change 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.
|Arc lamp carbon rod||8000|
|Jablochkoff candle carbon||4000|
|Carbonized parchmentized thread||4000 to 5000|
|Ordinary carbon filament from glow-lamp|
|“treated” or flashed||2400 to 2500|
|Deposited or secondary carbon||600 to 900|
|Graphite||400 to 500|
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.
|Ethyl ether||1.175 to 3.760||W. Kohlrausch.|
|Absolutely pure water approximates probably to||25.0 at 18° C.||Value estimated by F. Kohlrausch|
|and A. Heydweiler.|
|All very dilute aqueous salt solutions having a||1.00 at 18° C.||From results by F. Kohlrausch|
|concentration of about 0.00001 of an equivalent||and others.|
|gramme molecule per litre approximate to|
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 109 cms. (see Table VIII.).
Table VIII.—Electric Volume-Resistivity of Dielectrics reckoned in
|Glover’s vulcanized indiarubber||1,630||1.63||15°|
|Siemens’ ordinary pure vulcanized indiarubber||2,280||2.28||15°|
|Siemens’ high-insulating fibrous material||11,900||11.9||15°|
|Siemens’ special high-insulating indiarubber||16,170||16.17||15°|
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 term Temperature 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 become
- An equivalent gramme molecule is a weight in grammes equal numerically to the chemical equivalent of the salt. For instance, one equivalent gramme molecule of sodium chloride is a mass of 58.5 grammes. NaCl = 58.5.