Electricity (Kapp)/Chapter 5

by Gisbert Johann Eduard Kapp

CHAPTER V

THE ELECTRIC CURRENT

In Chapter II use has already been made of the term electric current. The term meant the transfer of a positive charge through a wire from a point where the potential is higher to one where the potential is lower. Observation shows that the quantity which can be transferred in unit time depends not only on the difference of potential, but also on the material and the cross section of the wire. A stout wire will transfer a bigger quantity in unit time than a thin wire, or, as we may also say, it is able to carry a bigger current. When it is a question of electricity in motion the conductor must have body, whilst as we have seen, with electricity at rest only the surface counts, or, to speak more correctly, only the capacity counts. But the capacity of a sphere in space, or of a Leyden jar, is quite independent of the thickness of the metal parts. A wooden sphere covered with the thinnest layer of gold-beater's skin will at the same potential hold exactly the same quantity of electricity as if it were made of solid brass or lead or any other metal. Electricity at rest resides entirely on the outside of a metal conductor. We might reduce the thickness of a shell to any degree, and still the charge is not altered.

Now let us follow this fact to its logical conclusion. What will happen if we reduce the thickness of the shell to zero? If thickness has nothing to do with the capacity, then by reducing it to nothing at all we should not alter the capacity. In other words, the body which holds a charge need not be a conductor at all. Its conducting property is only necessary to let the charge distribute itself over the whole of its surface, in fact to get a charge on to it at all. If, however, the charge is not transferred to the surface from outside, but actually produced on the surface, then there is no need that the surface should be the surface of a conductor. This will be clearly seen if we reflect that a glass rod, although a very good insulator, may be electrified by rubbing. Its insulating property is a positive advantage, since we may hold one end in our hand and yet electrify the surface at the other end. The charge is not able to slip about freely over the whole surface, as is the case with a charged conductor; hence, if we touch a particular point of the electrified part, we take off a little of the charge at that point, but the rest of the rod remains charged. We thus see that a charge can reside on the surface of an insulator, and it can be proved experimentally that the charge even penetrates a little way into the body of the insulator.

If a Leyden jar or a paper condenser be discharged and left standing a little while, a second though very much weaker discharge may be taken from it. It is as though the electricity had soaked into the body of the dielectric and some of it was thus prevented from getting out at the first discharge. When the jar has apparently been completely discharged, there is still left a small residual charge, which slowly leaks out on to the surface of the glass and is then ready to produce a second discharge spark. If the dielectric is mica, this phenomenon of soaking is much less pronounced, and if air is used as a dielectric, it is absent.

A very striking experiment may be made to show that the charge in a Leyden jar does not reside on the surface of the metal coatings, but on the surface of the glass. Imagine a metal beaker into which fits a glass beaker and into that a second metal beaker. The latter may have a stem and discharge knob much in the same way as an ordinary Leyden jar, the only difference being that the inner and outer coatings are not pasted on to the glass, but are removable. If, after charging this jar, we take out the inner metal beaker by insulated tongs, and also remove the glass beaker from its outer envelope, we have completely dissected the jar. The two metal coatings may be handled, the glass may be picked up by the hand touching the outside, and yet when we put the Leyden jar together again, we find that it still contains the original charge, less a certain unavoidable leakage, since no insulator is perfect. We thus see that any body, whether insulator or conductor, may hold a static charge on its surface.

Why then do we make the electrodes of an electric machine, such as that diagrammatically represented by Fig. 5, of brass and not of glass? For the simple reason that a glass electrode, although quite capable of holding a charge, is very ill-adapted for receiving it. The charge must be conveyed to it by a wire, and from the point where the wire joins it the charge must be able to flow to all points of the surface. This flow is impossible through the body of the glass, since glass is an insulator. Conversely, if we touch a charged glass sphere at one point we may take off a little of the charge, but not the whole of it, which is distributed over the sphere. Between electricity at rest and in motion, or as we may also say, between static charges and currents, there is thus the fundamental distinction that the static charge requires surface and the moving charge body.

The greater the current we wish to convey, the stouter must be the wire. The commercial unit of current is the Ampere, so named after the great French physicist. We may define the current existing in a particular point of the wire as the number of unit charges which pass that point during one second. The magnitude of the electrostatic unit of quantity has been defined in Chapter I, p. 13. By experiment it has been proved that one ampere is represented by the passage of 3000 millions of such units per second.

Man has no sense by which he can estimate the strength of a current flowing in a wire—by touching the wire he may get a shock and thus conclude that the wire is at a higher potential than he is himself when standing on the earth; and indeed wiremen, who have grown reckless in their calling, often resort to this simple test to find out whether a wire is what is technically termed "alive," but no amount of shocks will ever enable a man to say how many amperes are flowing in the wire. This can only be determined by observation of certain effects produced by the current. These effects may be chemical, thermal, magnetic or mechanical.

Chemical action of an electric current.—The substance of a copper wire carrying a current undergoes no change. It may get heated whilst the current flows, but chemically it remains unaltered. Even if the wire is an alloy of two metals there is no change in its chemical nature. Also with liquid conductors, such as mercury or molten iron, the passage of a current does not produce a chemical change, but if the liquid is some chemical compound there is such a change. Imagine two copper plates placed in a solution of copper sulphate and provided with terminals AB, such as shown in Fig. 1, p. 48. Attach to these terminals the wires leading to a dynamo machine or some other source from which an electric current flowing always in the same direction may be obtained. Let us also put into the circuit some instrument which will record the total quantity of electricity that has passed through the solution in a given time, such as a recording electricity meter used in the sale of electricity to householders. We shall find that the copper plate at which the current enters gets gradually thinner, and that at which the current issues gradually stouter exactly in the same measure, showing that the current has the effect of transporting copper from the one plate to the other.

An arrangement of this kind is called an electrolytic cell, and the process going on in the cell is called electrolysis. The plates are called the electrodes, and the liquid between them is the electrolyte. The electrode by which the current enters is also called the anode, and that by which it leaves is called the kathode. The current flows from the anode into the electrolyte and from the electrolyte to the kathode, taking the copper with it. If instead of copper sulphate the electrolyte contained some other metallic salt, the current would split this up chemically and take the metal, whatever it may be, with it and deposit it on the kathode. This is the principle on which objects are silver- or nickel-plated. It is also the principle on which copper is refined on a large scale. The Page:Electricity (1912) Kapp.djvu/124 the simplest case of the electrolyte being water, which has been rendered conducting by a slight addition of some chemical, such as sulphuric acid. The two substances out of which water is formed are the gases oxygen and hydrogen. The current, in passing through the water, tears these oxygen and hydrogen atoms asunder and carries them off, the hydrogen in the direction of its own flow, namely, to the kathode, and the oxygen in the opposite direction, that is to say, to the anode. Here the gases are deposited in the form of bubbles, which from time to time become detached and rise to the surface. By using an arrangement such as shown in Fig. 6 the gases may be separately collected and their volume measured. A and K are two platinum wires fused into the bottom of the glass vessel, which is filled with acidulated water. Over these electrodes are placed two inverted glass tubes also filled with water and closed at the top, so that the gases liberated at the electrodes may be collected and their volume measured. It is found that the space filled by hydrogen, H, is exactly twice as great as that filled by oxygen, O; and this is precisely the volumetric proportion in which these two gases form water. The direction of the current is shown by the arrow. There is a migration of hydrogen atoms in the direction of the arrow through the liquid, and a migration of oxygen atoms in the opposite direction. We actually see the bubbles forming on the kathode and anode, yet we see no bubbles passing through the liquid. The formation of bubbles shows that there is actually a tearing apart of the two gases close to the surface of the electrodes, but apparently there is no such tearing apart in the body of the liquid, for we see no bubbles there.

This apparent anomaly has been cleared up on the basis of an hypothesis by Grotthus, which may be put in homely language by reference to a ball-room. Let each male dancer stand for an oxygen atom and each woman for a hydrogen atom. Let the room be crowded, and all the dancers be properly paired. A man looking down on the throng sees only couples, but no single persons. Now suppose that by some rule of the dance, at a given signal one man at one end of the room must leave his partner and cling to the wall, whilst at the same moment a woman at the other end of the room must do the same. This will disturb the homogeneity of the throng, but that can immediately be restored if all the couples in a direct line between the two walls change partners and thus absorb the two partnerless persons again into the general dancing throng. Our observer on the gallery would then not notice any difference in the assembly; all remain properly paired.

The electrolysis of water is commercially utilised for the production of pure oxygen and hydrogen. The electrodes are of iron, and the electrolyte is a 16% soda solution. The cost of the process, including cost of power, labour, interest and depreciation, varies from 9d. to 1s. 2d. per one cubic meter oxygen + two cubic meters hydrogen, according to the magnitude of the plant and local conditions.

Electrolysis is not confined to liquids; it can also be produced in a solid, provided it is a conductor. Thus, if a current is sent through a lump of caustic potash, it is decomposed into oxygen and the metal potassium. Let, in Fig. 7, P be a platinum plate, C a lump of caustic potash, and M a globule of mercury placed into a cavity hollowed out of the solid electrolyte; then, on the passage of a current in the direction shown by the arrows, oxygen will collect on the surface of the platinum, and Page:Electricity (1912) Kapp.djvu/128 Page:Electricity (1912) Kapp.djvu/129 on the objects to be treated. Conversely, it is also possible to draw up a balance sheet showing how much zinc will be used up in a voltaic cell relatively to the amount of electricity obtained from the cell. Such a balance sheet shows that the production of electric currents in large quantities by voltaic cells is far too expensive for commercial use. It is only when feeble currents are required that it pays to produce current by electrolytic process; when current is required on a large scale, such as for lighting and power, and also for metallurgical work, copper refining and electro-plating on a large scale, it must be produced by dynamo machines. Electrolysis, then, is not of much importance for the production of electricity, but it is of enormous importance in the utilisation of electricity, forming the basis of copper refining and electro-plating, on which large industries carried on in Swansea, Birmingham, Sheffield and other places are built up.

Thermal action of an electric current.—An electric current flowing through any conductor heats it. The amount of heat developed depends on the material of the conductor, its length, cross section and the strength of the current. As the current is increased the heat increases also, but at a faster rate, so that if the conductor is a wire a point is reached when it becomes red-, or white-hot, and gives out light. This is, indeed, the principle on which incandescent lamps become sources of light. The wire may be a carbon filament, or a filament of tantalum, tungsten, or other highly refractory metal. Whatever the substance used for the filament of a lamp, it is subject to the same influence as any other conductor—it gets hot when traversed by a current. There is, however, this difference in degree. In the lamp we desire to produce heat at a high temperature, for only then do we get light as well as heat; in a conductor used for the purpose of transferring electricity from the source where it is generated to the apparatus where it is utilised, we desire to generate as little heat as possible. There is an advantage in producing a high temperature in the filament of the incandescent lamp, but there is no advantage whatever in producing heat in the wires that carry the current to the lamp. On the contrary, there is an objection to it; not only does the generation of heat mean a dissipation of energy, that is, of something which costs money, but it may be a positive danger, since a conductor becoming red-hot may set fire to a building.

To guard against this danger a short piece of the conductor is made very thin, so that in the event of the current becoming so strong that the rest of the conductor becomes sensibly hot, this little piece shall become so hot that it fuses, and thus interrupts the continuity of the conductor, that is, causes an interruption of the current. This is the principle of protecting electric circuits against overheating. The short bit of the conductor, intended by its destruction to save the rest, is called the fuse, and this is so placed that by its melting it cannot cause a fire. Such fuses are found in every domestic installation for lighting. The fuse wire is enclosed in a tube or plug of porcelain, and sometimes the cavity is filled in with carborundum powder to act as an absorbent of the heat momentarily generated by the explosive fusion of the wire.

In this connection it is interesting to note that the seemingly obvious is not always the best. At first fuse wires were made of tin or lead, simply because these metals fuse at a low temperature, and it seemed obvious that the lower the temperature of fusion the quicker would the device act. This is a fallacy. If lead or tin are used for the fuse wire, this must be much stouter than would be the case with copper or silver; consequently the amount of material, which by the heating is volatilised, becomes so great that the process resembles rather an explosion than a quiet melting, and the envelope may be shattered, letting out the flash, and thus the fuse itself may become a source of danger. In this respect the best material for fuse wires is silver. An exceedingly thin silver wire will carry a fairly large current, and if the current should rise to a dangerous value and the wire be fused, the amount of material volatilised is so small that there is hardly any explosive effect, especially if the wire is embedded in carborundum powder.

Now the reader may ask, why should a thin silver wire suffice if for the same current a stout lead wire is necessary? This comes from the physical fact that silver is far better adapted than lead for carrying an electric current, it conducts better, or, as we also may say, it has a higher "conductivity." By this we mean that to get the current through the wire the force which is pushing the electricity from one end to the other is much smaller with silver than with lead; silver offers less "resistance" to the flow of electricity than lead. Thus each conductor has a certain physical property called its electric resistance, and this depends on the length and section of the conductor, on its temperature and on its material. In order to compare different materials as regards resistance, we must eliminate those elements which may vary from case to case and reduce all to the same standard. The physicist takes as the standard length the centimetre, and as the standard cross section the square centimetre. The standard form for which the resistance is given is thus not a wire at all, but a cube. The engineer prefers to retain the shape of the wire for his standard, and defines the resistance of the material as that of a wire one metre long and one square millimetre in cross section, the test being made at the temperature of 15° C.

How is such a test to be made? G. S. Ohm, a Bavarian physicist (1787-1854), was the first to make such tests and to formulate a law, which bears his name, and which connects the three things on which the transfer of electricity from one end of a conductor to the other depends. Ohm found experimentally that the strength of the current is directly proportional to the e.m.f. applied at the ends of the wire, and inversely proportional to a particular physical property which, he called the "resistance" of the wire. Expressed mathematically, Ohm's law is

$I={\frac {E}{R}}$

where $I$ stands for current strength, $E$ for electromotive force, and $R$ for resistance. He also found that in a double length of wire the same e.m.f. will only produce half the current strength, whilst by increasing the cross section of the wire (which can conveniently be done by using two or more wires side by side), the current strength is proportionately increased. He thus found that the resistance of the conductor is directly proportional to its length and inversely proportional to its section. This, again expressed mathematically, is

$R=\varrho {\frac {L}{q}}$

where $L$ is the length and $q$ the section. The coefficient $\varrho$ depends on the material, and is called "the specific resistance." The two formulæ here given are generally valid, whatever may be the system of units chosen. They may, therefore, also be used with the practical units of the "ampere" for current strength and the "volt" for e.m.f., in which case the unit of resistance is called the "ohm." The following table gives the specific resistance reduced to a standard wire one metre in length and one square millimetre in cross section at ordinary room temperature—

Material.

Silver

Copper

Aluminium

Iron

Mercury

Platinum

Resistance in ohms.

0.0158

0.0165

0.0287

0.125

0.953

0.094

The fact that a column of mercury one metre long and one square millimetre in section has a resistance of nearly an ohm, has led to suggestions to adopt mercury as a standard of resistance, and indeed, before the true value of the ohm had been determined by electrodynamic investigation, the mercury column was taken as approximately representing an ohm. It might be thought that such a standard would be acceptable to physicists, because it would enable each investigator to reproduce the standard at any time for himself, and thus render him independent of others. It is, however, not at all easy to produce such a standard. There is not only the difficulty of obtaining a glass tube of absolutely even bore, but the further difficulty that the specific resistance of mercury, as of all metals, varies slightly with the degree of chemical purity in which the metal can be obtained, so that the so-called "mercury standard" has been discarded in favour of standards made of platinum.

Such standards are deposited in State Laboratories or Museums, and only serve as reference standards, such as the yard or the pound. For practical use other so-called secondary standards are made of some less expensive material, generally some alloy, such as German silver, manganin, platinoid, eureka metal, etc. These alloys have the advantage that their resistance is very little influenced by change in temperature, whereas copper increases its resistance sensibly when heated. For every degree centigrade of temperature rise above 15° C., the resistance of a copper conductor rises by about 0.38 per cent. All machines when at work become heated to a certain extent, since some of the energy which is passing through the machine is necessarily lost in the process of conversion from one form to another form. This lost energy is converted into heat, and thus the temperature of the machine is increased. The more efficient the machine, that is to say, the less of the energy passing through it is lost, the cooler will the machine run. Excessive heating in a machine is also objectionable on the ground that thereby some of the materials used in the construction may be destroyed.

If we have to deal with a dynamo machine this is especially important, since in the construction of such machine insulating materials such as cotton, tape, wood, etc., must be used. The machine should therefore be designed with due regard to a strictly limited temperature rise, and it is also important that the finished machine should be tested so as to make sure that the designer's intention has actually been realised. The heat is generated in the body of the materials used, and it has to leak out and be dissipated into the surrounding atmosphere from the surface of the machine. Thus it is quite possible that the temperature at the surface, which can be measured by a thermometer, is much below the internal temperature, just as the outer surface of a stove is not nearly so hot as the fire inside. To get the temperature of the hottest part, we should put a thermometer to the inside of the machine, but unless provision has been made in the construction of the machine for such application of thermometers, this may not be done. It is in this connection that the influence of temperature on the resistance of copper comes in very useful. We need only measure the resistance of the copper coils before the machine is set to work, that is to say, whilst it is at ordinary room temperature, and repeat the measurement after the machine has got hot through working. The increase of resistance thus found may be used to calculate the rise of temperature in the interior of the machine. According to the best modern practice, this rise should not exceed about 50° C.

Another important application of the fact that all metals increase their resistance with a rising temperature is made in the so-called "electric pyrometer," an instrument for measuring the very high temperatures in metallurgical furnaces. Essentially, the pyrometer consists of a porcelain tube containing a spiral of platinum wire, which is put into the furnace. The spiral is joined to other wires of low resistance, which lead to some kind of measuring instrument, indicating the resistance of the platinum spiral. The hotter the furnace, the higher becomes the resistance of the spiral, so that by a suitable graduation of the scale of the instrument, this may be used to show what temperature actually exists in the furnace.

The influence of temperature on the resistance of a material is a physical attribute of the material, such as its specific resistance itself, or, for the matter of that, as all its physical and chemical properties. We express this particular property by saying that the material has such and such a "temperature coefficient." Thus copper has a temperature coefficient of + 0.0038, meaning that the resistance increases by 0.38 per cent, for every degree of temperature increase. The + sign means that the coefficient is positive, that is, refers to an increase, not a decrease of resistance. There are, however, certain substances which have a negative temperature coefficient. In these materials the resistance diminishes as they get hotter. Most liquid conductors have this property, and of solid conductors carbon is a familiar example. The resistance of a carbon filament incandescent lamp is greater when the lamp is cold than when it is alight. In this case the heat is generated by the current passing through the filament. If then, by raising the e.m.f. of the supply more current passes through the lamp, the filament gets hotter, its resistance decreases, and still more current is permitted to pass. The result of this interaction is that an increase of voltage does not produce a proportional, but an exaggerated increase of current and vice versa, with a corresponding exaggerated variation in the light given. Such lamps are sensitive to changes in voltage, more so than the metal filament lamps which, by reason of their positive temperature coefficient, burn with greater stability.

The most sensitive of all filaments is, however, the pencil of a "Nernst" lamp. This, when cold, is not a conductor at all; to make it conducting it must be heated to a dull red heat by a platinum spiral placed near it in the lamp. When sufficiently hot the pencil becomes a conductor of considerable resistance, so that a much shorter length than the filament of a metal or carbon lamp offers sufficient resistance for a working e.m.f. of 200 or 220 volts. By the passage of the current the pencil is maintained at white heat, and a very brilliant light is emitted. The pencil is, however, very sensitive to changes in voltage. It has a very large negative temperature coefficient, and in consequence the exaggeration as regards changes in current strength mentioned on the previous page in connection with carbon lamps, is much greater; in fact, it is so great that the working becomes unstable if the pencil be used alone, even on a circuit of perfectly constant voltage. To make the use of such a pencil possible, it is necessary to protect it against excess of current and consequent disintegration. This is done by correcting its negative temperature coefficient by the addition of a conductor having a large positive temperature coefficient. Such a conductor is iron when near the point of red heat. The pencil and this additional resistance, termed technically a "ballast resistance" are arranged tandem-fashion, or, as it is called, "in series," so that the current first passes through the ballast resistance and then through the pencil. The object of the ballast resistance is to keep the current as near constant as possible; and this object is attained by the fact that, owing to the peculiar property of hot iron to very largely increase its resistance for even a slight increase of temperature, the e.m.f. absorbed by the ballast resistance becomes large even with a small increase of current, so that a further growth of current is efficiently checked. It is in this way that the working of the Nernst lamp is made stable.

The ballast resistance is made of fine iron wire; and if this were allowed to become nearly red-hot whilst exposed to the air, it would very soon burn out. It is therefore necessary to protect this delicate spiral of wire from the air, and this is done by enclosing it in a sealed glass tube. This tube is filled with hydrogen, since hydrogen has, of all gases which could be used in this case, the greatest heat capacity. It would obviously be a mistake to use an exhausted tube as a protecting envelope for the iron spiral, since through a vacuum very little heat can be transmitted, and it is obviously important to prevent the spiral from getting more than dull red-hot, otherwise it would be destroyed. If, then, a gaseous filling is indispensable for the conveyance of the heat generated in the spiral to the outside envelope, we must use a gas which will not burn the iron. Air is therefore inadmissible. Nitrogen or carbonic acid might be used, but these gases do not convey heat so readily as hydrogen, the lightest of all gases, and whose molecules are the most mobile. Similar resistances are also used as regulating devices in train lighting. Regulating resistances of this kind, but on a much larger scale, are now made for various industrial purposes where it is important to keep a current fairly constant, notwithstanding variations in resistance or e.m.f.