Theory and Calculation of Electric Circuits — part 2 of 15

ELECTRIC CONDUCTION 9 voltage, no permanent current flows through the electrolyte, or - rather only a very small “leakage’’ current or “‘diffusion’’ cur- rent, as shown in Fig. 3. When closing the circuit, however, a transient current flows. At the moment of circuit closing, no counter e.m.f. exists, and current flows under the full impressed voltage. This current, however, electrolytically produces a hy- drogen and an oxygen film at the electrodes, and with their grad- ual formation, the counter e.m.f. of polarization increases and de- creases the current, until it finally stops it. The duration of this transient depends on the resistance of the electrolyte and on the surface of the electrodes, but usually is fairly short. 7. This transient becomes a permanent with alternating im- pressed voltage. Thus, when an alternating voltage, of a maxi- o£ aan SERRE S==e AIR PP) Tt yt ty Fi tT Tt tt | eb Fia. 3. mum value lower than the polarization voltage, is impressed upon an electrolytic cell, an alternating current flows through the ; cell, which produces the hydrogen and oxygen.films which hold back the current flow by their counter e.m.f. The current thus . flows ahead of the voltage or counter e.m.f. which it produces, as a leading current, and the polarization cell thus acts like a : condenser, and is called an “‘electrolytic condenser.” It has an enormous electrostatic capacity, or “effective capacity,” but can stand low voltage only —1 volt or less—and therefore is of limited industrial value. As chemical action requires appreciable time, such electrolytic condensers show at commercial frequencies -high losses of power by what may be called “chemical hysteresis,” and therefore low efficiences, but they are alleged to become efficient at very low frequencies. For this reason, they have

' ! 10 ELECTRIC CIRCUITS been proposed in the secondaries of induction motors, for power- factor compensation. Iron plates in alkaline solution, as sodium carbonate, are often considered for this purpose. Norse.—The aluminum cell, consisting of two aluminum plates with an electrolyte which does not attack aluminum, often is called an electrolytic condenser, as its current is leading; that is, . itacts as capacity. It is, however, not an electrolytic condenser, and the counter e.m.f., which gives the capacity effect, is not electrolytic polarization. The aluminum cell is a true electro- static condenser, in which the film of alumina, formed on the . positive aluminum plates, is the dielectric. Its characteristic is, | that the condenser is self-healing; that is, a puncture of the alum- ; ina film causes a current to flow, which electrolytically produces ’ alumina at the puncture hole, and so closes it. The capacity is very high, due to the great thinness of the film, but the energy losses are considerable, due to the continual puncture and repair ; of the dielectric film. Pyroelectric Conductors ' 8. A third class of conductors are the pyroelectric conductors or pyroelectrolytes. In some features they are intermediate between the metallic conductors and the electrolytes, but in their essen- ; tial characteristics they are outside of the range of either. The | metallic conductors as well as the electrolytic conductors give a | '_-volt-ampere characteristic in which, with increase of current, the voltage rises, faster than the current in the metallic conductors, due to their positive temperature coefficient, slower than the current in the electrolytes, due to their negative temperature coefficient. The characteristic of the pyroelectric conductors, however, is such a very high negative temperature coefficient of resistance, that is, such rapid decrease of resistance with increase of tempera- ture, that over a wide range of current the voltage decreases with increase of current. Their volt-ampere characteristic thus has a shape as shown diagrammatically in Fig. 4—though not all such | conductors may show the complete curve, or parts of the curve | may be physically unattainable: for small currents, range (1), . the voltage increases approximately proportional to the current, | and sometimes slightly faster, showing the positive temperature , coefficient of metallic conduction. At a the temperature coeffi-

ELECTRIC CONDUCTION 11 cient changes from positive to negative, and the voltage begins to increase slower than the current, similar as in electrolytes, range (2). The negative temperature coefficient rapidly increases, and the voltage rise become slower, until at point b the negative temperature coefficient has become so large, that the voltage be- gins to decrease again with increasing current, range (3). The maximum voltage point 6 thus divides the range of rising charac- teristic (1) and (2), from that of decreasing characteristic, (3). ‘The negative temperature coefficient reaches a maximum and then decreases again, until at point c the negative temperature coefhi- cient has fallen so that beyond this minimum voltage point c the voltage again increases with increasing current, range (4), Lt PtE tT TTT Tt tt tT PTARETTE TT ETT Tt 7E IN TT ET TE TT Ty SRNR fom | | dT ET TT | | | I | PCCP INCE er Py | TE tT Peer AE TT dT TdT ET TT TE ET TT TE TT ET ET TE ET EE vt i} ttt tt tT tT TT Ty yy ARERR a Fia. 4, though the temperature coefficient remains negative, like in electrolytic conductors. In range (1) the conduction is purely metallic, in range (4) becomes purely electrolytic, and is usually accompanied by chemical action. . Range (1) and point a often are absent and the conduction . begins already with a slight negative temperature coefficient. The complete curve, Fig. 4, can be observed only in few sub- stances, such as magnetite. Minimum voltage point c and range (4) often is unattainable by the conductor material melting or ; being otherwise destroyed by heat before it is reached. Such, for instance, is the case with cast silicon. The maximum voltage point 6 often is unattainable, and the passage from range , (2) to range (3) by increasing the current therefore not feasible,

| | 12 ELECTRIC CIRCUITS ; because the maximum voltage point } is so high, that disruptive discharge occurs before it is reached. Such for instance is the case in glass, the Nernst lamp conductor, ete. 9. The curve, Fig 4 is drawn only diagrammatically, and the lower current range ‘exaggerated, to show the characteristics. Usually the current at point b is very small compared with that , at point c; rarely more than one-hundredth of it, and the actual proportions more nearly represented by Fig. 5. With pyro- electric conductors of very high value of the voltage b, the cur- rents in the range (1) and (2) may not exceed one-millionth of that at (3). Therefore, such volt-ampere characteristics are — ET TET T ET ty ttt? ett t ttt tg) (ye A tt NER PINT TTT TE tt tet tt Tt | ery, PLING TT ttt ttt ep eer tt Pit | PRR ET FLT TTT TTP ett tt ee tT ty PTET TET TT ttt et et tte yt | et pt by fe FETT? TET tT ttt eet et ett tt PT Tt tt ttt tT ET TT TE TT TT PT TTT TT Tt tee eT EE TTT Pt ttt tt ttt tet TT ETT TT TT I Seeerererrrrerrrrerr?s Rie. 5. , often plotted with ~/i as abscisse, to show the ranges in better proportions, . Pyroelectric conductors are metallic silicon, boron, some forms of carbon as anthracite, many metallic oxides, especially those of the formula M‘) M,") O,, where M®) is a bivalent, M®) a trivalent metal (magnetite, chromite), metallic sulphides, silicates such as glass, many salts, etc. . Intimate mixtures of conductors, as graphite, coke, powdered metal, with non-conductors as clay, carborundum, cement, also have pyroelectric conduction. Such are used, for instance, as “resistance rods” in lightning arresters, in some rheostats, as

ELECTRIC CONDUCTION 13 cement resistances for high-frequency power dissipation in re- actances, etc. Many, if not all so-called “insulators” probably are in reality pyroelectric conductors, in which the maximum voltage point b is so high, that the range (3) of decreasing charac- teristic can be reached only by the application of external heat, as in the Nernst lamp conductor, or can not be reached at all, because chemical dissociation begins below its temperature, as in organic insulators. Fig. 6 shows the volt-ampere characteristics of two rods of cast silicon, 10 in. long and 0.22 in. in diameter, with +/i as ab- PT eT tt ft | 8 | ent PL TL PT} ETT tte EE TT ttt ET PT TT TT TPT eT EET TE TT | ems. EAS et arma 1+ f ATT OF CAST SILICON HA Je EEN ET TT TTT ET TEE ET) 2,

• ef ft tt STIR NEEREe PUTT | PE NA ET TE EE ET a 9 CECA PT TT TATTLE SS TT el BSED ARR EE LAT ALT TT EE ET EE TT TTT Te HT TAT Tt tt vowremest to] Tt tT Veg iets tit etetet st il ; Kia. 6. scisse and Fig. 7 their approximate temperature-resistance characteristics. The curve II of Fig. 7 is replotted in Fig. 8, with log r as ordinates. Where the'resistivity varies over a very , wide range, it often is preferable to plot the logarithm of the resistivity. It is interesting to note that the range (3) of curve _ ITI, between 700° and 1400°, is within the errors of observation represented by the expression 9080 r=001E T where 7' is the absolute temperature (—273°C. as zero point). The difference between the two silicon rods is, that the one con- : >

| | 14 ELECTRIC CIRCUITS tains 1.4 per cent., the other only 0.1 per cent. carbon; besides this, the impurities are less than 1 per cent. As seen, in these silicon rods the range (4) is not yet reached at the melting point. _ Fig. 9 shows the volt-ampere characteristic, with +/7 as abscis- se, and Fig. 10 the approximate resistance temperature char- : nt | | ET TE EE et : wrt} AL | tb ot ttt} tT tht ttt Ha a RESISTANCE -TEMPERATURE iP 901 | CHARACTERIBTIC OF CAST SILICON 1 SARA Bene" 1 o || | TAT T ALT TTT : o | | tT A TE TE TT da a EEE APE eg ee ee mt tt TTY IN LT Tt te Itt ttt y | y het tt ta

• fool | | ttt Pt AE TT dad | o | | | | | AT IMAL TT TO | ems {LL AN. fa ‘salma | | | | UT | AY Ty Tl Foleo | | | | [Ve LINAT | TT. Prot | | fT TT TT AWN Tel T F PNa tt th AA loool | | Nett NE TT NAT wlool_| | INT [IN TT TN TI. rlsoo) PS PPENG TINT TE TT da bo sho 940 abo_oho cho 7h0aha_sbo 1400 ffooadoaéoo 14oo | Fig. 7. acteristic derived therefrom, with log r as ordinates, of a magnetic rod 6 in. long and 34 in. in diameter, consisting of 90 per cent. magnetite (Fe30,), 9 per cent. chromite (FeCr,0,) and 1 per cent. sodium silicate, sintered together.

10. As result of these volt-ampere characteristics, Figs. 4 to 10, pyroelectric conductors as structural elements of an electric circuit show some very interesting effects, which may be illus-

ELECTRIC CONDUCTION ; 15 trated on the magnetite rod, Fig. 9. The maximum terminal vol- tage, which can exist across this rod in stationary conditions, is 25 voltsat lamp. With increasing terminal voltage, the current thus gradually increases, until 25 volts is reached, and then with- out further increase of the impressed voltage the current rapidly rises to short-circuit values. Thus, such resistances can be used as excess-voltage cutout, or, when connected between circuit and ground, as excess-voltage grounding device: below 24 volts, it A ae reoz { tT NT | CAST SILICON ROD acer 6 CM.LENGTH 0.66 CM. DIAMETER ) a DOTTED CURVE 7r=0.01€ 2% mt | | TARE TT EE Ty SSN ee pp NEE P|. fit ttt AP tT yt ty “hel | ET TT TN ET TET TT TI PEt TTT TIN; EET TTL | SNe wt ttt ei ty PA EE of |i tt ttt tT TNT ol | ttt ttt tt TNT vt TE tt tT Tt ty tT TNE TE | Ee eceeeeeeneae 90200 800 400 500 600 700 800 900 1000 1100 1800 1900 1400 | Fia. 8. . ! bypasses a negligible current only, but if the voltage rises above | 25 volts, it short-circuits the voltage and so stops a further rise, or | operates the circuit-breaker, etc. As the decrease of resistance is | the result of temperature rise, it is not instantaneous; thus the rod | does not react on transient voltage rises, but only on lasting ones. | Within a considerable voltage range—between 16 and 25 volts —three values of current exist for the same terminal voltage. Thus at 20 volts between the terminals of the rod in Fig. 9, the : current may be 0.02 amp., or 4.1 amp., or 36 amp. That is, in | |

16 . ELECTRIC CIRCUITS series in @ constant-current circuit of 4.1 amp. this rod would show the same terminal voltage as in a 0.02-amp. or a 36-amp. constant-current circuit, 20 volts. On constant-potential supply, however, only the range (1) and (2), and the range (4) is stable, but the range (3) is unstable, and here we have a conductor, which is unstable in a certain range of currents, from point b at 1 amp. to point.c at 20 amp. At 20 volts impressed upon the rod, 0.02 amp. may pass through it, and the conditions are stable. That J is, a tendency to increase of current would check itself by requir- , ing an increase of voltage beyond that supplied, and a decrease of FT ai tile tet st sb [ota | | Pt Tt tt fomrerest+—t>t TTT TdT TT] BERET Pao TT EE EE ET TE TT ETE 7E tL ALTE LETT TET | Tree | Hi | [Nat | TTT ETE Pr, | | Pitt Witt Tei Tt tt Tt, See ==" 4 eee a | PET TTT TTT TTT TT yy TT PT TT te ttt} Tt te et Ty | | | [ | [|] YOlr- AMPERE CGHARACTERISTIC | | rT | [Tf MAGNETITE RESISTANCE || | PTT TTT TET eT tT Tyee Ty, Pt titi tT tt ty tT Tt TT EY | | ft ff apreres| >] | TT TT Tt Tl Ftd de} ete te tetas Td | . Fia. 9. current would reduce the voltage consumption below that em- : ployed, and thus be checked. At the same impressed 20 volts, 36 amp. may pass through the rod—or 1800 times as much as before—and the conditions again are stable. A current of 4.1 amp. also would consume a terminal voltage of 20, but the condi- . tion now is unstable; if the current increases ever so little, by a momentary voltage rise, then the voltage consumed by the rod . decreases, becomes less than the terminal voltage of 20, and the current thus increases by the supply voltage exceeding the consumed voltage. This, however, still further decreases the . . |

ELECTRIC CONDUCTION 17 consumed voltage and thereby increases the current, and the cur- rent rapidly rises, until conditions become stable at 36 amp. In- versely, a momentary decrease of the current below 4.1 amp. in- creases the voltage required by the rod, and this higher voltage not being available at constant supply voltage, the current decreases.

• ro Re Ce eee ee Sah eae Coa 2 PA mee TI ae | Weegee TTT tT Tt da ee - 8 CARRE fale 8 i ee eee PT IN TET TT Tt T lee PTT ATT YE ET TT de PT TTX TT TTT TT fa | tf | PE TT Ty Ty tT rE Ld : Rp fe | PET TTT NE EET To PTT TTP NET TT ta | H+} | PEt TT ETT Tt ttt a Pt tt ety tee ETT | Pt ttt ttt ty et et tf | | | LT TT deowgesfe | | | | | | [sho abo_slo_ 0 sooo mo sto to 100 1100 sho |_| | | Fia. 10. | This, however, still further increases the required voltage and | . decreases the current, until conditions become stable at 0.02 amp. With the silicon rod II of Fig. 6, on constant-potential supply, yo with increasing voltage the current and the temperature increases gradually, until 57.5 volts are reached at about 450°C.; then, without further voltage increase, current and temperature rapidly increase until the rod melts. Thus: 2

: | | 18 ELECTRIC CIRCUITS |

Condition of stability of a conductor on constant-voltage sup- ply is, that the volt-ampere characteristic is rising, that is, an in- crease of current requires an increase of terminal voltage.

7 A conductor with falling volt-ampere characteristic, that is, a conductor in which with increase of current the terminal voltage decreases, is unstable on constant-potential supply.

11. An important application of pyroelectric conduction has ; been the glower of the Nernst lamp, which before the develop- ment of the tungsten lamp was extensively used for illumination.

Pyroelectrolytes cover the widest range of conductivities; the alloys of silicon with iron and other metals give, depending on their composition, resistivities from those of the pure metals up to the lower resistivities of electrolytes: 1 ohm per cm.; borides, carbides, nitrides, oxides, etc., gave values from 1 ohm per cm.? or less, up to megohms per cm., and gradually merge into the

. materials which usually are classed as “insulators.”

The pyroelectric conductors thus are almost the only ones available in the resistivity range between the metals, 0.0001 ohm- cm. and the electrolytes, 1 ohm-cm.

Pyroelectric conductors are industrially used to a considerable extent, since they are the only solid conductors, which have re-

sistivities much higher than metallic conductors. In most of the . industrial uses, however, the dropping volt-ampere characteristic ‘ is not of advantage, is often objectionable, and the use is limited to the range (1) and (2) of Fig. 3. It, therefore, is of importance to realize their pyroelectric characteristics and the effect which _ they have when overlooked beyond the maximum voltage point. Thus so-called “graphite resistances” or ‘“carborundum resist- ances,’’ used in series to lightning arresters to limit the discharge, when exposed to a continual discharge for a sufficient time to reach high temperature, may practically short-circuit and there-

by fail to limit the current.

12. From the dropping volt-ampere characteristic in some pyroelectric conductors, especially those of high resistance, of very high negative temperature coefficient and of considerable cross-section, results the tendency to unequal current distribution

. and the formation of a “luminous streak,” at a sudden applica- tion of high voltage. Thus, if the current passing through a graphite-clay rod of a few hundred ohms resistance is gradually increased, the temperature rises, the voltage first increases and then decreases, while the rod passes from range (2) into the

ELECTRIC CONDUCTION 19 -

range (3) of the volt-ampere characteristic, but the temperature and thus the current density throughout the section of the rod is fairly uniform. If, however, the full voltage is suddenly applied, such as by a lightning discharge throwing line voltage on the series resistances of a lightning arrester, the rod heats up very rapidly, too rapidly for the temperature to equalize throughout the ‘ rod section, and a part of the section passes the maximum voltage point b of Fig. 4 into the range (3) and (4) of low resistance, high current and high temperature, while most of the section is still in the high-resistance range (2) and never passes beyond this range, as it is practically short-circuited. Thus, practically all the cur- rent passes by an irregular luminous streak through a small sec- tion of the rod, while most of the section is relatively cold and practically does not participate in the conduction. Gradually, by heat conduction the temperature and the current density may become more uniform, if before this the rod has not been de- stroyed by temperature stresses. Thus, tests made on such con- ductors by gradual application of voltage give no information on their behavior under sudden voltage application. The liability to the formation of such luminous streaks naturally increases with | decreasing heat conductivity of the material, and with increasing resistance and temperature coefficient of resistance, and with con- ductors of extremely high temperature coefficient, such as silicates, oxides of high resistivity, etc., it is practically impossible to get current to flow through any appreciable conductor section, but the conduction is always streak conduction.

Some pyroelectric conductors have the characteristic that their resistance increases permanently, often by many hundred per cent. when the conductor is for some time exposed to high-fre- quency electrostatic discharges.

Coherer action, that is, an abrupt change of conductivity by an electrostatic spark, a wireless wave, etc., also is exhibited by some

_ pyroelectric conductors.

13. Operation of pyroelectric conductors on a constant-voltage circuit, and in the unstable branch (3), is possible by the insertion of a series resistance (or reactance, in alternating-current circuits) of such value, that the resultant volt-ampere characteristic is stable, that is, rises with increase of current. Thus, the con- ductor in Fig. 4, shown as J in Fig. 11, in series with the metallic resistance giving characteristic A, gives the resultant characteris- | tic IJ in Fig. 11, which is stable over the entire range. J in series |

. 20 ELECTRIC CIRCUITS with a smaller resistance, of characteristic B, gives the resultant : characteristic ZZ. In this, the unstable range has contracted to from b’ to c’. Further discussion of the instability of such con- ductors, the effect of resistance in stablizing them, and the result- PTT TT ET tT ETT Tt ty PTET TET TT tT ttt tM || PYRO ELECTRIC CONDUCTOR P| tt A 4 PTT TTT TTT ttt tat de pti ttt ttt tt tA PTT TTT Tt Tey TY d, PTT TTT Ty PY Te Kk SERRE Ane AP | PTT TTT Ty vy eet PETE TT Le Be oT ag P| | Py re | ae pt tel | | ee beet Pieler | ee tt ifel | VT eke tT TT | WVANAA Ter TT EE Wl iN tT TT tt ta eg fo a fy Feet | | tet TE EEE Zaaaawererrerrrs Fig. 11, ant “‘stability curve” are found in the chapter on “Instability . of Electric Circuits,’’ under “Arcs and Similar Conductors.” 14. It is doubtful whether the pyroelectric conductors really form one class, or whether, by the physical nature of their conduc- tion, they should not be divided into at least two classes:

1. True pyroelectric conductors, in which the very high nega- tive temperature coefficient is a characteristic of the material. . | | | |

| ELECTRIC CONDUCTION 21 , In this class probably belong silicon and its alloys, boron, mag- netite and other metallic oxides, sulphides, carbides, etc. 2. Conductors which are mixtures of materials of high conduc- tivity, and of non-conductors, and derive their resistance from the contact resistance between the conducting particles which are separated by non-conductors. As contact resistance shares with arc conduction the dropping volt-ampere characteristic, such mixtures thereby imitate pyroelectric conduction. In this class probably belong the graphite-clay rods industrially used. Powders of metals, gfaphite and other good conductors also belong in this class. . The very great increase of resistance of some conductors under electrostatic discharges probably is limited to this class, and is the result of the high current density of the condenser discharge burning off the contact points. Coherer action probably is limited also to those conductors, and is the result of the minute spark at the contact points initiating conduction. Carbon . 15. In some respects outside of the three classes of conductors thus far discussed, in others intermediate between them, is one of | ttt OF CARBON Ly! | SERRA PE TT TT TE et Tt Aree Pt TT eT rt ree PEER re SU Lt} tt tt Per TE EP Peter EE Pst T TT Tree EE ET EE PEt tT tT ere EE EE SERRE ASC CRE BEEV AP ZR eee SEZec aR eee Pp Yat tT df abecres—t>] TT | Tt TT Aet itt tt ttt tt eT PET TT Fig. 12. the industrially most important conductors, carbon. It exists in a large variety of modifications of different resistance characteris- re

• I 22 ELECTRIC CIRCUITS tics, which all are more or less intermediate between three typical . forms:

1. Metallic Carbon.—It is produced from carbon deposited on an incandescent filament, from hydrocarbon vapors at a partial . vacuum, by exposure to the highest temperatures of the electric furnace. Physically, it has metallic characteristics: high elas- . | |] RESisTANCE-TEMPERATURE | | | | f- CHARACTERISTIC OF CARBON Ea an RESISTIVITY IN OHM-CENTIMETERS lor ‘ PTT TTT TT TTT Ty ty Ter Pt ttt tty Tye eer hl ry | TT ET TE TT eT TT peesit Jf fas] fe a . tal LT TTT TT Prt TTT TT _ ed ET ET Ter | al | | | d |] PUT LE ETT TT Tet AND ZR ” lel NPAT TT TT TE ET TT far ° | PN oA | ett tt tt tT | pA SSE AR AEA} + 4 PET et Tt ee te yet ty Pt tT tit tty ee ty ey PTT TTT TT ee ey PTT TTT TT eee yy yy ey SRR SE | | | | | [APproxmareiremrerature’c | | [| | | sho sho sho abo abo abo ‘bo sho po 100 1400120 spo 1450 1eh0 abo 1-0 | Fia. 13. . ticity, metallic luster, etc., and electrically it has a relatively low resistance approaching that of metallic conduction, and a positive temperature coefficient of resistance, of about 0.1 per cent. per degree C.—that is, of the same magnitude as mercury or cast iron. The coating of the ‘‘Gem”’ filament incandescent lamp con- sists of this modification of carbon. |

, ELECTRIC CONDUCTION 23

2. Amorphous carbon, as produced by the carbonization of cellulose. In its purest form, as produced by exposure to the highest temperatures of the electric furnace, it is characterized by a relatively high resistance, and a negative temperature coeffi- cient of resistance, its conductivity increasing by about 0.1 per cent. per degree C.

3. Anthracite.—It has an extremely high resistance, is prac- tically an insulator, but has a very high negative temperature coefficient of resistance, and thus becomes a fairly good conductor at high temperature, but its heat conductivity is so low, and the negative temperature coefficient of resistance so high, that the conduction is practically always streak conduction, and at the high temperature of the conducting luminous streak, conversion to graphite occurs, with a permanent decrease of resistance.

(1) thus shows the characteristics of metallic conduction, (2) those of electrolytic conduction, and (3) those of pyroelectric conduction.

Fig. 12 shows the volt-ampere characteristics, and Fig. 13 the resistance-temperature characteristics of amorphous carbon— curve I—and metallic carbon— curve II. ;

Insulators .

16. As a fourth class of conductors may be considered the so- called ‘‘insulators,’”’ that is, conductors which have such a high specific resistance, that they can not industrially be used for con- veying electric power, but on the contrary are used for restraining the flow of electric power to the conductor, or path, by separating the conductor from the surrounding space by such an insulator. The insulators also have a conductivity, but their specific resist- ance is extremely high. For instance, the specific resistance of fiber is about 10", of mica 10", of rubber 10!* ohm-cm., etc.

As, therefore, the distinction between conductor and insulator is only qualitative, depending on the application, and more par- ticularly on the ratio of voltage to current given by the source of power, sometimes a material may be considered either as insulator orasconductor. Thus, when dealing with electrostatic machines, which give high voltages, but extremely small currents, wood, . paper, etc., are usually considered as conductors, while for the low-voltage high-current electric lighting circuits they are insula- tors, and for the high-power very high-voltage transmission cir-

a”

| | 2A ELECTRIC CIRCUITS , cuits they are on the border line, are poor conductors and poor insulators. Insulators usually, if not always, have a high negative tempera- ture coefficient of resistance, and the resistivity often follows approximately the exponential law, . r = rok ~ oT (3) where 7’ = temperature. That is, the resistance decreases by the same percentage of its value, for every degree C. For instance, it decreases to one-tenth for every 25°C. rise of temperature, so that at 100°C. it is 10,000 times lower than at 0°C. Some tem- perature-resistance curves, with log r as ordinates, of insulating . materials are given in Fig. 14. ; As the result of the high negative temperature coefficient, for a sufficiently high temperature, the insulating material, if not de- stroyed by the temperature, as is the case with organic materials, becomes appreciably conducting, and finally becomes a fairly . good conductor, usually an electrolytic conductor. Thus the material of the Nernst lamp (rare oxides, similar to the Welsbach mantle of the gas industry), is a practically perfect insulator at ordinary temperatures, but becomes conducting at high temperature, and is then used as light-giving conductor. Fig. 15 shows for a number of high-resistance insulat- ing materials the temperature-resistance curve at the range ; where the resistivity becomes comparable with that of other conductors. 17. Many insulators, however, more particularly the organic materials, are chemically or physically changed or destroyed, -before the temperature of appreciable conduction is reached, though even these show the high negative temperature coefficient. With some, as varnishes, etc., the conductivity becomes sufficient, at high temperatures, though still below carbonization tempera- ture, that under high electrostatic stress, as in the insulation of high-voltage apparatus, appreciable energy is represented by the leakage current through the insulation, and in this case rapid #r heating and final destruction of the material may result. That is, such materials, while excellent insulators at ordinary temperature, are unreliable at higher temperature. ‘It is quite probable that there is no essential difference between the true pyroelectric conductors, and the insulators, but the latter are merely pyroelectric conductors in which the initial resistivity |

ELECTRIC CONDUCTION 25 and the voltage at the maximum point b are so high, that the change from the range (2) of the pyroelectrolyte, Fig, 4, to the . range (3) can not be produced by increase of voltage. That is, : the distinction between pyroelectric conductor and insulator would be the quantitative one, that in the former the maximum : eH INO TAA SS insutatons || eo NK] MI ON TT tt ET | PEEISNNEEXEEELEEELY moa_| | NUT IN | 1 ae ’ PUR ENE nm | {| {| Wel Set hI a ACCC co. | ptt LN LE CECA ERS SE eR RES CS EEE ET Pt mp FLL AN oN INTE TOME IN | ON | | pa | Be PIN ET TS PCC Re RETRO aol _| | | | MIN | TL | Per ) Pt PP ET AN EEE wy {| [| | | | TP PSs HEC CESS | bb bb hb ww mm Wo to to wo 0 0 7 Fig. 14. voltage point of the volt-ampere characteristic is within experi- | mental reach, while with the latter it is beyond reach. Whether this applies to all insulators, or whether among or- ganic compounds as oils, there are true insulators, which are not pyroelectric conductors, is uncertain.

| , 26 ELECTRIC CIRCUITS Positive temperature coefficient of resistivity is very often met | in insulating materials such as oils, fibrous materials, etc. In this case, however, the rise of resistance at increase of temperature usually remains permanent after the temperature is again lowered, | Re eee) RESISTIVITY -TEM ATU | CCEDG| mon a tions [2 jroyer wor || | | | | | {| {ct df, | erst NE ETT TET TT tT i) . Pt tT TEIN | TEE TPE e ty. | EERE EENERRE Pt tT tT tT tt NOVA ET , Pt tT tT TT NG Yockon jure | |. i -} ANE NE -HNee et | SERRNGAGEERC er | | PTT INN? EE Et TT, . EEL LNG Frepecpo TT | | [rue nyer| | recpnstrugreoiavy | | | | | ! wrt Tt tT EET TT TE TT | Pi tT TET tT tT te tT TTT Td, 7 Pitt ttt tt tt tt tt he PT TTT Tee yt ey tT Tel Pit tT ttt ede rE ET TE ET PT TT ETT TE TTT TT PTT tT tT tT Te TT TT Ett | smo sho sho ao ojo elo nyo ojo oo wpo'd | | | | | Fia. 15, and the apparent positive temperature coefficient was due to the expulsion of moisture absorbed by the material. With insulators | of very high resistivity, extremely small traces of moisture may decrease the resistivity many thousandfold, and the conductivity of insulating materials very often is almost entirely moisture con-

ELECTRIC CONDUCTION - 27 duction, that is, not due to the material proper, but due to the moisture absorbed by it. In such a case, prolonged drying may increase the resistivity enormously, and when dry, the material then shows the negative temperature coefficient of resistance, incident to pyroelectric conduction. | | |

CHAPTER II ELECTRIC CONDUCTION. GAS AND VAPOR CONDUCTORS — ; Gas, Vapor and Vacuum Conduction

18. As further, and last class may be considered vapor, gas and vacuum conduction. Typical of this is, that the volt-ampere characteristic is dropping, that is, the voltage decreases with in- crease of current, and that luminescence accompanies the con- . duction, that is, conversion of electric energy into light.

Thus, gas and vapor conductors are unstable on constant- potential supply, but stable on constant current. On constant | potential they require a series resistance or reactance, to produce stability. |

Such conduction may be divided into three distinct types: spark conduction, arc conduction, and true electronic conduction.

In spark conduction, the gas or vapor which fills the space be- tween the electrodes is the conductor. The light given by the gaseous conductor thus shows the spectrum of the gas or vapor which fills the space, but the material of the electrodes is imma- terial, that is, affects neither the light nor the electric behavior of the gaseous conductor, except indirectly, in so far as the section of the conductor at the terminals depends upon the terminal sur- face.

In are conduction, the conductor is a vapor stream issuing from the negative terminal or cathode, and moving toward the anode | at high velocity. The light of the arc thus shows the spectrum of the negative terminal material, but not that of the gas in the surrounding space, nor that of the positive terminal, except indi- | rectly, by heat luminescence of material entering the arc con- | ductor from the anode or from surrounding space.

In true electronic conduction, electrons existing in the space, or produced at the terminals (hot cathode), are the conductors. Such conduction thus exists also in a perfect vacuum, and may be accompanied by practically no luminescence.

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ELECTRIC CONDUCTION 29 . Disruptive Conduction 19. Spark conduction at atmospheric pressure is the disruptive , spark, streamers, and corona. In a partial vacuum, it is the Geissler discharge or glow discharge. Spark conduction is dis- continuous, that is, up to a certain voltage, the “disruptive voltage,”? no conduction exists, except perhaps the extremely small true electronic conduction. At this voltage conduction begins and continues as long as the voltage persists, or, if the source of power is capable of maintaining considerable current, the spark conduction changes to arc conduction, by the heat de- veloped at the negative terminal supplying the conducting arc vapor stream. The current usually is small and the voltage high. Especially at atmospheric pressure, the drop of the volt- ampere characteristic is extremely steep, so that it is practically impossible to secure stability by series resistance, but the con- duction changes to arc conduction, if sufficient current is avail- able, as from power generators, or the conduction ceases by the voltage drop of the supply source, and then starts again by the recovery of voltage, as with an electrostatic machine. Thus spark conduction also is called disruptive conduction and discon- . tinuous conduction. . . Apparently continuous—though still intermittent—spark con- duction is produced at atmospheric pressure by capacity in series ; . to the gaseous conductor, on an alternating-voltage supply, as . corona, and as Geissler tube conduction at a partial vacuum, by an alternating-supply voltage with considerable reactance or resistance in series, or from a direct-current source of very high voltage and very limited current, as an electrostatic machine. In the Geissler tube or vacuum tube, on alternating-voltage supply, the effective voltage consumed by the tube, at constant temperature and constant gas pressure, is approximately con- stant and independent of the effective current, that is, the volt- ampere characteristic a straight horizontal line. The Geissler tube thus requires constant current or a steadying resistance or reactance for its operation. The voltage consumed by the Geiss- | ler tube consists of a potential drop at the terminals, the ‘termi- nal drop,’’ and a voltage consumed in the luminous stream, the “stream voltage.”’ Both greatly depend on the gas pressure, and vary, with changing gas pressure, in opposite directions: ‘the terminal drop decreases and the stream voltage increases with increasing gas pressure, and the total voltage consumed by the

. | 30 ELECTRIC CIRCUITS | tube thus gives a minimum at some definite gas pressure. This | pressure of minimum voltage depends on the length of the tube, BLL ELITE | | [ f mpnslenessoed eT de ERNERSEEZAE Netra 7 | PT meg A Tt lel | |) Nghe te COP eC Pt | PA EELeeNEEEE PT TTT EARL ITT | aol | | | wer | | td tC Fia. 16. AE - | Pt fmmneteesrel? Tt Lda - ENE PLL Nigra vetoes SEREC COP ARE | EERUGRES ABEL Pt LIN: fos 1 TTT Saee SCCM , , SEP aka See Pt ttt | | |r ty wo! | | bear] | tt kT Fia. 17. and the longer the tube, the lower is the gas pressure which gives minimum total voltage.

_ ELECTRIC CONDUCTION 31

Fig. 16 shows the voltage-pressure characteristic, at constant current of 0.1 amp. and 0.05 amp., of a Geissler tube of 1.3 cm. internal diameter and 200 cm. length, using air as conductor, and - Fig. 17 the characteristic of the same tube with mercury vapor as conductor. Figs. 16 and 17 alsoshow the two component voltages, the terminal drop and the stream voltage, separately. As ab- scisse are used the log of the gas pressure, in millimeter mercury column. As seen, the terminal drop decreases with increasing gas pressure, and becomes negligible compared with the stream voltage, at atmospheric pressure.

The voltage gradient, per centimeter length of stream, varies from 5 to 20 volts, at gas or vapor pressure from 0.06 to 0.9 mm. At atmospheric pressure (760 mm.) the disruptive voltage gradient, which produces corona, is 21,000 volts effective per centimeter. The specific resistance ofthe luminous stream is from 65 to 500 ohms per cm.’ in the Geissler tube conduction of Figs. 16 and 17—though this term has little meaning in gas conduction. The specific resistance of the corona in air, as it appears on trans- mission lines at very high voltages, is still very much higher.

Arc Conduction

20. In the electric arc, the current is carried across the space

• between the electrodes or arc terminals by a stream of electrode vapor, which issues from a spot on the negative terminal, the so-called cathode spot, as a high-velocity blast (probably of a velocity of several thousand feet per second). If the negative terminal is fluid, the cathode spot causes a depression, by the reaction of the vapor blast, and is in a more or less rapid motion,

depending on the fluidity. .

As the are conductor is a vapor stream of electrode material, this vapor stream must first be produced, that is, energy must be expended before arc conduction can take place. The arc, there- fore, does not start spontaneously between the arc terminals, if sufficient voltage is supplied to maintain the arc (as is the case with spark conduction) but the arc has first to be started, that is, the conducting vapor bridge be produced. This can be done by bringing the electrodes into contact and separating them, or by a high-voltage spark or Geissler discharge, or by the vapor stream of another arc, or by producing electronic conduction, as by an incandescent filament. Inversely, if the current in the arc

32 ELECTRIC CIRCUITS . stopped even for a moment, conduction ceases, that is, the are

extinguishes and has to be restarted. Thus, arc conduction may

also be called continuous conduction.