The Project Gutenberg eBook ofEncyclopaedia Britannica, 11th Edition, "Conduction, Electric"

The Project Gutenberg eBook ofEncyclopaedia Britannica, 11th Edition, "Conduction, Electric"This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.Title: Encyclopaedia Britannica, 11th Edition, "Conduction, Electric"Author: VariousRelease date: April 19, 2010 [eBook #32063]Most recently updated: January 6, 2021Language: EnglishCredits: Produced by Marius Masi, Don Kretz, Juliet Sutherland, andthe Online Distributed Proofreading Team athttps://www.pgdp.net*** START OF THE PROJECT GUTENBERG EBOOK ENCYCLOPAEDIA BRITANNICA, 11TH EDITION, "CONDUCTION, ELECTRIC" ***

This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online atwww.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.

Title: Encyclopaedia Britannica, 11th Edition, "Conduction, Electric"Author: VariousRelease date: April 19, 2010 [eBook #32063]Most recently updated: January 6, 2021Language: EnglishCredits: Produced by Marius Masi, Don Kretz, Juliet Sutherland, andthe Online Distributed Proofreading Team athttps://www.pgdp.net

Title: Encyclopaedia Britannica, 11th Edition, "Conduction, Electric"

Author: Various

Release date: April 19, 2010 [eBook #32063]Most recently updated: January 6, 2021

Language: English

Credits: Produced by Marius Masi, Don Kretz, Juliet Sutherland, andthe Online Distributed Proofreading Team athttps://www.pgdp.net

*** START OF THE PROJECT GUTENBERG EBOOK ENCYCLOPAEDIA BRITANNICA, 11TH EDITION, "CONDUCTION, ELECTRIC" ***

Articles in This Slice

CONDUCTION, ELECTRIC

CONDUCTION, ELECTRIC.The electric conductivity of a substance is that property in virtue of which all its parts come spontaneously to the same electric potential if the substance is kept free from the operation of electric force. Accordingly, the reciprocal quality, electric resistivity, may be defined as a quality of a substance in virtue of which a difference of potential can exist between different portions of the body when these are in contact with some constant source of electromotive force, in such a manner as to form part of an electric circuit.

All material substances possess in some degree, large or small, electric conductivity, and may for the sake of convenience be broadly divided into five classes in this respect. Between these, however, there is no sharply-marked dividing line, and the classification must therefore be accepted as a more or less arbitrary one. These divisions are: (1) metallic conductors, (2) non-metallic conductors, (3) dielectric conductors, (4) electrolytic conductors, (5) gaseous conductors. The first class comprises all metallic substances, and those mixtures or combinations of metallic substances known as alloys. The second includes such non-metallic bodies as carbon, silicon, many of the oxides and peroxides of the metals, and probably also some oxides of the non-metals, sulphides and selenides. Many of these substances, for instance carbon and silicon, are well-known to have the property of existing in several allotropic forms, and in some of these conditions, so far from being fairly good conductors, they may be almost perfect non-conductors. An example of this is seen in the case of carbon in its three allotropic conditions—charcoal, graphite and diamond. As charcoal it possesses a fairly well-marked but not very high conductivity in comparison with metals; as graphite, a conductivity about one-four-hundredth of that of iron; but as diamond so little conductivity that the substance is included amongst insulators or non-conductors. The third class includes those substances which are generally called insulators or non-conductors, but which are better denominated dielectric conductors; it comprises such solid substances as mica, ebonite, shellac, india-rubber, gutta-percha, paraffin, and a large number of liquids, chiefly hydrocarbons. These substances differ greatly in insulating power, and according as the conductivity is more or less marked, they are spoken of as bad or good insulators. Amongst the latter many of the liquid gases hold a high position. Thus, liquid oxygen and liquid air have been shown by Sir James Dewar to be almost perfect non-conductors of electricity.

The behaviour of substances which fall into these three classes is discussed below in section I., dealing with metallic conduction.

The fourth class, namely the electrolytic conductors comprises all those substances which undergo chemical decomposition when they form part of an electric circuit traversed by an electric current. They are discussed in section II., dealing with electrolytic conduction.

The fifth and last class of conductors includes the gases. The conditions under which this class of substance becomes possessed of electric conductivity are considered in section III., on conduction in gases.

In connexion with metallic conductors, it is a fact of great interest and considerable practical importance, that, although the majority of metals when in a finely divided or powdered condition are practically non-conductors, a mass of metallic powder or filings may be made to pass suddenly into a conductive condition by being exposed to the influence of an electric wave. The same is true of the loose contact of two metallic conductors. Thus if a steel point, such as a needle, presses very lightly against a metallic plate, say of aluminium, it is found that this metallic contact, if carefully adjusted, is non-conductive, but that if an electric wave is created anywhere in the neighbourhood, this non-conducting contact passes into a conductive state. This fact, investigated and discovered independently by D. E. Hughes, C. Onesti, E. Branly, O. J. Lodge and others, is applied in the construction of the “coherer,” or sensitive tube employed as a detector or receiver in that form of “wireless telegraphy” chiefly developed by Marconi. Further references to it are made in the articlesElectric WavesandTelegraphy:Wireless.

International Ohm.—The practical unit of electrical resistance was legally defined in Great Britain by the authority of the queen in council in 1894, as the “resistance offered to an invariable electric current by a column of mercury at the temperature of melting ice, 14.4521 grammes in mass, of a constant cross-sectional area, and a length 106.3 centimetres.” The same unit has been also legalized as a standard in France, Germany and the United States, and is denominated the “International or Standard Ohm.” It is intended to represent as nearly as possible a resistance equal to 10° absolute C.G.S. units of electric resistance. Convenient multiples and subdivisions of the ohm are the microhm and the megohm, the former being a millionth part of an ohm, and the latter a million ohms. The resistivity of substances is then numerically expressed by stating the resistance of one cubic centimetre of the substance taken between opposed faces, and expressed in ohms, microhms or megohms, as may be most convenient. The reciprocal of the ohm is called the mho, which is the unit of conductivity, and is defined as the conductivity of a substance whose resistance is one ohm. The absolute unit of conductivity is the conductivity of a substance whose resistivity is one absolute C.G.S. unit, or one-thousandth-millionth part of an ohm. Resistivity is a quality in which material substances differ very widely. The metals and alloys, broadly speaking, are good conductors, and their resistivity is conveniently expressed in microhms per cubic centimetre, or in absolute C.G.S. units. Very small differences in density and in chemical purity make, however, immense differences in electric resistivity; hence the values given by different experimentalists for the resistivity of known metals differ to a considerable extent.

I.Conduction in Solids

It is found convenient to express the resistivity of metals in two different ways: (1) We may state the resistivity of one cubic centimetre of the material in microhms or absolute units taken between opposed faces. This is called thevolume-resistivity; (2) we may express the resistivity by stating the resistance in ohms offered by a wire of the material in question of uniform cross-section one metre in length, and one gramme in weight. This numerical measure of the resistivity is called themass-resistivity. The mass-resistivity of a body is connected with its volume-resistivity and the density of the material in the following manner:—The mass-resistivity, expressed in microhms per metre-gramme, divided by 10 times the density is numerically equal to the volume-resistivity per centimetre-cube in absolute C.G.S. units. The mass-resistivity per metre-gramme can always be obtained by measuring the resistance and the mass of any wire ofuniform cross-section of which the length is known, and if the density of the substance is then measured, the volume-resistivity can be immediately calculated.

If R is the resistance in ohms of a wire of length l, uniform cross-section s, and density d, then taking ρ for the volume-resistivity we have 109R = ρl/s; but lsd = M, where M is the mass of the wire. Hence 109R = ρdl2/M. If l = 100 and M = 1, then R = ρ′= resistivity in ohms per metre-gramme, and 109ρ′ = 10,000dρ, or ρ = 105ρ′/d, and ρ′ = 10,000MR/l2.The following rules, therefore, are useful in connexion with these measurements. To obtain the mass-resistivity per metre-gramme of a substance in the form of a uniform metallic wire:—Multiply together 10,000 times the mass in grammes and the total resistance in ohms, and then divide by the square of the length in centimetres. Again, to obtain the volume-resistivity in C.G.S. units per centimetre-cube, the rule is to multiply the mass-resistivity in ohms by 100,000 and divide by the density. These rules, of course, apply only to wires of uniform cross-section. In the following Tables I., II. and III. are given the mass and volume resistivity of ordinary metals and certain alloys expressed in terms of the international ohm or the absolute C.G.S. unit of resistance, the values being calculated from the experiments of A. Matthiessen (1831-1870) between 1860 and 1865, and from later results obtained by J. A. Fleming and Sir James Dewar in 1893.Table I.—Electric Mass-Resistivity of Various Metals at 0° C., or Resistance per Metre-gramme in International Ohms at 0° C.(Matthiessen.)Metal.Resistance at 0° C.in International Ohmsof a Wire 1 Metre longand Weighing 1 Gramme.Approximate TemperatureCoefficient near 20° C.Silver (annealed).15230.00377Silver (hard-drawn).1657..Copper (annealed).14210.00388Copper (hard-drawn).1449 (Matthiessen’s Standard)..Gold (annealed).40250.00365Gold (hard-drawn).4094..Aluminium (annealed).0757..Zinc (pressed).4013..Platinum (annealed)1.9337..Iron (annealed).765..Nickel (annealed)1.0581..Tin (pressed).96180.00365Lead (pressed)2.22680.00387Antimony (pressed)2.37870.00389Bismuth (pressed)12.855410.00354Mercury (liquid)12.88520.00072The data commonly used for calculating metallic resistivities were obtained by A. Matthiessen, and his results are set out in the Table II. which is taken from Cantor lectures given by Fleeming Jenkin in 1866 at or about the date when the researches were made. The figures given by Jenkin have, however, been reduced to international ohms and C.G.S. units by multiplying by (π/4)×0.9866 × 105= 77,485.Subsequently numerous determinations of the resistivity of various pure metals were made by Fleming and Dewar, whose results are set out in Table III.Table II.—Electric Volume-Resistivity of Various Metals at 0° C., or Resistance per Centimetre-cube in C.G.S. Units at 0° C.Metal.Volume-Resistivity.at 0° C. in C.G.S.UnitsSilver (annealed)1,502Silver (hard-drawn)1,629Copper (annealed)1,594Copper (hard-drawn)1,6303Gold (annealed)2,052Gold (hard-drawn)2,090Aluminium (annealed)3,006Zinc (pressed)5,621Platinum (annealed)9,035Iron (annealed)10,568Nickel (annealed)12,4294Tin (pressed)13,178Lead (pressed)19,580Antimony (pressed)35,418Bismuth (pressed)130,872Mercury (liquid)94,8965Resistivity of Mercury.—The volume-resistivity of pure mercury is a very important electric constant, and since 1880 many of the most competent experimentalists have directed their attention to the determination of its value. The experimental process has usually been to fill a glass tube of known dimensions, having large cup-like extensions at the ends, with pure mercury, and determine the absolute resistance of this column of metal. For the practical details of this method the following references may be consulted:—“The Specific Resistance of Mercury,” Lord Rayleigh and Mrs Sidgwick,Phil. Trans., 1883, part i. p. 173, and R. T. Glazebrook,Phil. Mag., 1885, p. 20; “On the Specific Resistance of Mercury,” R. T. Glazebrook and T. C. Fitzpatrick,Phil. Trans., 1888, p. 179, orProc. Roy. Soc., 1888, p. 44, orElectrician, 1888, 21, p. 538; “Recent Determinations of the Absolute Resistance of Mercury,” R. T. Glazebrook,Electrician, 1890, 25, pp. 543 and 588. Also see J. V. Jones, “On the Determination of the Specific Resistance of Mercury in Absolute Measure,”Phil. Trans., 1891, A, p. 2. Table IV. gives the values of the volume-resistivity of mercury as determined by various observers, the constant being expressed (a) in terms of the resistance in ohms of a column of mercury one millimetre in cross-section and 100 centimetres in length, taken at 0° C.; and (b) in terms of the length in centimetres of a column of mercury one square millimetre in cross-section taken at 0° C. The result of all the most careful determinations has been to show that the resistivity of pure mercury at 0° C. is about 94,070 C.G.S. electromagnetic units of resistance, and that a column of mercury 106.3 centimetres in length having a cross-sectional area of one square millimetre would have a resistance at 0° C. of one international ohm. These values have accordingly been accepted as the official and recognized values for the specific resistance of mercury, and the definition of the ohm. The table also states the methods which have been adopted by the different observers for obtaining the absolute value of the resistance of a known column of mercury, or of a resistance coil afterwards compared with a known column of mercury. A column of figures is added showing the value in fractions of an international ohm of the British Association Unit (B.A.U.), formerly supposed to represent the true ohm. The real value of the B.A.U. is now taken as .9866 of an international ohm.Table III.—Electric Volume-Resistivity of Various Metals at 0° C., or Resistance per Centimetre-cube at 0° C. in C.G.S. Units.(Fleming and Dewar,Phil. Mag., September 1893.)Metal.Resistance at 0° C.per Centimetre-cubein C.G.S. Units.Mean TemperatureCoefficient between0° C. and 100° C.Silver (electrolytic and well annealed)61,4680.00400Copper (electrolytic and well annealed)61,5610.00428Gold (annealed)2,1970.00377Aluminium (annealed)2,6650.00435Magnesium (pressed)4,3550.00381Zinc5,7510.00406Nickel (electrolytic)66,9350.00618Iron (annealed)9,0650.00625Cadmium10,0230.00419Palladium10,2190.00354Platinum (annealed)10,9170.003669Tin (pressed)13,0480.00440Thallium (pressed)17,6330.00398Lead (pressed)20,3800.00411Bismuth (electrolytic)7110,0000.00433Table IV.—Determinations of the Absolute Value of the Volume-Resistivity of Mercury and the Mercury Equivalent of the Ohm.Observer.Date.Method.Value of B.A.U.in Ohms.Value of 100Centimetres ofMercury inOhms.Value of Ohmin Centimetresof Mercury.Lord Rayleigh1882Rotating coil.98651.94133106.31Lord Rayleigh1883Lorenz method.98677..106.27G. Wiedemann1884Rotation through 180°....106.19E. E. N. Mascart1884Induced current.98611.94096106.33H. A. Rowland1887Mean of several methods.98644.94071106.32F. Kohlrausch1887Damping of magnets.98660.94061106.32R. T. Glazebrook1882/8Induced currents.98665.94074106.29Wuilleumeier1890.98686.94077106.31Duncan and Wilkes1890Lorenz.98634.94067106.34J. V. Jones1891Lorenz...94067106.31Mean value.98653Streker1885An absolute determination.94056106.32Hutchinson1888of resistance was not.94074106.30E. Salvioni1890made. The value .98656.94054106.33E. Salvioni..value .98656 has been used.94076106.30Mean value.94076106.31H. F. Weber1884Induced currentAbsolute measurements105.37H. F. Weber..Rotating coilcompared with German106.16A. Roiti1884Mean effect of induced currentsilver wire coils issued by105.89F. Himstedt1885Siemens and Streker105.98F. E. Dorn1889Damping of a magnet106.24Wild1883Damping of a magnet106.03L. V. Lorenz1885Lorenz method105.93For a critical discussion of the methods which have been adopted in the absolute determination of the resistivity of mercury, and the value of the British Association unit of resistance, the reader may be referred to theBritish Association Reportsfor 1890 and 1892 (Report of Electrical Standards Committee), and to theElectrician, 25, p. 456, and 29, p. 462. A discussion of the relative value of the results obtained between 1882 and 1890 was given by R. T. Glazebrook in a paper presented to the British Association at Leeds, 1890.Resistivity of Copper.—In connexion with electro-technical work the determination of the conductivity or resistivity values of annealed and hard-drawn copper wire at standard temperatures is a very important matter. Matthiessen devoted considerable attention to this subject between the years 1860 and 1864 (seePhil. Trans., 1860, p. 150), and since that time much additional work has been carried out. Matthiessen’s value, known asMatthiessen’s Standard, for the mass-resistivity of pure hard-drawn copper wire, is the resistance of a wire of pure hard-drawn copper one metre long and weighing one gramme, and this is equal to 0.14493 international ohms at 0° C. For many purposes it is more convenient to express temperature in Fahrenheit degrees, and the recommendation of the 1899 committee on copper conductors8is as follows:—“Matthiessen’s standard for hard-drawn conductivity commercial copper shall be considered to be the resistance of a wire of pure hard-drawn copper one metre long, weighing one gramme which at 60° F. is 0.153858 international ohms.” Matthiessen also measured the mass-resistivity of annealed copper, and found that its conductivity is greater than that of hard-drawn copper by about 2.25% to 2.5% As annealed copper may vary considerably in its state of annealing, and is always somewhat hardened by bending and winding, it is found in practice that the resistivity of commercial annealed copper is about 1¼% less than that of hard-drawn copper. The standard now accepted for such copper, on the recommendation of the 1899 Committee, is a wire of pure annealed copper one metre long, weighing one gramme, whose resistance at 0° C. is 0.1421 international ohms, or at 60° F., 0.150822 international ohms. The specific gravity of copper varies from about 8.89 to 8.95, and the standard value accepted for high conductivity commercial copper is 8.912, corresponding to a weight of 555 lb per cubic foot at 60° F. Hence the volume-resistivity of pure annealed copper at 0° C. is 1.594 microhms per c.c., or 1594 C.G.S. units, and that of pure hard-drawn copper at 0° C. is 1.626 microhms per c.c., or 1626 C.G.S. units. Since Matthiessen’s researches, the most careful scientific investigation on the conductivity of copper is that of T. C. Fitzpatrick, carried out in 1890. (Brit. Assoc. Report, 1890, Appendix 3, p. 120.) Fitzpatrick confirmed Matthiessen’s chief result, and obtained values for the resistivity of hard-drawn copper which, when corrected for temperature variation, are in entire agreement with those of Matthiessen at the same temperature.

The following rules, therefore, are useful in connexion with these measurements. To obtain the mass-resistivity per metre-gramme of a substance in the form of a uniform metallic wire:—Multiply together 10,000 times the mass in grammes and the total resistance in ohms, and then divide by the square of the length in centimetres. Again, to obtain the volume-resistivity in C.G.S. units per centimetre-cube, the rule is to multiply the mass-resistivity in ohms by 100,000 and divide by the density. These rules, of course, apply only to wires of uniform cross-section. In the following Tables I., II. and III. are given the mass and volume resistivity of ordinary metals and certain alloys expressed in terms of the international ohm or the absolute C.G.S. unit of resistance, the values being calculated from the experiments of A. Matthiessen (1831-1870) between 1860 and 1865, and from later results obtained by J. A. Fleming and Sir James Dewar in 1893.

Table I.—Electric Mass-Resistivity of Various Metals at 0° C., or Resistance per Metre-gramme in International Ohms at 0° C.(Matthiessen.)

The data commonly used for calculating metallic resistivities were obtained by A. Matthiessen, and his results are set out in the Table II. which is taken from Cantor lectures given by Fleeming Jenkin in 1866 at or about the date when the researches were made. The figures given by Jenkin have, however, been reduced to international ohms and C.G.S. units by multiplying by (π/4)×0.9866 × 105= 77,485.

Subsequently numerous determinations of the resistivity of various pure metals were made by Fleming and Dewar, whose results are set out in Table III.

Table II.—Electric Volume-Resistivity of Various Metals at 0° C., or Resistance per Centimetre-cube in C.G.S. Units at 0° C.

Resistivity of Mercury.—The volume-resistivity of pure mercury is a very important electric constant, and since 1880 many of the most competent experimentalists have directed their attention to the determination of its value. The experimental process has usually been to fill a glass tube of known dimensions, having large cup-like extensions at the ends, with pure mercury, and determine the absolute resistance of this column of metal. For the practical details of this method the following references may be consulted:—“The Specific Resistance of Mercury,” Lord Rayleigh and Mrs Sidgwick,Phil. Trans., 1883, part i. p. 173, and R. T. Glazebrook,Phil. Mag., 1885, p. 20; “On the Specific Resistance of Mercury,” R. T. Glazebrook and T. C. Fitzpatrick,Phil. Trans., 1888, p. 179, orProc. Roy. Soc., 1888, p. 44, orElectrician, 1888, 21, p. 538; “Recent Determinations of the Absolute Resistance of Mercury,” R. T. Glazebrook,Electrician, 1890, 25, pp. 543 and 588. Also see J. V. Jones, “On the Determination of the Specific Resistance of Mercury in Absolute Measure,”Phil. Trans., 1891, A, p. 2. Table IV. gives the values of the volume-resistivity of mercury as determined by various observers, the constant being expressed (a) in terms of the resistance in ohms of a column of mercury one millimetre in cross-section and 100 centimetres in length, taken at 0° C.; and (b) in terms of the length in centimetres of a column of mercury one square millimetre in cross-section taken at 0° C. The result of all the most careful determinations has been to show that the resistivity of pure mercury at 0° C. is about 94,070 C.G.S. electromagnetic units of resistance, and that a column of mercury 106.3 centimetres in length having a cross-sectional area of one square millimetre would have a resistance at 0° C. of one international ohm. These values have accordingly been accepted as the official and recognized values for the specific resistance of mercury, and the definition of the ohm. The table also states the methods which have been adopted by the different observers for obtaining the absolute value of the resistance of a known column of mercury, or of a resistance coil afterwards compared with a known column of mercury. A column of figures is added showing the value in fractions of an international ohm of the British Association Unit (B.A.U.), formerly supposed to represent the true ohm. The real value of the B.A.U. is now taken as .9866 of an international ohm.

Table III.—Electric Volume-Resistivity of Various Metals at 0° C., or Resistance per Centimetre-cube at 0° C. in C.G.S. Units.(Fleming and Dewar,Phil. Mag., September 1893.)

Table IV.—Determinations of the Absolute Value of the Volume-Resistivity of Mercury and the Mercury Equivalent of the Ohm.

For a critical discussion of the methods which have been adopted in the absolute determination of the resistivity of mercury, and the value of the British Association unit of resistance, the reader may be referred to theBritish Association Reportsfor 1890 and 1892 (Report of Electrical Standards Committee), and to theElectrician, 25, p. 456, and 29, p. 462. A discussion of the relative value of the results obtained between 1882 and 1890 was given by R. T. Glazebrook in a paper presented to the British Association at Leeds, 1890.

Resistivity of Copper.—In connexion with electro-technical work the determination of the conductivity or resistivity values of annealed and hard-drawn copper wire at standard temperatures is a very important matter. Matthiessen devoted considerable attention to this subject between the years 1860 and 1864 (seePhil. Trans., 1860, p. 150), and since that time much additional work has been carried out. Matthiessen’s value, known asMatthiessen’s Standard, for the mass-resistivity of pure hard-drawn copper wire, is the resistance of a wire of pure hard-drawn copper one metre long and weighing one gramme, and this is equal to 0.14493 international ohms at 0° C. For many purposes it is more convenient to express temperature in Fahrenheit degrees, and the recommendation of the 1899 committee on copper conductors8is as follows:—“Matthiessen’s standard for hard-drawn conductivity commercial copper shall be considered to be the resistance of a wire of pure hard-drawn copper one metre long, weighing one gramme which at 60° F. is 0.153858 international ohms.” Matthiessen also measured the mass-resistivity of annealed copper, and found that its conductivity is greater than that of hard-drawn copper by about 2.25% to 2.5% As annealed copper may vary considerably in its state of annealing, and is always somewhat hardened by bending and winding, it is found in practice that the resistivity of commercial annealed copper is about 1¼% less than that of hard-drawn copper. The standard now accepted for such copper, on the recommendation of the 1899 Committee, is a wire of pure annealed copper one metre long, weighing one gramme, whose resistance at 0° C. is 0.1421 international ohms, or at 60° F., 0.150822 international ohms. The specific gravity of copper varies from about 8.89 to 8.95, and the standard value accepted for high conductivity commercial copper is 8.912, corresponding to a weight of 555 lb per cubic foot at 60° F. Hence the volume-resistivity of pure annealed copper at 0° C. is 1.594 microhms per c.c., or 1594 C.G.S. units, and that of pure hard-drawn copper at 0° C. is 1.626 microhms per c.c., or 1626 C.G.S. units. Since Matthiessen’s researches, the most careful scientific investigation on the conductivity of copper is that of T. C. Fitzpatrick, carried out in 1890. (Brit. Assoc. Report, 1890, Appendix 3, p. 120.) Fitzpatrick confirmed Matthiessen’s chief result, and obtained values for the resistivity of hard-drawn copper which, when corrected for temperature variation, are in entire agreement with those of Matthiessen at the same temperature.

The volume resistivity of alloys is, generally speaking, much higher than that of pure metals. Table V. shows the volume resistivity at 0° C. of a number of well-known alloys, with their chemical composition.

Table V.—Volume-Resistivity of Alloys of known Composition at 0° C. in C.G.S. Units per Centimetre-cube. Mean Temperature Coefficients taken at 15° C.(Fleming and Dewar.)Alloys.Resistivityat 0° C.TemperatureCoefficientat 15° C.Composition in per cents.Platinum-silver31,582.000243Pt 33%, Ag 66%Platinum-iridium30,896.000822Pt 80%, Ir 20%Platinum-rhodium21,142.00143Pt 90%, Rd 10%Gold-silver6,280.00124Au 90%, Ag 10%Manganese-steel67,148.00127Mn 12%, Fe 78%Nickel-steel29,452.00201Ni 4.35%, remaining percentagechiefly iron, but uncertainGerman silver29,982.000273Cu5Zn3Ni2Platinoid941,731.00031Manganin46,678.0000Cu 84%, Mn 12%, Ni 4%Aluminium-silver4,641.00238Al 94%, Ag 6%Aluminium-copper2,904.00381Al 94%, Cu 6%Copper-aluminium8,847.000897Cu 97%, Al 3%Copper-nickel-aluminium14,912.000643Cu 87%, Ni 6.5%, Al 6.5%Titanium-aluminium3,887.00290Generally speaking, an alloy having high resistivity has poor mechanical qualities, that is to say, its tensile strength and ductility are small. It is possible to form alloys having a resistivity as high as 100 microhms per cubic centimetre; but, on the other hand, the value of an alloy for electro-technical purposes is judged not merely by its resistivity, but also by the degree to which its resistivity varies with temperature, and by its capability of being easily drawn into fine wire of not very small tensile strength. Some pure metals when alloyed with a small proportion of another metal do not suffer muchchange in resistivity, but in other cases the resultant alloy has a much higher resistivity. Thus an alloy of pure copper with 3% of aluminium has a resistivity about 5½ times that of copper; but if pure aluminium is alloyed with 6% of copper, the resistivity of the product is not more than 20% greater than that of pure aluminium. The presence of a very small proportion of a non-metallic element in a metallic mass, such as oxygen, sulphur or phosphorus, has a very great effect in increasing the resistivity. Certain metallic elements also have the same power; thus platinoid has a resistivity 30% greater than German silver, though it differs from it merely in containing a trace of tungsten.

Table V.—Volume-Resistivity of Alloys of known Composition at 0° C. in C.G.S. Units per Centimetre-cube. Mean Temperature Coefficients taken at 15° C.(Fleming and Dewar.)

Generally speaking, an alloy having high resistivity has poor mechanical qualities, that is to say, its tensile strength and ductility are small. It is possible to form alloys having a resistivity as high as 100 microhms per cubic centimetre; but, on the other hand, the value of an alloy for electro-technical purposes is judged not merely by its resistivity, but also by the degree to which its resistivity varies with temperature, and by its capability of being easily drawn into fine wire of not very small tensile strength. Some pure metals when alloyed with a small proportion of another metal do not suffer muchchange in resistivity, but in other cases the resultant alloy has a much higher resistivity. Thus an alloy of pure copper with 3% of aluminium has a resistivity about 5½ times that of copper; but if pure aluminium is alloyed with 6% of copper, the resistivity of the product is not more than 20% greater than that of pure aluminium. The presence of a very small proportion of a non-metallic element in a metallic mass, such as oxygen, sulphur or phosphorus, has a very great effect in increasing the resistivity. Certain metallic elements also have the same power; thus platinoid has a resistivity 30% greater than German silver, though it differs from it merely in containing a trace of tungsten.

The resistivity of non-metallic conductors is in all cases higher than that of any pure metal. The resistivity of carbon, for instance, in the forms of charcoal or carbonized organic material and graphite, varies from 600 to 6000 microhms per cubic centimetre, as shown in Table VI.:—

Table VI.—Electric Volume-Resistivity in Microhms per Centimetre-cube of Various Forms of Carbon at 15° C.

The resistivity of liquids is, generally speaking, much higher than that of any metals, metallic alloys or non-metallic conductors. Thus fused lead chloride, one of the best conducting liquids, has a resistivity in its fused condition of 0.376 ohm per centimetre-cube, or 376,000 microhms per centimetre-cube, whereas that of metallic alloys only in few cases exceeds 100 microhms per centimetre-cube. The resistivity of solutions of metallic salts also varies very largely with the proportion of the diluent or solvent, and in some instances, as in the aqueous solutions of mineral acids; there is a maximum conductivity corresponding to a certain dilution. The resistivity of many liquids, such as alcohol, ether, benzene and pure water, is so high, in other words, their conductivity is so small, that they are practically insulators, and the resistivity can only be appropriately expressed in megohms per centimetre-cube.

In Table VII. are given the names of a few of these badly-conducting liquids, with the values of their volume-resistivity in megohms per centimetre-cube:—

Table VII.—Electric Volume-Resistivity of Various Badly-Conducting Liquids in Megohms per Centimetre-cube.

The resistivity of all those substances which are generally called dielectrics or insulators is also so high that it can only be appropriately expressed in millions of megohms per centimetre-cube, or in megohms per quadrant-cube, the quadrant being a cube the side of which is 109cms. (see Table VIII.).

Table VIII.—Electric Volume-Resistivity of Dielectrics reckoned in Millions of Megohms (Mega-megohms) per Centimetre-cube, and in Megohms per Quadrant-cube, i.e. a Cube whose Side is109cms.

Effects of Heat.—Temperature affects the resistivity of these different classes of conductors in different ways. In all cases, so far as is yet known, the resistivity of a pure metal is increased if its temperature is raised, and decreased if the temperature is lowered, so that if it could be brought to the absolute zero of temperature (-273° C.) its resistivity would be reduced to a very small fraction of its resistance at ordinary temperatures. With metallic alloys, however, rise of temperature does not always increase resistivity: it sometimes diminishes it, so that many alloys are known which have a maximum resistivity corresponding to a certain temperature, and at or near this point they vary very little in resistance with temperature. Such alloys have, therefore, a negative temperature-variation of resistance at and above fixed temperatures. Prominent amongst these metallic compounds are alloys of iron, manganese, nickel and copper, some of which were discovered by Edward Weston, in the United States. One well-known alloy of copper, manganese and nickel, now called manganin, which was brought to the notice of electricians by the careful investigations made at the Berlin Physikalisch-Technische Reichsanstalt, is characterized by having a zero temperature coefficient at or about a certain temperature in the neighbourhood of 15° C. Hence within a certain range of temperature on either side of this critical value the resistivity of manganin is hardly affected at all by temperature. Similar alloys can be produced from copper and ferro-manganese. An alloy formed of 80% copper and 20% manganese in an annealed condition has a nearly zero temperature-variation of resistance between 20° C. and 100° C. In the case of non-metals the action of temperature is generally to diminish the resistivity as temperature rises, though this is not universally so. The interesting observation has been recorded by J. W. Howell, that “treated” carbon filaments and graphite are substances which have a minimum resistance corresponding to a certain temperature approaching red heat (Electrician, vol. xxxviii. p. 835). At and beyond this temperature increased heating appears to increase their resistivity; this phenomenon may, however, be accompanied by a molecular change and not be a true temperature variation. In the case of dielectric conductors and of electrolytes, the action of rising temperature is to reduce resistivity. Many of the so-called insulators, such as mica, ebonite, indiarubber, and the insulating oils, paraffin, &c., decrease in resistivity with great rapidity as the temperature rises. With guttapercha a rise in temperature from 0° C. to 24° C. is sufficient to reduce the resistivity of one-twentieth part of its value at 0° C., and the resistivity of flint glass at 140° C. is only one-hundredth of what it is at 60° C.

A definition may here be given of the meaning of the termTemperature Coefficient. If, in the first place, we suppose that the resistivity (ρt) at any temperature (t) is a simple linear function of the resistivity (ρ0) at 0° C., then we can write ρt= ρ0(1 + αt), or α = (ρt− ρ0)/ρ0t.The quantity α is then called the temperature-coefficient, and its reciprocal is the temperature at which the resistivity would becomezero. By an extension of this notion we can call the quantity dρ/ρdt the temperature coefficient corresponding to any temperature t at which the resistivity is ρ. In all cases the relation between the resistivity of a substance and the temperature is best set out in the form of a curve called a temperature-resistance curve. If a series of such curves are drawn for various pure metals, temperature being taken as abscissa and resistance as ordinate, and if the temperature range extends from the absolute zero of temperature upwards, then it is found that these temperature-resistance lines are curved lines having their convexity either upwards or downwards. In other words, the second differential coefficient of resistance with respect to temperature is either a positive or negative quantity. An extensive series of observations concerning the form of the resistivity curves for various pure metals over a range of temperature extending from -200° C. to +200° C. was carried out in 1892 and 1893 by Fleming and Dewar (Phil. Mag.Oct. 1892 and Sept. 1893). The resistance observations were taken with resistance coils constructed with wires of various metals obtained in a state of great chemical purity. The lengths and mean diameters of the wires were carefully measured, and their resistance was then taken at certain known temperatures obtained by immersing the coils in boiling aniline, boiling water, melting ice, melting carbonic acid in ether, and boiling liquid oxygen, the temperatures thus given being +184°.5 C., +100° C., 0° C., -78°.2 C. and -182°.5 C. The resistivities of the various metals were then calculated and set out in terms of the temperature. From these data a chart was prepared showing the temperature-resistance curves of these metals throughout a range of 400 degrees. The exact form of these curves through the region of temperature lying between -200° C. and -273° C. is not yet known. As shown on the chart, the curves evidently do not converge to precisely the same point. It is, however, much less probable that the resistance of any metal should vanish at a temperature above the absolute zero than at the absolute zero itself, and the precise path of these curves at their lower ends cannot be delineated until means are found for fixing independently the temperature of some regions in which the resistance of metallic wires can be measured. Sir J. Dewar subsequently showed that for certain pure metals it is clear that the resistance would not vanish at the absolute zero but would be reduced to a finite but small value (see “Electric Resistance Thermometry at the Temperature of Boiling Hydrogen,”Proc. Roy. Soc.1904, 73, p. 244).The resistivity curves of the magnetic metals are also remarkable for the change of curvature they exhibit at the magnetic critical temperature. Thus J. Hopkinson and D. K. Morris (Phil. Mag.September 1897, p. 213) observed the remarkable alteration that takes place in the iron resistance temperature curve in the neighbourhood of 780° C. At that temperature the direction of the curvature of the curve changes so that it becomes convex upwards instead of convex downwards, and in addition the value of the temperature coefficient undergoes a great reduction. The mean temperature coefficient of iron in the neighbourhood of 0° C. is 0.0057; at 765° C. it rises to a maximum value 0.0204; but at 1000° C. it falls again to a lower value, 0.00244. A similar rise to a maximum value and subsequent fall are also noted in the case of the specific heat of iron. The changes in the curvature of the resistivity curves are undoubtedly connected with the molecular changes that occur in the magnetic metals at their critical temperatures.A fact of considerable interest in connexion with resistivity is the influence exerted by a strong magnetic field in the case of some metals, notably bismuth. It was discovered by A. Righi and confirmed by S. A. Leduc (Journ. de Phys.1886, 5, p. 116, and 1887, 6, p. 189) that if a pure bismuth wire is placed in a magnetic field transversely to the direction of the magnetic field, its resistance is considerably increased. This increase is greatly affected by the temperature of the metal (Dewar and Fleming,Proc. Roy. Soc.1897, 60, p. 427). The temperature coefficient of pure copper is an important constant, and its value as determined by Messrs Clark, Forde and Taylor in terms of Fahrenheit temperature isρt= ρ32{1 + 0.0023708(t − 32) + 0.0000034548(t − 32)²}.

The quantity α is then called the temperature-coefficient, and its reciprocal is the temperature at which the resistivity would becomezero. By an extension of this notion we can call the quantity dρ/ρdt the temperature coefficient corresponding to any temperature t at which the resistivity is ρ. In all cases the relation between the resistivity of a substance and the temperature is best set out in the form of a curve called a temperature-resistance curve. If a series of such curves are drawn for various pure metals, temperature being taken as abscissa and resistance as ordinate, and if the temperature range extends from the absolute zero of temperature upwards, then it is found that these temperature-resistance lines are curved lines having their convexity either upwards or downwards. In other words, the second differential coefficient of resistance with respect to temperature is either a positive or negative quantity. An extensive series of observations concerning the form of the resistivity curves for various pure metals over a range of temperature extending from -200° C. to +200° C. was carried out in 1892 and 1893 by Fleming and Dewar (Phil. Mag.Oct. 1892 and Sept. 1893). The resistance observations were taken with resistance coils constructed with wires of various metals obtained in a state of great chemical purity. The lengths and mean diameters of the wires were carefully measured, and their resistance was then taken at certain known temperatures obtained by immersing the coils in boiling aniline, boiling water, melting ice, melting carbonic acid in ether, and boiling liquid oxygen, the temperatures thus given being +184°.5 C., +100° C., 0° C., -78°.2 C. and -182°.5 C. The resistivities of the various metals were then calculated and set out in terms of the temperature. From these data a chart was prepared showing the temperature-resistance curves of these metals throughout a range of 400 degrees. The exact form of these curves through the region of temperature lying between -200° C. and -273° C. is not yet known. As shown on the chart, the curves evidently do not converge to precisely the same point. It is, however, much less probable that the resistance of any metal should vanish at a temperature above the absolute zero than at the absolute zero itself, and the precise path of these curves at their lower ends cannot be delineated until means are found for fixing independently the temperature of some regions in which the resistance of metallic wires can be measured. Sir J. Dewar subsequently showed that for certain pure metals it is clear that the resistance would not vanish at the absolute zero but would be reduced to a finite but small value (see “Electric Resistance Thermometry at the Temperature of Boiling Hydrogen,”Proc. Roy. Soc.1904, 73, p. 244).

The resistivity curves of the magnetic metals are also remarkable for the change of curvature they exhibit at the magnetic critical temperature. Thus J. Hopkinson and D. K. Morris (Phil. Mag.September 1897, p. 213) observed the remarkable alteration that takes place in the iron resistance temperature curve in the neighbourhood of 780° C. At that temperature the direction of the curvature of the curve changes so that it becomes convex upwards instead of convex downwards, and in addition the value of the temperature coefficient undergoes a great reduction. The mean temperature coefficient of iron in the neighbourhood of 0° C. is 0.0057; at 765° C. it rises to a maximum value 0.0204; but at 1000° C. it falls again to a lower value, 0.00244. A similar rise to a maximum value and subsequent fall are also noted in the case of the specific heat of iron. The changes in the curvature of the resistivity curves are undoubtedly connected with the molecular changes that occur in the magnetic metals at their critical temperatures.

A fact of considerable interest in connexion with resistivity is the influence exerted by a strong magnetic field in the case of some metals, notably bismuth. It was discovered by A. Righi and confirmed by S. A. Leduc (Journ. de Phys.1886, 5, p. 116, and 1887, 6, p. 189) that if a pure bismuth wire is placed in a magnetic field transversely to the direction of the magnetic field, its resistance is considerably increased. This increase is greatly affected by the temperature of the metal (Dewar and Fleming,Proc. Roy. Soc.1897, 60, p. 427). The temperature coefficient of pure copper is an important constant, and its value as determined by Messrs Clark, Forde and Taylor in terms of Fahrenheit temperature is

ρt= ρ32{1 + 0.0023708(t − 32) + 0.0000034548(t − 32)²}.

Time Effects.—In the case of dielectric conductors, commonly called insulators, such as indiarubber, guttapercha, glass and mica, the electric resistivity is not only a function of the temperature but also of the time during which the electromotive force employed to measure it is imposed. Thus if an indiarubber-covered cable is immersed in water and the resistance of the dielectric between the copper conductor and the water measured by ascertaining the current which can be caused to flow through it by an electromotive force, this current is found to vary very rapidly with the time during which the electromotive force is applied. Apart from the small initial effect due to the electrostatic capacity of the cable, the application of an electromotive force to the dielectric produces a current through it which rapidly falls in value, as if the electric resistance of the dielectric were increasing. The current, however, does not fall continuously but tends to a limiting value, and it appears that if the electromotive force is kept applied to the cable for a prolonged time, a small and nearly constant current will ultimately be found flowing through it. It is customary in electro-technical work to consider the resistivity of the dielectric as the value it has after the electromotive force has been applied for one minute, the standard temperature being 75° F. This, however, is a purely conventional proceeding, and the number so obtained does not necessarily represent the true or ohmic resistance of the dielectric. If the electromotive force is increased, in the case of a large number of ordinary dielectrics the apparent resistance at the end of one minute’s electrification decreases as the electromotive force increases.

Practical Standards.—The practical measurement of resistivity involves many processes and instruments (seeWheatstone’s BridgeandOhmmeter). Broadly speaking, the processes are divided intoComparison MethodsandAbsolute Methods. In the former a comparison is effected between the resistance of a material in a known form and some standard resistance. In theAbsolute Methodsthe resistivity is determined without reference to any other substance, but with reference only to the fundamental standards of length, mass and time. Immense labour has been expended in investigations concerned with the production of a standard of resistance and its evaluation in absolute measure. In some cases the absolute standard is constructed by filling a carefully-calibrated tube of glass with mercury, in order to realize in a material form the official definition of the ohm; in this manner most of the principal national physical laboratories have been provided with standard mercury ohms. (For a full description of the standard mercury ohm of the Berlin Physikalisch-Technische Reichsanstalt, see theElectrician, xxxvii. 569.) For practical purposes it is more convenient to employ a standard of resistance made of wire.

Back to Index Next