Hawkins Electrical Guide, Vol 5 , by Nehemiah Hawkins

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.

If two identical simple alternators have their armature shafts coupled in such a manner, that when a given armature coil on one is directly under a field pole, the corresponding coil on the other is midway between two poles of its field, the two currents generated will differ in phase by a half alternation, and will be two phase current.

Ans. It must have two independent windings, and these must be so spaced out that when the volts generated in one of the two phases are at a maximum, those generated in the other are at zero.

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.

The windings of the two phases must, of course, be kept separate, hence the armature will have four terminals, or if it be a revolving armature it will have four collector rings.

As must be evident the phase difference may be of any value between 0° and 360°, but in practice it is almost always made 90°.

Ans. A two phase system requires four lines for its distribution; two lines for each phase as in fig. 1,253. It is possible, but not advisable, to reduce the number to 3, by employing one rather thicker line as a common return for each of the phases as in fig. 1,256.

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.

Ans. The mid point of the windings of the two phases may be united in the alternator at a common junction.

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.

Ans. The two circuits may be separate, each having two collector rings, as shown in fig. 1,257, or the two circuits may be coupled at a common middle as in fig. 1,258, or the two circuits may be coupled in the armature so that only three collector rings are required as shown in fig. 1,259.

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.

Three Phase Current.—A three phase current consists of three alternating currents of equal frequency and amplitude, but differing in phase from each other by one-third of a period. Three phase current as represented by sine curves is shown in fig. 1,260, and by hydraulic analogy in fig. 1,262. Inspection of the figures will show that when any one of the currents is at its maximum, the other two are of half their maximum value, and are flowing in the opposite direction.

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.

Ans. It requires three equal windings on the alternator armature, and they must be spaced out over its surface so as to be successively ⅓ and ⅔ of the period (that is, of the double pole pitch) apart from one another.

Six wires, as in fig. 1,260, might be used where it is desired to supply entirely independent circuits, or as is more usual only three wires are used as shown in fig. 1,261. In this case it should be observed that if the voltage generated in each one of the three phases separately E (virtual) volts, the voltage generated between any two of the terminals will be equal to √3 × E. Thus, if each of the three phases generate 100 volts, the voltage from the terminal of the A phase to that of the B phase will be 173 volts.

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.

Inductance.—Each time a direct current is started, stopped or varied in strength, the magnetism changes, and induces or tends to induce a pressure in the wire which always has a direction opposing the pressure which originally produced the current. This self-induced pressure tends to weaken the main current at the start and prolong it when the circuit is opened.

If the direct current maintains the same strength and flow steadily, there will be no variations in the magnetic field surrounding the wire and no self-induction, consequently the only retarding effect of the current will be the "ohmic resistance" of the wire.

If an alternating current be sent through a circuit, there will be two retarding effects:

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.

Ans. Upon the frequency of the alternating current, the shape of the conductor, and nature of the surrounding medium.

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.

Ans. It is the total magnetic flux threading the circuit per unit current which flows in the circuit, and which produces the flux.

In this it must be understood that if any portion of the flux thread the circuit more than once, this portion must be added in as many times as it makes linkage.

Inductance, or the coefficient of self-induction is the capacity which an electric circuit has of producing induction within itself.

Inductance is considered as the ratio between the total induction through a circuit to the current producing it.

Ans. A coil has an inductance of one henry when the product of the number of lines enclosed by the coil multiplied by the number of turns in the coil, when a current of one ampere is flowing in the coil, is equal to 100,000,000 or 10⁸.

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.

The henry [2] is too large a unit for use in practical computations, which involves that the millihenry, or ¹/_1,000th henry, is the accepted unit. In pole suspended lines the inductance varies as the metallic resistance, the distance between the wires on the cross arm and the number of cycles per second, as indicated by accepted tables. Thus, for one mile of No. 8 B. & S. copper wire, with a resistance of 3,406 ohms, the coefficient of self-induction with 6 inches between centers is .00153, and, with 12 inches, .00175.

[2] NOTE.—The American physicist, Joseph Henry, was born in 1798 and died 1878. He was noted for his researches in electromagnetism. He developed the electromagnet, which had been invented by Sturgeon in England, so that it became an instrument of far greater power than before. In 1831, he employed a mile of fine copper wire with an electromagnet, causing the current to attract the armature and strike a bell, thereby establishing the principle employed in modern telegraph practice. He was made a professor at Princeton in 1832, and while experimenting at that time, he devised an arrangement of batteries and electromagnets embodying the principle of the telegraph relay which made possible long distance transmission. He was the first to observe magnetic self-induction, and performed important investigations in oscillating electric discharges (1842), and other electrical phenomena. In 1846 he was chosen secretary of the Smithsonian Institution at Washington, an office which he held until his death. As chairman of the U. S. Lighthouse Board, he made important tests in marine signals and lights. In meteorology, terrestrial magnetism, and acoustics, he carried on important researches. Henry enjoyed an international reputation, and is acknowledged to be one of America's greatest scientists.

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.

Ans. It is least with an air core; with an iron core, it is greater in proportion to the permeability [3] of the iron.

The coefficient L for a given coil is a constant quantity so long as the magnetic permeability of the material surrounding the coil does not change. This is the case where the coil is surrounded by air. When iron is present, the coefficient L is practically constant, provided the magnetism is not forced too high.

In most cases arising in practice, the coefficient L may be considered to be a constant quantity, just as the resistance R is usually considered constant. The coefficient L of a coil or circuit is often spoken of as its inductance.

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.

Ques. Why is the iron core of an inductive coil made with a number of small wires instead of one large rod?

Ans. It is laminated in order to reduce eddy currents and consequent loss of energy, and to prevent excessive heating of the core.

EXAMPLE.—An air core coil has an average radius of 10 centimeters and is 20 centimeters long, there being 500 turns, what is the inductance?

Substituting these values in formula (1)

L = 4 × (3.1416)² × 10² × 500² ÷ (20 × 10⁹) = .00494 henry

Ans. No; the henry being a very large unit, it is usual to express inductance in thousandths of a henry, that is, in milli-henrys. The answer then would be .04935 × 1,000 = 49.35 milli-henrys.

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.

EXAMPLE.—An air core coil has an inductance of 50 milli-henrys; if an iron core, having a permeability of 600 be inserted, what is the inductance?

The inductance of the air core coil will be multiplied by the permeability of the iron; the inductance then is increased to

50 × 600 = 30,000 milli-henrys, or 30 henrys.

Ohmic Value of Inductance.—The rate of change of an alternating current at any point expressed in degrees is equal to the product of 2π multiplied by the frequency, the maximum current, and the cosine of the angle of position θ; that is (using symbols)

The numerical value of the rate of change is independent of its positive or negative sign, so that the sign of the cos φ is disregarded.

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.

The period of greatest rate of change is that at which cos φ has the greatest value, and the maximum value of a cosine is when the arc has a value of zero degrees or of 180 degrees, its value corresponding, being 1. (See fig. 1,037, page 1,068.)

The pressure due to inductance is equal to the product of the rate of change by the inductance; that is, calling the inductance L, the pressure due to it at the point of maximum value or

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.

The frequency of a current being the number of periods or waves per second, then, if T = the time of a period, the frequency of a current may be obtained by dividing 1 second by the time of a period; that is

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.

Capacity.—When an electric pressure is applied to a condenser, the current plays in and out, charging the condenser in alternate directions. As the current runs in at one side and out at the other, the dielectric becomes charged, and tries to discharge itself by setting up an opposing electric pressure. This opposing pressure rises just as the charge increases.

A mechanical analogue is afforded by the bending of a spring, as in fig. 1,279, which, as it is being bent, exerts an opposing force equal to that applied, provided the latter do not exceed the capacity of the spring.

Ans. It is exactly opposite to that of inductance, that is, it assists the current to rise to its maximum value sooner than it would otherwise.

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.

Ques. Is it necessary to have a continuous metallic circuit for an alternating current?

Ans. No, it is possible for an alternating current to flow through a circuit which is divided at some point by insulating material.

Ans. Its flow depends on the capacity of the circuit and accordingly a condenser may be inserted in the circuit as in fig. 1,286, thus interposing an insulated gap, yet permitting an alternating flow in the metallic portion of the circuit.

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.

Ans. The unit of capacity is called the farad and its symbol is C. A condenser is said to have a capacity of one farad if one coulomb (that is, one ampere flowing one second), when stored on the plates of the condenser will cause a pressure of one volt across its terminals.

It should be noted that the microfarad is used only for convenience, and that in working out problems, capacity should always be expressed in farads before substituting in formulæ, because the farad is chosen with respect to the volt and ampere, as above defined, and hence must be used in formulæ along with these units.

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.

Ans. It is proportional to the area of the plates, and inversely proportional to the thickness of the dielectric between the plates, a correction being required unless the thickness of dielectric be very small as compared with the dimensions of the plates.

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.

Specific Inductive Capacity.—Faraday discovered that different substances have different powers of carrying lines of electric force. Thus the charge of two conductors having a given difference of pressure between them depends on the medium between them as well as on their size and shape. The number indicating the magnitude of this property of the medium is called its specific inductive capacity, or dielectric constant.

The specific inductive capacity of air, which is nearly the same as that of a vacuum, is taken as unity. In terms of this unit the following are some typical values of the dielectric constant: water 80, glass 6 to 10, mica 6.7, gutta-percha 3, India rubber 2.5, paraffin wax 2, ebonite 2.5, castor oil 4.8.

In underground cables for very high pressures, the insulation, if homogeneous throughout, would have to be of very great thickness in order to have sufficient dielectric strength. By employing material of high specific inductive capacity close to the conductor, and material of lower specific inductive capacity toward the outside, that is, by grading the insulation, a considerably less total thickness affords equally high dielectric strength.

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".

Ans. They may be connected in parallel as in fig. 1,283, or in series (cascade) as in fig. 1,284.

Ans. This may be done by the aid of a standard condenser, trigger key, and an astatic or ballistic galvanometer.

		N × T
L	=		(1)
		10⁸

			L
X_i	=	2π
			T