried on the alternator shaft at the end farthest from the pulley. In the smaller sizes the magnet frame is bolted to the bearing bracket, but in the larger sizes special construction is used depending upon the conditions to be met. On all alternators of standard design, the field is built for 125 volts excitation and on account of the increased danger from induced voltage, in case the machine is used as a synchronous motor, the builders consider any higher voltage undesirable.

Fig. 1,482.—Section of General Electric Alternator showing method of dovetailing core laminations to frame. The latter is made in two general styles, known as the box type and skeleton type. The box type consists of a single casting for the smaller sizes, but for large capacity alternators the frame castings are usually divided into upper and lower sections. The skeleton type consists of two side castings between which substantial spacing rods are set at regular intervals. The core consists of the usual sheet iron lamination slotted and assembled; they are mounted on the inner periphery of the frame, making lap joints (that is "staggered" as in fig. 1,480), each section being dovetailed to the frame. Heavy clamping rings or end plates are mounted on both sides of the core by means of bolts, and supporting fingers extend along the slot projections. The design is such as to provide for air circulation as shown in figs. 1,483 and 1,484.

Fig. 1,483.—Section of General Electric alternator frame showing air ducts and supporting fingers extending along the slot projections. The air circulation is provided for by means of ducts formed by suitable spacing blocks inserted at intervals between the laminations, as shown here and in fig. 1,484. The armature coils are form wound and designed so they can be readily replaced in case of injury. They are taped and treated with an impregnating compound, in the usual way, then inserted in the armature slots in an armour of horn fibre and retaining wedges of wood are dovetailed into the slot walls.

Fig. 1,484.—Section of General Electric stationary armature showing method of assembling the coils. These are form wound and are held in the slots by suitable wedges, the open slot construction permitting the use of form wound coils that can be easily removed and replaced in case of damage. Where heavy windings project beyond the laminations, an additional support is provided by means of an insulated metal ring, to which the outer ends of the coils are fastened; the coils are thereby protected from mechanical displacement, or distortion due to the magnetic disturbances caused by violent fluctuations of the load or short circuits. The figure shows a section of a supporting ring of this type and indicates the method of connecting the coils to it. In order to admit of the prompt replacement of damaged coils, sufficient space is usually provided between the alternator bearings to allow ample movement of the armature to permit of ready access to both armature and field coils. Where space necessitates the use of a short shaft, access to the windings may be had by disconnecting some of the coils and lifting the upper half of the armature.

Fig. 1,485.—Section of Western Electric stationary armature core showing laminations clamped in place, and ventilating ducts. The stator or stationary armature consists of soft iron laminations assembled in the magnet frame with stator coils embedded in the core slots. The laminations are punched separately and then carefully annealed to reduce hysteresis losses. After annealing, a coat of japan is applied, effectively preventing the flow of eddy currents in the assembled core. The frame is cast iron and of the box type construction. The frames of the smaller sizes are cast in one piece, while frames of the larger sizes are split to facilitate installation. Large openings are provided in the box type frame, in order to improve the ventilation. The laminations are securely held in place in the frame by heavy end rings and by steel clamping fingers which are firmly bolted to the frame. The outer circumference of the core is dovetailed to the frame, and the inner circumference is slotted to receive the windings. The alignment of the slots is insured by means of metal wedges, and no filing is done on the slots, so that each lamination is always insulated from the next one. Numerous ventilating ducts allow the free circulation of cool air through and around the coils. The open slot construction is employed and the coils are fitted into insulating troughs which offer excellent mechanical and electric protection. The coils are held in place by suitable wedges.

Fig. 1,486.—Method of assembling form wound coils. The picture shows a section of a General Electric armature with part of the coils in place. A layer of insulating material is first placed in the slots, before inserting the coils as seen at the left. When the coils are in place and surrounded by this layer of insulating material the retaining wedges are inserted in the notches, thus closing the slots and protecting the coils from mechanical injury. A few wedges are seen in position at the right.

Fig. 1,487.—Section of General Electric stationary armature ventilating ducts and winding in position.

Figs. 1,488 and 1,489.—Elementary bipolar alternators with half coil and whole coil windings. In a half coil winding there is one coil per phase per pair of poles; in a whole coil winding there is one coil per phase per pole.

Fig. 1,490.—Multi-polar revolving armature alternator with half coil winding, shown in radially developed diagram to clearly indicate the path of the winding. A half coil or hemitropic winding has a slightly higher reactance than a winding in which two distinct coils are used in the same slot, one going forward and the other backward. The most usual three phase windings are of the half coil type as the three sets of coils are equispaced over a pair of poles.

Fig. 1,491.—Multi-polar revolving armature alternator with whole coil winding shown in radially developed diagram to clearly indicate the path of the winding.

Figs. 1,492 and 1,493.—Concentrated windings. A concentrated winding is one in which the armature has only one tooth per phase per pole, that is, the number of teeth equals the number of poles. A concentrated winding of the half coil type has only one side of a coil in each slot as in fig. 1,492. In the whole coil variety, each slot contains neighboring sides of adjacent coils, as in fig. 1,493. In construction, wedges are generally used for retaining the half coils, and with whole coils the teeth have projecting horns for this purpose.

Fig. 1,494.—Laminated core with two coils in position; type of punchings used on some machines having concentrated whole coil windings. The manner of assembling the coils is shown in fig. 1,495.

Fig. 1,495.—Westinghouse single phase concentrated coil armature; view showing method of placing coils. The coils are machine wound on formers and after being taped, varnished and baked, are spread out slightly so as to pass over the teeth and are then forced into place in the deep slots by means of wooden wedges, being securely held in place by retaining wedges, as shown in fig. 1,494.

Figs. 1,496 to 1,498.—Alternator coils, showing difference between the concentrated, partially distributed, and fully distributed forms. Fig. 1,496 shows a concentrated coil in which all the wire is wound in one large coil; in the partially distributed type fig. 1,497, the wire of fig. 1,496, is wound in two or more coils or "sections" connected as shown, leaving some space inside not taken up by the subdivisions. In fig. 1,498 the wire of fig. 1,496 is fully distributed, being wound in a series of coils, so that all the interior space is taken up by the wire, that is to say, the spaces not occupied by the wire (the teeth when placed on the armature) are of equal size.

Fig. 1,499.—Partially distributed winding. Each coil unit is here divided into two concentric coils of different dimensions and connected in series, as shown in detail in fig. 1,497. This being a "whole coil" winding the several units are so connected that the winding of adjacent units proceeds in opposite directions, that is, one coil is wound clockwise, and the next counter clockwise, etc., so that the induced currents flow in a common direction as indicated by the arrows for the position shown.

Fig. 1,500.—Fully distributed winding. In this type of winding each coil consists of so many sub-coils that the winding occupies the entire surface of the armature core; that is, there are no extensive spaces unoccupied, the spacing being uniform as shown.

Fig. 1,501.—Developed diagram of single phase concentrated whole coil winding in two slot stamping for six pole alternator. If the sides of adjacent whole coils be slightly separated by placing the winding in a two slot stamping the electrical result will not differ materially from the monotooth whole coil winding, but if the winding be hemitropic, as in fig. 1,502, and has coils of two sizes as shown, it will be suitable for high voltages.

Fig. 1,502.—Developed diagram of single phase partially distributed half coil winding for six pole alternator in two slot stamping, same as in fig. 1,501. In this arrangement the direction of rotation is not reversed. It is a question as to how far the coils of a single-phase armature may be spread with advantage. There is not much advantage in reducing the interior breadth of the coils below that of the pole face, nor in widening the exterior breadth beyond that of the pole pitch.

Fig. 1,503.—Developed diagram of single phase winding with fully distributed coils. As explained, excessive spreading lowers the value of the "Kapp" coefficient, and consequently the voltage; also the use of a larger number of inductors to obtain the same voltage results in an increase of armature self-induction. On the other hand, if the winding were concentrated in fewer slots and these slots were closer together, the result will be an increase in distorting and demagnetizing reactions of the armature. Therefore, a compromise between these two disadvantages must be made. The common practice is to wind in two or three slots per pole per phase.

Fig. 1,504.—Allis-Chalmers lap wound coils forming a three slot distributed coil unit. In construction, after the coils have been covered with insulating materials and treated with insulating compound, the parts that lie in the slots are pressed to exact size in steam-heated moulds. This runs the insulating material into all the small spaces in the coil, excluding moisture and rendering the insulation firm and solid. The ends of the coils, where they project beyond the slots, are heavily taped.

Fig. 1505.—Allis-Chalmers armature construction; view showing section of frame and two layer winding.

Figs. 1,506 and 1,507.—Effect of breadth of coils in distributed windings. In the section of the alternator shown in fig. 1,506 the directions of the pressures induced as the armature rotates clockwise are represented by dots for those which act towards the reader, and by crosses for those which act from the reader (the dots and crosses representing respectively the heads and tails of arrows). Since the field is not uniform but maximum at the center and gradually weakening towards the extremities, it is obvious that the maximum pressure is induced in any inductor as it passes the center of the pole, this variation being indicated by the heavier dots and crosses toward the center. Now if a number of these inductors be connected up to form a distributed coil as in fig. 1,507, the pressures induced in each will be added, but all the maximum pressure will not be induced in all at the same time, hence the total pressure induced in the distributed coil is less than it would be if the coil were concentrated as in fig. 1,509.

Fig. 1,508.—Diagram of distributed coil whose inner breadth is less than the breadth of the pole face, showing the disadvantage of such arrangement. The pressures induced in the inner windings of such a coil are opposing each other at the instant depicted, that is, while the inductors are under the pole face, such action of course being objectionable.

Fig. 1,509.—Simple form of alternator coil, consisting of numerous turns of insulated wire wound around a form, then covered with a tape winding, varnished and baked.

Figs. 1,510 and 1,511.—Multi-wire inductors. When the cross section of inductor necessary to carry the current is large, the use of a single wire would present difficulties in winding on account of its stiffness. Accordingly two or more smaller wires are used in parallel to secure the required cross section. Bare wire is used and the several sections encased in insulation as shown, the combination being more flexible than an equivalent single wire.

Fig. 1,512.—Two coil slot for whole coil winding. The slot has two recesses A and B for the reception of separate coils. In assembling the winding, the inner wedge is first placed in position and then the slot line with the insulating material. This usually consists of alternate layers of mica and pressboard. The coils composed of several turns of wire or copper strip are wound in place, and after covering with a layer of insulation, the outer wedge is pushed in place to retain the inductors in position.

Fig. 1,513.—Method of winding a coil containing a large number of turns, when there is considerable difference of pressure between the layers. In such cases to guard against short circuits or breakdown of the insulation, each layer of turns is insulated from the next layer by the insulating strips A, B, C, in addition to the regular insulation around each wire. After the coil is made up it is wound with insulating tape, varnished and baked.

Figs. 1,514 and 1,515.—Single and double layer multi-wire inductors and methods of placing them on the core. Here the term layer means unit, in fact each unit is made up of several "layers" of wires. In fig. 1,514, where so many wires are bunched together in one unit, each layer of turns is separated from those adjacent by insulating strips on account of the considerable difference of pressure between layers. This insulation is not necessary in fig. 1,515 where there are two units or so called layers. In both cases the inductors are held in place by wedges driven into dovetail grooves.

Fig. 1,516.—Copper strap or ribbon with insulation. These are generally from ¹/₃₂ to ¹/₁₆ inch thick with rounded edges as shown to avoid cutting the insulation.

Fig. 1,517.—Bar inductor. Its shape enables putting the maximum cross section of copper into the slot and is used to advantage on machines which generate large currents.

Fig. 1,518.—Style of armature core stamping used with bar wound machines. This construction, since there are no indentations in the teeth for wedges, makes it necessary to provide bands to hold the bars in place.

Figs. 1,519 and 1,520.—Bent bar inductor and method of connection with soldered joint. Fig. 1,519 shows one bar and shape of bent ends. The portion from C to D is placed in the slot; B to C and D to E, bent or connector sections; A to B and E to F, ends bent parallel to slot for soldering. Fig. 1,520 shows two bar inductors connected.

Figs. 1,521 and 1,522.—Method of avoiding a soldered joint at one end of a bar inductor by using a bar of twice the length shown in fig. 1,519, and bending it into a long U form, as in fig. 1,521, after which it is spread out forming two inductors, as in fig. 1,522.

Fig. 1,523.—Arrangement in slot of two layer bar winding. With bar inductors, as must be evident from the illustration, the maximum cross section of copper can be placed in a slot of given dimension, hence a bar winding is used to advantage for alternators designed to carry a large current. Bar inductors, on account of the shape of their ends, must be placed in the slots from the top, because the bent ends do not admit of pushing them in. Straight slots are therefore necessary, the inductors being held in place by wooden strips and tie bands as shown.

Fig. 1,524.—Diagram of single phase multi-coil or distributed winding to show characteristic differences in action and construction from single coil or concentrated winding.

Fig. 1,525.—Vector diagram of pressures induced in the single phase multi-coil or distributed winding shown in diagram in fig. 1,524.

Fig. 1,526.—Developed diagram of a single phase monotooth or one slot bar winding; it is suitable only for operation at low voltage.

Fig. 1,527.—Diagram of six pole single phase revolving armature alternator, with monotooth or concentrated whole coil winding. For 3,000 volts at 900 revolutions per minute, 120 inductors are required. And in the case of a concentrated or monotooth winding they may be arranged in "whole coils" as above or in "half coils" (hemitropic) as in fig. 1,528.

Fig. 1,528.—Diagram of six pole single phase alternator with concentrated half coil or hemitropic winding of same capacity as in fig. 1,527. There are an equal number of inductors, but in this case arranged in three instead of six coils. In this winding the direction of winding is alternately reversed so that the induced pressures do not oppose one another.

Fig. 1,529.—Two phase concentrated whole coil winding. In this style winding the total number of slots is twice the number of poles, or one slot per pole per phase. It comprises two windings identical with fig. 1,527, being spaced 90 polar degrees as shown. The two circuits are independent, the windings terminating at the four collector rings.

Fig. 1,530.—Two phase winding in two slots per pole per phase. This stamping distributes the coils of each phase into two sections, as A and B. The coils are of the "whole" type and with six poles the total number of slots is 4 × 6 = 24, uniformly spaced as shown.

Figs. 1,531 and 1,532.—Developed diagram of the single phase monotooth windings shown in figs. 1,527 and 1,528.

Fig. 1,533.—Two phase winding in three slots per pole per phase. The coils of each phase are of the partially distributed type, each coil being made up of three sections as shown. The direction of winding is alternately reversed.

Fig. 1,534.—Section of two phase winding showing shaping of the coil ends. Every other coil is flat, while the alternates have their ends bent down as shown. With respect to the shaping of the coil ends, it is called a two range winding.

Fig. 1,535.—Section of Triumph armature showing method of arranging the three phase winding.

Fig. 1,536.—Three phase winding with distributed coils—wound in four slots per pole per phase; diagram showing placement of the coils.

Fig. 1,537.—Treatment of coil ends in two phase, two range windings. In this arrangement straight out (B) and bent up (A) coils are used which are placed on the armature as is clearly shown in the illustration.

Fig. 1,538.—Three phase, 10 pole, 30 slot winding in two ranges. In this winding perfect symmetry occurs after every four poles. Accordingly in the case of an odd number of pairs of pole, one of the coils must necessarily be askew going from the inner to the outer range as at M.

Fig. 1,539.—Three phase 10 pole 30 slot winding in three ranges. The coils of each phase are alike, those of the A phase being all in the straight out range, those in the B phase, in a bent up range, and those in the C phase in a bent down range. This arrangement has the disadvantage, that by reason of the third range, the field magnet cannot be withdrawn. This treatment of the coil ends is more clearly shown in fig. 1,540.

Figs. 1,540 and 1,541.—Treatment of coil ends in three phase, three range windings. Fig. 1,540, inadmissible arrangement in which the field magnet cannot be withdrawn; fig. 1,541, admissible arrangement in which the armature segments can be divided. This enables the top half of armature to be removed by disconnection without unwinding any coil.

Fig. 1,542.—Three phase winding with half coils. The advantage of employing half coils is that the ends may be arranged in two ranges as shown. There is one slot per phase per pole, that is, total number of slots = 3 × number of poles.

Fig. 1,543.—Three phase winding with whole coils. Two sides of adjacent coils come in one slot. Number of coils per phase = number of poles per phase. Total number of slots = 3 multiplied by number of poles per phase. Whole coils require the ends arranged in three ranges as indicated. The coils are concentrated.

Fig. 1,544.—Diagram of two phase star grouping.

Fig. 1,545.—Diagram of two phase mesh grouping.

Fig. 1,546.—Diagram of three phase star grouping, commonly called Y grouping owing to its resemblance of the letter Y. The current in each main is obviously equal to the current in each phase winding, but the terminal pressure is the vector sum of the pressures in the component phase windings, that is, √3 multiplied by the pressure in one phase.

Fig. 1,547.—Radial diagram of three phase, one slot winding with Y connection.

Fig. 1,548.—Radial diagram of three phase one slot winding with delta connection.

Fig. 1,549.—Diagram of three phase mesh grouping, commonly called delta grouping owing to its resemblance to the Greek letter Δ. The voltage at the terminals is equal to the voltage in one phase, and the current in each line is equal to the vector sum of the currents in two phases, that is, it is equal to √3 multiplied by the current in one phase.

Fig. 1,550.—Three phase winding with short coils. The use of short coils as here shown, in which the coil breadth = ⅔ pole pitch, avoids the necessity of overlapping.

Fig. 1,551.—Radial diagram of three phase lap winding with star connection.

Fig. 1,552.—Radial diagram of three phase wave winding with star connection.

Figs. 1,553 and 1,554.—Gramme ring armatures showing three phase star and mesh connections, respectively, with direction of currents in the coils. In the figures, the coils A, B, C, are spaced at equidistant positions on the ring core. The arrow heads represent the directions of the induced pressures or currents for the position shown, the rotation being clockwise. In coil A the pressure is increasing, in coil B it is diminishing, but is in the same direction as in A, whereas in coil C it is also diminishing, but is in the opposite direction to what it is in coils A and B. As the rings rotate the three coils have similar alternations of pressure induced in them, but differ in phase. If a, b and c be joined to collector rings three phase currents can be supplied to the outer circuits. In fig. 1,553 at the instant represented a and b are giving their current to their lines, while c is receiving from its line a current equal to the sum of a and b. In fig. 1,554, at the instant represented, the currents sent out from a will be equal to the sum of the currents in x and y, and intermediate between them in phase. The current from b will be equal to the difference of the currents in z and y, and of intermediate phase, while similarly the current received by c will be equal to the sum of the currents in x and z.

Figs. 1,555 to 1,557.—Separate coils, and section of Allis-Chalmers alternator with coils in place. Numerous openings are provided in the frame through which air currents, set up by the revolving field, can pass freely and carry off heat. Shields are provided to protect the armature coils where they project beyond the core. In assembling the core spacing segments are placed at intervals to form ventilating ducts. After the coils have been covered with insulating materials and treated with insulating compound, the parts that are to lie in the slots are pressed to exact size in steam heated moulds. This runs the insulating material into all the small spaces in the coil so as to exclude moisture, it also makes the coil structure firm and solid. The projecting ends of the coils are heavily taped, suitable supports being provided for the coil connections so that they cannot become displaced on account of stresses due to short circuits or other causes. On high pressure machines the armature terminals are arranged so that it is impossible for an attendant to make accidental contact with them.

Fig. 1,558.—Diagram of Westinghouse two phase composite wound alternator, showing connections between two phase armature and a single phase rectified and composite field winding. The arrangement makes use of a series transformer, mounted on the spokes of the armature. By means of this series transformer the voltage delivered to the rectifying commutator and the fields is much less than that generated by the machine. The armature of this machine is of the closed coil single winding type, all the armature inductors being connected with each other to form a closed circuit which resembles to a certain extent the ordinary drum winding of a multipolar direct current machine. This winding is tapped out at two points per pole just as is the continuous winding of a two phase rotary converter, these taps running to collector rings through which the currents are delivered to the outside circuits. On account of this connection of both phases to one winding there is a definite voltage set up between the inductors of phase A, and of phase B, this voltage being shown by the figures given in the diagram. The arrangement is adapted for two phase work by fitting the series transformer for the auxiliary field excitation with two primaries connected respectively in one leg of each of the two phases; thus the transformer is excited by two currents normally ¼ period out of phase with each other. The result upon the secondary is a combination of the effects of the two primary currents, the voltage delivered by the secondary being intermediate in phase between those pressures which would be separately set up by the two primaries. This combination effect is shown in the small diagram in the upper right hand corner of the illustration. If OA be the effect set up in the secondary of the series transformer by the primary current of phase A, and OB be the effect set up by the primary current of phase B, OC represents in magnitude and phase relation the resultant effect upon the secondary. It is readily seen that this resultant is not equal to the arithmetical sum of the two components since, to a certain extent, they work at cross purposes. However, if either one of them increase the resultant effect increases, although not in exact proportion. If the load remain balanced, the two components remaining equal to each other, the resultant OC varies in exact proportion to any changes in the components. If the load become unbalanced, the resultant swings around more nearly into phase with the larger load; thus if OB become greater, OA remaining the same, OC swings around, becoming more nearly horizontal. This requires a readjustment of the position of the brushes on the commutator to set them properly for minimum sparking, an adjustment exactly similar to that required when the power factor of the load changes.

Fig. 1,559.—Diagram of Westinghouse three phase composite wound alternator. The armature inductors are of the closed coil or delta connected type, but are tapped at three points per pair or poles to the three collector rings. All three connections between the armature coils and the collector rings run through primary circuits of the series transformer within the armature, these three primaries each giving their own effect upon the secondary. Since the resultant of three equal alternating electromotive forces 120° apart is zero, so that some special arrangement must be adopted to make these electromotive forces act with instead of against each other. The arrangement is a reversal of the connections of one of the primaries of the series transformer. This is shown in the case of the lowest primary indicated in the diagram. The combination of the effects of the three primaries is again indicated in the small vector diagram in the upper right hand corner. Here OA is the effect of one primary, OB that of another ⅓ of a period displaced from the former in phase, and OC that which the third would exert were it not reversed, but the reversal brings the effect of this third coil into the phase relation OD, so that the three are only 60° apart. The combination of OA and OB is equal to OC, which combined again with OD gives a resultant effect, OE. In this case, as in the other, the effect upon the series field does not remain exactly proportional to the load unless the latter is balanced; in fact, an increased current through the one leg represented by OD, affects the series field as much as an equal increase in each of the other legs put together. Practically, however, any increase of the load—distributed as it must be in two legs at least—increases the field excitation so that proper regulation is secured.

Fig. 1,560.—Diagram showing determination of path and value of current flowing in delta connected armature.

Fig. 1,561.—Triumph brushes and brush holder. The holder is of the box type provided with an adjustable tension spring, making the brushes self-feeding. Each holder is carried on insulated studs attached to a cast iron yoke which is mounted on the bearing.

Fig. 1,562.—Diagram of Y connection with a common return wire. When the three lines leading from a, b and c are equal in resistance and reactance, or in other words when the system is balanced, the currents of the three phases are equal and are 120° apart in phase (each current lagging behind its pressure by the same amount as the others) and their sum is at each instant equal to zero. In this case the resultant current being equal to zero there is no need of a common return wire. However, in some cases, where power is distributed from transformers or three wire systems, the different branches are liable to become unbalanced. Under such circumstances the common return wire is sometimes used, being made large enough to take care of the maximum unbalancing that may occur in operation. The return wire is used sometimes on alternators that furnish current mostly for lighting work.

Fig. 1,563.—Diagram showing chain winding. In this method of winding the coils are all similar with long and short sides. It obviates the extra cost of making coils of several different shapes. The diagram represents a winding for one slot per pole per phase.

Fig. 1,564.—General Electric terminal board showing cables leading to three phase winding.

Fig. 1,565.—Section of armature winding of Allis-Chalmers 500 kw. three phase water wheel alternator. The coils are of the concentrated "half" type. Each coil is completely insulated before being placed on the core and no insulation is placed in the slot itself. The ends of the coils where they project beyond the slots are heavily taped. Where necessary suitable supports are provided for the coil connections so that they cannot become displaced on account of stresses due to short circuits or other causes. The winding is of the "chain" type. This is shown by the way the coils are connected together at the right. The armature terminals are either provided with insulated connectors or are led to a marble terminal board on which the terminals are so mounted and protected that it is impossible for an attendant to make accidental contact with them. The position of the illustration would indicate a horizontal alternator but the machine is of the vertical type; the lug on the right shows this, being used for adjusting the alternator on the foundation.

Figs. 1,566 to 1,568.—Views of a section of skew coil winding; so called on account of the skew shape given to the coil ends in order that all the coils may be of one shape.

Fig. 1,569.—Diagram showing a spiral coil. This type of coil is one in which each successive turn lies entirely within the previous turn, starting with the outermost turn of the coil. The successive turns of a spiral coil are thus not of the same size, and are not overlapping as in a "lap" coil.

Fig. 1,570.—Frame and armature winding of Westinghouse pedestal bearing alternator. Armature frames are of cast iron and ventilated. Interior transverse ribs strengthen the frame and support the core laminations. The armature core is built up of annealed and japanned punched laminations. Armature slots are open. Armature coils are form wound, impregnated, and interchangeable; they are held in place with fiber wedges. Ventilating spaces are provided at intervals in the armature core and also between all coil ends.

Figs. 1,571 and 1,572.—Diagram of creeping windings. Fig. 1,571, three coils subtending four poles; fig. 1,572, nine coils subtending eight poles.

Figs. 1,575 and 1,576.—Westinghouse turbine alternator armature construction. Fig. 1,575. View showing dovetail grooves in armature casting; fig. 1,576, laminæ assembled in dovetail grooves of armature casting.

Fig. 1,577.—Armature of Westinghouse turbine alternator with end bells removed showing method of bracing the coil ends.

Fig. 1,578.—Stationary armature of Westinghouse turbine alternator with part of the winding in place. Because of the small number of coils in a turbine alternator as compared with a slow speed machine of the same kva. rating, each coil carries a great amount of power on large load, particularly at times of short circuits or grounds on the external circuit. The "throw" of the coils is large, leaving a considerable part of the winding in the end turns unsupported by the armature core. For these reasons great stresses, which are dangerous, if effective means be not adopted to withstand them, may exist between the coils. The inductors are of such cross section that they can be made rigid and insulated satisfactorily. The end turns are given a fan like form as shown, affording ventilation and effective bracing as shown in fig. 1,577. Cord lashings are, except in the smallest frames, used only for holding in the small spacing blocks between the coils. They are not depended on to support the coils. Malleable iron braces, hard maple blocks, and brass or steel bolts with brass washers are used to withstand the mechanical stresses imposed on the armature coils by external short circuits.

Fig. 1,579.—Two pole radial slot field. Radial slot fields are used on very small and very large alternators. The field diameters are so small that the end turns of the winding can be effectively bound into place, such binding being necessary with a radial slot machine. The shaft and disc are a one piece forging of steel.

Figs. 1,580 to 1,582.—Westinghouse two pole parallel slot field with ends removed showing construction. The parallel slot design of field construction is used in Westinghouse machines up to 10,000 kva. capacity. In fig. 1,581, the large holes at the end near the circumference of the cylinder are for the accommodation of the bolts that hold the bronze end discs and stub shafts. In winding, the cylinder is mounted on a horizontal turntable that rotates in a horizontal plane. The copper strap field coil winding is wound turn by turn under pressure and strip insulation is wound in between. When completed the turns are held rigidly in position with heavy brass wedges. An end disc made of bronze holds the stub shaft and is bolted to each end of the steel center. When the leads are attached to the collector rings the field is complete.

Fig. 1,583.—Westinghouse two pole parallel slot turbine alternator field.

Fig. 1,584.—Westinghouse four pole parallel slot turbine alternator field.