CHAPTER I ELECTRIC CONDUCTION. SOLED AND LIQUID CONDUCTORS 1, When electric power flows through a circuit, we find phe- nomena taking place outside of the conductor which directs the flow of power, and also inside thereof. The phenomena outside of the conductor are conditions of stress in space which are called the electric field, the two main components of the electric field being the electromagnetic component, characterized by the cir- cuit constant inductance, L, and the electrostatic component, characterized by the electric circuit constant capacity, C. Inside of the conductor we find a conversion of energy into heat; that is, electric power is consumed in the conductor by what may be considered as a kind of resistance of the conductor to the flow of electric power, and so we speak of resistance of the conductor as an electric quantity, representing the power consumption in the conductor. Electric conductors have been classified and divided into dis- tinct groups. We must realize, however, that there are no dis- tinct classes in nature, but a gradual transition from type to type. Metallic Conductors 2. The first class of conductors are the metallic conductors. They can best be characterized by a negative statement — that is, metallic conductors are those conductors in which the conduction of the electric current converts energy into no other form but heat. That is, a consumption of power takes place in the metallic con- 1 2 ELECTRIC CIRCUITS ductors by conversion into heat, and into beat only. Indirectly, we may get light, if the heat produced raises the temperature high enough to get visible radiation as in the incandescent lamp filament, but this radiation is produced from heat, and directly the conversion of electric energy takes place into beat. Most of the metaUic conductors cover, as regards their specific resist- ance, a rather narrow range, between about 1.6 microhm-cm. {1.6 X 10~*) for copper, to about 100 microhm-cm. for cast iron, mercury, high-resistance alloys, etc. They, therefore, cover a range of less than 1 to 100. RESISTANCE-TEMPERATURE CHARACTERISTIC | \ I PURE METALS II ALLOYS III ELECT BOUrTE III \ -II A B K -^ " ' ■-' 11 A _ -J II " \ y S X -^ 1 n\ s / III ■- /- ' / _, ^ . 'i '^ r" ^■' -^ •-- ' ^■' '^' ■'_, _' ■^ m , io , L Fig. 1. A characteristic of metallic conductoi^ is that the resistance is approximately constant, varying only slightly with the tem- perature, and this variation is a rise of resistance with increase of temperature — that is, they have a positive temperature co- efficient. In the pure metals, the resistance apparently is ap- proximately proportional to the absolute temperature — that is, the temperature coefficient of resistance is constant and such that the resistance plotted as function of the temperature is a straight line which points toward the absolute zero of temperature, or, in other words, which, prolonged backward toward falling tem- ELECTRIC CONDUCTION 3 perature, would reach zero at — 273°C., as illustrated by curves I on Fig. 1. Thus, the resistance may be expressed by r = roT (1) where T is the absolute temperature. In alloys of metals we generally find a much lower temperature coefficient, and find that the resistance curve is no longer a straight line, but curved more or less, as illustrated by curves II, Fig. 1, so that ranges of zero temperature coefficient, as at A in curve II, and even ranges of negative temperature coefficient, as at £ in curve II, Fig. 1, may be found in metalUc conductors which are alloys, but the general trend is upward. That is, if we extend the investigation over a very wide range of temperature, we find that even in those alloys which have a negative temperature coefficient for a limited temperature range, the average temperature co- efficient is positive for a very wide range of temperature — that is, the resistance is higher at very high and lower at very low tem- perature, and the zero or negative coefficient occurs at a local flexure in the resistance curve. 3. The metallic conductors are the most important ones in industrial electrical engineering, so much so, that when speak- ing of a "conductor,'' practically always a metallic conductor is understood. The foremost reason is, that the resistivity or specific resistance of all other classes of conductors is so very much higher than that of metallic conductors that for directing the flow of current only metallic conductors can usually come into consideration. As, even with pure metals, the change of resistance of metallic conductors with change of temperature is small — about J^ per cent, per degree centigrade — and the temperature of most ap- paratus during their use does not vary over a wide range of tem- perature, the resistance of metalUc conductors, r, is usually assumed as constant, and the value corresponding to the operat- ing temperature chosen. However, for measuring temperature rise of electric currents, the increase of the conductor resistance is frequently employed. Where the temperature range is very large, as between room temperature and operating temperature of the incandescent lamp filament, the change of resistance is very considerable; the resist- ance of the tungsten filament at its operating temperature is about 4 ELECTRIC CIRCUITS nine times its cold resistance in the vacuum lamp, twelve times in the gas-filled lamp. Thus the metallic conductors are the most important. They require little discussion, due to their constancy and absence of secondary energy transformation. Iron makes an exception among the pure metals, in that it has an abnormally high temperature coefficient, about 30 per cent, higher than other pure metals, and at red heat, when approaching the temperature where the iron ceases to be magnetizable, the temperature coefficient becomes still higher, until the temperature is reached where the iron ceases to be magnetic. At this point its temperature coefficient becomes that of other pure metals. Iron wire — usually mounted in hydrogen to keep it from oxidizing — ^thus finds a use as series resistance for current limitation in vacuum arc circuits, etc. Electrolytic Conductors 4. The conductors of the second class are the electrolytic conductors. Their characteristic is that the conduction is ac- companied by chemical action. The specific resistance of elec- trolytic conductors in general is about a miUion times higher than that of ihe metallic conductors. They are either fused compounds, or solutions of compounds in solvents, ranging in resistivity from 1.3 ohm-cm., in 30 per cent, nitric acid, and still lower in fused salts, to about 10,000 ohm-cm. in pure river water, and from there up to infinity (distilled water, alcohol, oils, etc.). They are all liquids, and when frozen become insulators. Characteristic of the electrolytic conductors is the negative tem- perature coefficient of resistance; the resistance decreases with in- creasing temperature — ^not in a straight, but in a curved line, as illustrated by curves III in Fig. 1. When dealing with electrical resistances, in many cases it is more convenient and gives a better insight into the character of the conductor, by not considering the resistance as a function of the temperature, but the voltage consumed by the conductor as a function of the current under stationary condition. In this case, with increasing current, and so increasing power consumption, the temperature also rises, and the curve of voltage for increasing current so illustrates the electrical effect of increasing tempera- ture. The advantage of this method is that in many cases we get ELECTRIC CONDUCTION 5 a better view of the action of the conductor in an electric circuit by eliminating the temperature, and relating only electrical quan- tities with each other. Such volt-ampere characteristics of elec- tric conductore can easily and very accurately be determined, and, if desired, by the radiation law approximate values of the temperature be derived, and therefrom the temperature-resist- ance curve calculated, while & direct measurement of the resist- VOLT-AMPERE CHARACTERISTIC 1 PURE METALS n ALLOYS m ELECTROLYTES , / t I / / ' f / II / / /. % < /■ s / / 1 / -/ / III -- 'y ^ " y '/ y <^ ^ / / AM ER s / Fig. 2. ance over a very wide range of temperature is extremely difficult, and often no more accurate. In Fig. 2, therefore, are shown such volt-ampere characteristics of conductors. The dotted straight line is the curve of absolutely confltant resistance, which does not exist. Curves I and II show characteristics of metallic conductors, curve III of electrolytic conductors. As seen, for higher currents I and II rise faster, and III slower than for low currents. 6 ELECTRIC CIRCUITS It must be realized, however, that the volt-ampere character- istic depends not only on the material of the conductor, as the temperature-resistivity curve, but also on the size and shape of the conductor, and its surroundings. For a long and thin con- ductor in horizontal position in air, it would be materially differ- ent numerically from that of a short and thick conductor in dif- ferent position at different surrounding temperature. However, qualitatively it would have the same characteristics, the same characteristic deviation from straight line, etc., merely shifted in their numerical values. Thus it characterizes the general nature of the conductor, but where comparisons between different con- ductor materials are required, either they have to be used in the same shape and position, when determining their volt-ampere characteristics, or the volt-ampere characteristics have to be re- duced to the resistivity-temperature characteristics: The volt- ampere characteristics become of special importance with those conductors, to which the term resistivity is not physically appli- cable, and therefore the "effective resistivity'' is of little meaning, as in gas and vapor conduction (arcs, etc.). 6. The electrolytic conductor is characterized by chemical action accompanying the conduction. This chemical action follows Faraday's law: The amount of chemical action is proportional to the current and to the chemical equivalent of the reaction. The product of the reaction appears at the terminals or "elec- trodes," between the electrolytic conductor or ^'electrolyte," and the metallic conductors. Approximately, 0.01 mg. of hydro- gen are produced per coulomb or ampere-second. From this electrochemical equivalent of hydrogen, all other chemical reac- tions can easily be calculated from atomic weight and valency. For instance, copper, with atomic weight 63 and valency 2, has the equivalent 63/2 = 31.5 and copper therefore is deposited at the negative terminal or "cathode," or dissolved at the positive terminal or "anode," at the rate of 0.315 mg. per ampere-second; aluminum, atomic weight 28 and valency 3, at the rate of 0.093 mg. per ampere-second, etc. The chemical reaction at the electrodes represents an energy transformation between electrical and chemical energy, and as the rate of electrical energy supply is given by current times vol- tage, it follows that a voltage drop or potential difference occurs at the electrodes in the electrolyte. This is in opposition to the ELECTRIC CONDUCTION 7 current, or a counter e.m.f., the "counter e.m.f. of electrochem- ical polarization," and thus consumes energy, if the chemical reaction requires energy — ^as the deposition of copper from a solu- tion of a copper salt. It is in the same direction as the current, thus producing electric energy, if the chemical reaction produces energy, as the dissolution of copper from the anode. As the chemical reaction, and therefore the energy required for it, is proportional to the current, the potential drop at the elec- trodes is independent of the current density, or constant for the same chemical reaction and temperature, except in so far as sec- ondary reactions interfere. It can be calculated from the chem- ical energy of the reaction, and the amount of chemical reaction as given by Faraday's law. For instance: 1 amp.-sec. deposits 0.315 mg. copper. The voltage drop, e, or polarization voltage, thus must be such that e volts times 1 amp.-sec, or e watt-sec. or joules, equals the chemical reaction energy of 0.315 mg. copper in combining to the compound from which it is deposited in the electrolyte. If the two electrodes are the same and in the same electrolyte at the same temperature, and no secondary reaction occurs, the reactions are the same but in opposite direction at the two elec- trodes, as deposition of copper from a copper sulphate solution at the cathode, solution of copper at the anode. In this case, the two potential differences are equal and opposite, their resultant thus zero, and it is said that "no polarization occurs. " If the two reactions at the anode and cathode are different, as the dissolution of zinc at the anode, the deposition of copper at the cathode, or the production of oxygen at the (carbon) anode, and the deposition of zinc at the cathode, then the two potential differences are unequal and a resultant remains. This may be in the same direction as the current, producing electric energy, or in the opposite dh-ection, consuming electric energy. In the first case, copper deposition and zinc dissolution, the chemical energy set free by the dissolution of the zinc and the voltage produced by it, is greater than the chemical energy consumed in the deposition of the copper, and the voltage consumed by it, and the resultant of the two potential differences at the electrodes thus is in the same direction as the current, hence may produce this current. Such a device, then, transforms chemical energy into electrical energy, and is called a primary cell and a number of them, a bdUery. In the second case, zinc deposition and oxygen produo- 8 ELECTRIC CIRCUITS tion at the anode, the resultant of the two potential differences at the electrodes is in opposition to the current; that is, the device consumes electric energy and converts it into chemical energy, as electrolytic cell. " Both arrangements are extensively used: the battery for pro- ducing electric power, especially in small amounts, as for hand lamps, the operation of house bells, etc. The electrolytic cell is used extensively in the industries for the production of metals as aluminum, magnesium, calcium, etc., for refining of metals as copper, etc., and constitutes one of the most important industrial appUcations of electric power. A device which can efficiently be used, alternately as battery and as electrolytic cell, is the secondary cell or storage battery. Thus in the lead storage battery, when discharging, the chemical reaction at the anode is conversion of lead peroxide into lead oxide, at the cathode the conversion of lead into lead oxide; in charging, the reverse reaction occurs. 6. Specifically, as "polarization cell'' is understood a combina- tion of electrolytic conductor with two electrodes, of such char- acter that no permanent change occurs during the passage of the current. Such, for instance, consists of two platinum electrodes in diluted sulphuric acid. During the passage of the current, hydrogen is given off at the cathode and oxygen at the anode, but terminals and electrolyte remain the same (assuming that the small amount of dissociated water is replaced). In such a polarization cell, if eo = counter e.m.f . of polarization (corresponding to the chemical energy of dissociation of water, and approximately 1.6 volts) at constant temperature and thus constant resistance of the electrolyte, the current, i, is proportional to the voltage, e, minus the counter e.m.f. of polarization, 6o: i = '-^^^ (2) In such a case the curve III of Fig. 2 would with decreasing current not go down to zero volts, but would reach zero amperes at a voltage e = Co, and its lower part would have the shape as shown in Fig. 3. That is, the current begins at voltage, co, and below this voltage, only a very small "diffusion'' current flows. When dealing with electrolytic conductors, as when measuring their resistance, the counter e.m.f. of polarization thus must be considered, and with impressed voltages less than the polarization 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, electroljrtically 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- e ^-- ^ V. "^7 y"""^^ eo ( • ' % 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. Note. — 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, it acts 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 electroljrtically 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. P3nroelectric 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-atnpere 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 increaee slower than the current, similar as in electrolytes, range (2). Thenegativeteraperature 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 b 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 coeffi- cient has fallen so that beyond this minimum voltage point c the voltage again increases with increasing current, range (4), b I 1+^1====== mm Fig. 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 be^ns 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 pwint 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 6 is so high, that disruptive dischai^e occurs before it is reached. Such for instance is the case in glass, the Nemst lamp conductor, etc. 9. The curve, Fig. 3, is drawn only diagranunatically, 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 « c \ V J s — ' 18 -- ^ __ " jj ■i 2 !> 2 * ? i i 1 1 ' f 2 G t 8 1 ; a J « B 8 t a Fig. 5. often plotted with -\/i as abscissae, 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'^' Ma'*' Oa, where M'** is a bivalent, M'"' a trivaient metal (magnetite, chromite), metaUic sulphides, silicates such aa 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 6 is so high, that the range (3) of decreasing charac- teristic can be reached only by the application of external heat, as in the Nemst 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- i IS "wPERfs— <■ ? 1* vo -IS n VOLT-AMPERE CHARACTERISTIC OF CAST SILICON \ m \ \ rr S r fea / == A , / ,/ / / . 1 i scissie and Fig. 7 their approximate temperature-resistance characteristics. The curve 11 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 II, between 700° and 1400°, is within the errors of observation represented by the expression = O.OIE where T 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 impuritiea 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 y/T as abscis- 8se, and Fig. 10 the approximate resistance temperature char- 11 I.« 11 -BW 430 - ,r -> n - RESIST CHARACTER RESISTIVITY NCE -TEMPERATURE mc OF CAST SILICON [in OHM-pENTlMETER ^ ir __ ^ > „ ^ in \ \ \ \ n \ \ \ \ ' m \ I' \ \ ^ \ ^\ a ' \ S S 1(10 \ " \ k\ 200 ^T"E \ \ kN , \ \ 1 , u a K.SO0. x)^c » I >i>flSQ_9O0J_ WoltOO-KOOJ. ffiU M acteristic derived therefrom, with log r as ordinates, of a magnetic rod 6 in. long and % in. in diameter, consisting of 90 per cent, magnetite (FejOO, 9 per cent, chromite (FeCr204) and 1 per cent, sodium silicate, sintered together. 10. As result of these volf^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 maximuin terminal vol- tage, which can exist across this rod in stationary conditions, is 25 volts at 1 amp. 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 \ RESISTIVITY TEMPERATURE 1 ^■ \ CAST SILICON ROD !B CM. LENGTH 0.56 CM. DIAMETER DOTTED CURVE r-O.OlE ^ — -^ \ ^ s , \ \ \ N \ \ s N s s N s flT c EGR p^ c a a « i it a B a a J M 800 » » 10 »u »I3 »I3 au « bypasses a negUgible current only, but if the voltage rieea above 25 volte, it shor^circulte the voltage and so stops a further rise, or operates the circuif^breaker, etc. As the decrease of resistance is the result of temperature rise, it is not instantaneous; thus the rod •ioes not react on transient voltage rises, but only on lasting ones. Within a considerable voltage range — between 16 and 25 volte "Hhree values of current exist for the same terminal voltage, ^us at 20 volte 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 a 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. constantnjurrent 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 6 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 is, a tendency to increase of current would check itself by requir- ing an increase of voltage beyond that supplied, and a decrease of i ,1 36 « VO •TS ^ / \ / 1,1 \ A / \ X VOLT- AMPERE CHARACTERISTIC MAGNETIT£°RESISTANCE -10- ^ iPE SIT - -i- 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 ao 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 conaumed 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. J 1 \ Li > RESISTIV TV-TEMPERATURE CHARACTERISTIC OF MAGNETITE ROD 15 X 1.9 CM. tt \ ^ \ fl v] \ fit \ f« \ \ f1 ^ Tn ia» LE5 G. 1 D a B u B a n Tl D a D 81 D 1 » U » 1 M Fig. 10. This, however, still further increases the required voltage and decreases the current, until conditions become stable at 0.02 amp. With tbe silicon rod II of Fig. 6, on constant-potential supply, 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: 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. 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 maximima 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 Ughtning 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 imiform, 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 / in Fig. 11, in series with the metalUc resistance giving characteristic Ay gives the resultant characteris- tic II in Fig. 11, which is stable over the entire range. / in series 20 ELECTRIC CIRCUITS with a smaller resistaiice, of characteristic B, gives the resultant characteristic ///. In this, the unstable ran)^ has contracted to from b' to c*. Further discussion of the instabihty of such con- ductors, the effect of resistance in stablizing them, and the result- /; - STABILITY CURVES OF PYRO ELECTRIC CONDUCTOR / / / 'in / / / / " / ■V / 4, V / / n / / / / / / ">■ -•s; y y ^ ■^ Z' / ■^ ir ,/ / ^ f- ^ ./ II i / ?■ y /// \ / .-^ '/ / x ,.^ I ^ , / ^ / , e — — -" / / ^-' £ '•^ '' , , , < * Fw. 11. ant "stabiUty 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 cega- tive temperature coefficient is a characteristic of the material. ELECTRIC CONDUCTION 21 In this class probably belong silicon and ita alloys, boron, m^- 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, graphite and other good conductors also beJong 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 16. In some respects outside of the three classes of conductors thus far discussed, in others intermediate between them, is one of VOLT-AMPERE CHARACTERISTIC y OF CARBON y. y y. / ' / / / 1 y / ", ^ / s V / y / IT ^ / ^ / A BE S— 1 ■* ^ the industrially most important conductors, carbon. It exists in a large variety of modifications of different resistance charaeteris- 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 vacumn, by exposure to the highest temperatures of the electric furnace. Physically, it has metallic characteristics: high elas- RESISTANCE -TEMPERATURE CHARACTERISTIC OF CARBON RESISTIVITY IN OHM-CENTIMETERS n n. ^ ^ in 1 ^ tr X ^ -^ 1. C X I / > / i ^ / % > i, w / «/ ■— 1 z '" — -_ _ 1 - '""H re pi PE IKt UR X D » a \> ' wa .. «. „ )0I L Fig. 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 quaUtative, 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 or as conductor. 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- 24 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 = roS-"^ (3) where T = 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 i^r heating and final destruction of the material may result. That is, such materials, while excellent insulators at ordinary temperature, are imreliable 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 LOG f. ^ 1 1 1 M 1 1 \ \ ^ RESISTIVITY-TEMPERATURE CHARACTERISTICS OF INSULATORS - ■s \ 1?™ \ \ S s s »« \ ■^ \ \ 11 ro \i ^ Si ^ \\ \. \ Irti \ \\ ^ \ \ r- V ~-J t. % k "~~ \ ft. V \ s \ h \ 1 %N «ni s V \\ \ ■ s ^ >. \°^ " ■^ ntn < \ — "- \ ~ ~ ^- ^ ** ": ^ =; I i 1 D . ( c 1 1 I W 1 10 1 volt^e 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 coefHcient 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, \ Mill \ RESISTIVIir-TEMPERATURE CHARACTERISTIC OF HIGH TEMPERATURE INSULATORS \ ER IMIT Of \ )NS mi m ILS \ \ \ Tr \ \ \ \ BO RON NITR D \ s \ v\ \ ^ ED AGN ESIA \ V 'l- V. \ ■~~ ORC '"' PU EB ER ONS TED CATE " D a D » . « D B a 61 a 71 D a 1) 91 a 1 JO* Fio. 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 coeflSicient of resistance, incident to pyroelectric conduction.