K4 Electrokinetics

Electric current

Discharge by conduction. Electric current

By means of an electric machine, you can charge two insulated bodies to differently high potentials. If you then connect them by a conductor, the electricity flows from the body with the higher potential to the other body as long as their potentials differ (that is, between them acts an electro-motoric force). If you arrange for them to be at different potentials (in spite of the flow of electricity between them), this will continue enduringly.

An analogue to this process: Two water containers at different levels are linked by a pipe; in spite of water flowing from the higher one to the lower one, their different levels are maintained, for example, by a pump which raises the water from the lower container to the higher container. The electric machine corresponds to the pump, which maintains the level difference between the two containers.

This transit of electricity is called an electric current. The electric current, which continuously transports electricity along a conductor and the dielectric polarization of the insulators, which separates electricities into individual molecules (Fig. 449), are processes of the same kind. The difference between them is only quantitative and is linked to the difference between insulators and conductors. In both cases, electricity is transported, but in insulators the transport is finished very soon. In contrast, in conductors, the transport never ends; the state of polarization of the particles does not endure, but renews itself continuously and does not end. Maxwell said about this phenomenon:

"The only difference between electric displacement in a dielectric and electric current in a conductor is that the first has to fight a resistance, which can be compared with the resistance of an elastic body against displacements of its particles, so that the electricity moves immediately back as soon as the electro-motoric force ceases to act, while the second feeds in more electricity and the electricity is enduringly conducted from location to location.

A characteristic of electricity in motion is that it behaves in a certain sense like a fluid: In a condenser (Fig. 466), the plates A and B are, on the one hand, insulated from each other by the dielectric, on the other hand, they are connected one to the other by the wire W. By means of an electro-motoric force (EMF), we transport through the wire W a certain quantity Q of positive electricity from B to A; then there appears on B the same amount of negative electricity. The charges on A and B then exercise together an EMF, which causes through the dielectric an electric transport from A to B. The amount of electricity, which during this process passes through each cross-section of the dielectric in the direction A - B, is then equal to the amount of electricity Q, which simultaneously has been transported through the conductor W in the direction B - A. "In this sense", says Maxwell, "the motion of electricity obeys the same law as that of an incompressible fluid, as a result of which in a closed space as much electricity must enter as is leaving. Hence an electric current always returns to itself."

In this sense, the track of an electric current is called a circuit. While the electricity flows through the conductor - said figuratively: downhill, that is, from a higher potential to a lower one - we must, if we want to maintain in spite of this flowing away the potential difference at its old height, continue to rotate the electric machine, that is, we can maintain the current only by the work which we perform on the machine. We expend the energy of our muscles at the machine and exchange it for current. Hence we must view an electric current as a form of energy, that is, as something which can perform work. Water, which flows through a conduct from a higher water level to a lower one, is a falling mass and performs work by its falling . Exactly the same is the case with electricity which flows to a lower potential. Hence, if we connect an induction machine, which we connect by a conducting wire to a second one, so that electricity can flow through the combs C and D to the rotatable disk, the disk starts to rotate as a result of the attraction, which the fixed coverings B and B' exert on it (Fig. 465).

Hence we can convert mechanical energy into electric energy and, consequently, conduct this energy away through a conductor as electric current - you say: transfer - and eventually reconvert it at its final location into mechanical energy. This process is referred to as electric transfer of energy or, also less correctly, as electric transfer of force. You can produce various motions by suitable apparatus, through which current flows. The electrical bell, the electrical telegraph writer, etc. are mechanical systems, in which the current sets certain movable components into motion. In all of them, the form of energy taken in is the same - electric current; however, the type of work which the reconverted energy performs depends on the final apparatus (bell, telegraph, etc.). A counterpart is offered by our own body. Current flows through a nerve like through a telegraph wire. If the nerve ends in the eye, the current generates a light sensation, in the ear, a sound sensation, in a muscle, a spasm.

If you interrupt the path of the current, for example, by cutting the wire, the current bridges for an instant the cut in the form of a spark and heats up the ends of the wire. However, it does so not only where it forms the spark, but it generates heat all along the wire. This is shown clearly by the air thermometer of Riess 1805-1883 (Fig. 457). A current flows through the platinum wire H inside the glass container; the wire becomes hot and heats up the air around it, which then expands and thereby moves the fluid in the calibrated tube. It was introduced by Braun as hot wire current meter into wireless telegraphy.

Ohm's law

Before continuing the discussion of the work capacity of electric current and its conversion into other forms of energy, we must become familiar with the fundamental law of electric current. For this purpose, we compare again an electric current with streaming water - two charged bodies at different potentials with two water containers at different levels - and the conductor between the two bodies with a tube joining the two containers. First of all, we employ this comparison, in order to explain the concept of current intensity.

The velocity at which the water flows from the container with the higher level through the tube into the container at the lower level, that is, how many litres per second pass through a water meter in the tube (with a given cross-section) depends on the width of the tube as well as on the difference in the heights of the water levels in the containers, that is, the difference in the pressures at the two ends of the tube. The wider the tube and the larger the water level height difference, the faster moves the water, that is, the more litres pass each second through the water meter. It is similar with electric current. The thicker the connecting wire and the larger the difference between the potentials (EMF), the more electricity passes each second through any cross-section of the conductor or also through the electricity counter, installed in the conductor, the counterpart to the water meter. In this sense, one speaks of current intensity. We understand thereby the amount of electricity which passes per second through a cross-section of the conductor.We will assume that we have already measured its value I and that the potential difference is E. Ohm's law, which we have in mind, is called after its discoverer Ohm: If you double, triple,etc., the potential difference, also the current intensity is doubled, tripled, etc. Hence, if the initial potential difference is E and the corresponding current intensity I, the current intensities 2I, 3I, ··· , nI correspond to the potential differences 2E, 3E, ···, nE, or else, the ratio of the potential difference to the current intensity is a constant, denoted by W:

2E/2I = 3E/3I = ··· = nE/nI = E/I = W.

The magnitude of W in a given case depends on the dimensions of the conductor, that is, its length and thickness as well as its chemical make up. The last means: If you replace an iron conductor by another one of the same dimension, but made out of a different material, for example, out of silver, then W changes (for iron, it is several times the value for silver). Its meaning is obtained by writing instead of E/I = W the equation in the form I = E·1/W; but this is only recognized after becoming familiar with the concept of current intensity. We return again to the example of the water conduct. We assess there the strength of the flow by the mass of water, which passes a cross-section in a given time interval, for example, how many litres per minute pass through the cross-section at the end of the pipe. We obtain the same number, if we measure the passing litres of water at any other cross-section, irrespectively of its width, because the tube is filled up all along and its walls are rigid, whence the volume is always the same; as much water leaves the end of the tube as enters its starting section. Hence the same amount of water passes per second through every cross-section, whence you call the flow stationary and we can say: The flow intensity in the water pipe is the amount of water in litres, which pass each second through a cross-section of the pipe. The same argument takes us to the current intensity of electric current. We know already the quantity and the unit of electricity: The quantity of electricity is the counterpart to the quantity of water, the unit of electricity to the litre and the cross-section of the conductor to that of the water pipe. Hence we define current intensity as the quantity of electricity, expressed in units of electricity, which passes per second through a cross-section of the conductor. We thereby have implied what experience indeed teaches, that the current intensity at all cross-sections of the same conductor is equally large, so that electricity in a conductor in this respect behaves like an incompressible fluid in a rigid pipe.

This definition of current intensity yields together with the unit of electricity a measure of current intensity. We define that current as the unit of current intensity, which during one second transports one unit of electricity through the cross-section of a conductor. This current is so small that also the weakest, practical current intensities, for example, in a telegraph cable, are millions times this unit. Hence, in practice, you employ 3·10⁸ as large a current intensity as the unit.

Thus, the quantity I in the equation I = E·1/W denotes a certain number of units of electricity per second. Experience shows: The current intensity I does not only depend on E; in other words: Constancy of E does not guarantee constancy of I. The current intensity I is influenced to a great extent by the body employed as a conductor: Its dimensions (length and thickness), its chemical constitution and certain physical properties, for example, its temperature, also contribute. In order to understand the influence of its dimensions, consider a straight, cylindrical wire. Experience tells us: If we change its length, that is, if we use a wire 2-, 3-, ···, l times as long as the initial length, the current has 1/2, 1/3, ···,1/l its initial intensity. Moreover: If we change the cross-section of the conductor and use a wire with 2-, 3-, ···, q times the initial cross-section, the current intensity is 2-, 3-, ···, q times as large as the initial intensity. If we denote the initial current intensity, which passes through the conductor when it has a cross-section of 1 mm² by I'₁, the current through wires with cross-sections of 2, 3, ···, q mm² is 2I'₁, 3I'₁, ···, qI'₁. (In this context, it is immaterial whether we employ, for example, a wire with a 5 mm² cross-section (Fig. 468) or 5 wires of 1 mm² cross-section, twisted into a single wire (Fig. 469).) Hence, if we denote the current intensity in a 1 m long wire with a 1 mm² cross-section by I_1,1, and that in a l m long with cross-section q mm² by I_l,q, experience tells that I_l,q, = I_1,1,·q/l.

Accordingly, the current intensity remains unchanged, if the length and thickness of the wire are changed simultaneously so that lengthening weakens the current as the cross-section strengthens it.. For example, if you make a conductor with a wire length of 1 m and cross-section of 1 mm², and then one of length 5 m and 5 mm², the current intensity in both will be the same. Introducing the subscripts l and q into the equation of Ohm's law, we will write

E/I_l,q = W_l,q or I_l,q = E·1/W_l,q.

For example, in the case of a wire of length 1 m and cross-section 1 mm²:

E/I_1,1 = s or I_1,1 = E·1/s,

that is, we set W_1,1 = s . For the following, we will assume that the conductor is 1 m long and its cross-section 1 mm².

Resistance of a conductor

Experience tells: Even if the potential difference E and the dimensions of a circuit remain the same, the current intensity has a different value according to the substance out of which it is made. It is larger (more units of electricity per second pass the meter) if the wire is made out of silver than if it is made our of iron; it is smaller, if the wire if made out of steel than if it is made out of iron. Hence we say: Silver conducts better than iron, iron conducts better than steel and speak of the conductivities of silver, iron, steel. According to Ohm's law: I_1,1 = E·1/s, that is, the current intensity at equal potential difference is the larger (smaller) the larger (smaller) is 1/s. Hence the number of electric units passing each second through a meter depends for a constant potential difference E and wire dimension, that is, leaving everything unchanged, only on the magnitude of 1/s. This fraction measures the conductivity. An increase in s reduces the conductivity, whence s represents a resistance to the flow of electricity.

However note: s is the resistance of a wire of length 1 m and cross-section 1 mm². The magnitude of the resistance of a 1 m long wire with a cross-section of 1 mm² is given by Ohm's law. We have

I_1,1 = E·1/s and I_l,q = E·1/W_l,q.

Hence the quantities 1/W_l,q and W_l,q are for a l m long circuit with a q mm² cross-section what 1/s and s are for a 1 meter long wire with a 1 mm² cross-section. However, I_1,1/I_l,q = (1/s)/(1/W_l,q) = W_l,q/s, and, on the other hand (cf. above), I_1,1/I_l,q = l/q, whence W_l,q = s · l/q.

This is the reason why you call W_l,q the resistance of an l m long wire with a q mm² cross-section; it depends on the magnitude of s - the resistance of a 1 m long wire with a 1 mm² cross-section. The quantities l and q have only an arithmetic significance, s is characteristic for the material of the circuit. Ohm's law divulges with the electric conductivity of substances a new link between electricity and matter; it tells us of a property of matter, hitherto unknown to us, and of its measure. Ordered according to their conductivity, you have: Silver, copper, gold, aluminium, magnesium, zinc, cadmium, nickel, iron, platinum, lead, (solid) mercury, steel.

In order to determine the conductivity of a metal, you measure for a piece of wire its resistance, length and cross-section and compute the resistance for a wire of length 1m and 1 mm² cross-section. (The relation s = W_l,q · q/l yields the magnitude of s and.1/s .) However, in order to be able to measure the resistance of a circuit, we must first define a unit of resistance, which is what the cm is for length measurements, and we must know methods for a comparison of an unknown resistance with that unit.

The magnitude of such a unit resistance is indicated by Ohm's law: The unit of potential difference has already been attended to. If we now set the potential difference between the ends of a conductor equal to 1 and select it so that the current intensity 1 passes through it, then the equation for the conductor is E/I = W with E = 1 and I = 1, that is, we denote the resistance of this conductor by 1. In other words: The resistance 1 belongs to that conductor with potential difference 1, through which flows a current of unit intensity or:

Unit resistance = unit potential difference/unit current intensity,

The potential difference, current intensity and resistance have a decisive role wherever electric currents occur, that is, also in trade. This is the reason why these units have been fixed in Germany by law in 1898. The technical units of potential difference, current intensity and resistance are the Volt, the Ampere and the Ohm, respectively.

The Volt is 1/300 of the earlier defined unit of electrostatic potential, the Ampere the current by which 3000 millions (1 Coulomb) = 3·10⁹ earlier defined units of electricity pass a cross-section during each second, that is, it is 3000 millions as strong as the earlier defined unit of current intensity. Hence

1 Volt = 1/300 electro-statically measured unit of potential,
1 Ampere = 3·10⁹ electro-statically measure unit of current intensity,
1 Ohm = resistance of a wire, through which passes 1 Ampere while 1 Volt acts between its ends.

A cylindrical mercury column of length 106.3 cm and 1 mm² cross-section has the resistance of 1 Ohm at - this is important! - 0°C. (The comparison of this resistance measure with other resistances is given later on.)

The statement 1 kilometre of iron wire with a diameter of 4 mm² has 10½ Ohm means: This wire has the same resistance as a mercury column of 10½ *106.3 length and 1 mm² cross-section at 0ºC. You must state the temperature (0ºC), because the conductivity of all materials depends on their temperature. A mercury column of 1 m length and cross-section 1 mm² has at 0ºC only 0.94 Ohm; it would have to be 1063 mm long, in order to have at 0º 1 Ohm, but it has 1 Ohm at about 83ºC. Every conductor has a specific resistance r. This is the resistance of a cube with 1 cm long edges, whence, the resistance of a wire of length 1 m and cross-section 1 mm² is 10⁴·r (abbreviated: s); the reciprocal value of r is called conductivity (k = 1/r). The table presents the values of 10⁴·r₁₈, that is, at the temperature of 18ºC.

If a conductor has at the temperatures t and t' resistances R and R', the temperature coefficient of the resistance is a in the equation R' = R[1 + a(t' - t)]. If you measure R' and R at the temperatures 100º and 0º, you find a = (1/100)·(r₁₀₀ - r₀)/r₀. The table presents a·1000.

Super-conductivity Note: All materials change their conductivity with the temperature: Iron and nickel very strongly, certain alloys like constantan (60 Cu, 40 Ni) and manganin (84 Cu, 4 Ni, 12 Mn) very little. In general, the purer a metal, the smaller is its specific resistance and the larger its temperature coefficient. Annealing to a definite temperature lowers the first to a minimum and raises the second to a maximum. Impurities cause excess resistance, which depends little on the temperature; as the temperature drops, the resistance of an annealed, pure metal drops quickly and becomes so small that the impurities dominate; the conductivity at very low temperatures is a measure of the purity of a metal.

How behaves the resistance near the absolute zero? Onnes 1911 has answered this question experimentally with the aid of liquid helium and thereby discovered super- conductivity - apparently a state of infinite conductivity. The resistance of a thread of mercury, which at 0º is 172.7 Ohm, could not be measured at the helium temperature due to its smallness. Just below 4.2º abs, the resistance jumped from a still measurable value to one, which could be set equal to zero, as it became impossible to measure it. The jumping point temperature of tin lies at 3.78º abs, that of lead too high to be detectable in liquid helium (it lies probably at 6º abs). Platinum has throughout the temperature range below 4.3º abs constant resistance, so do gold, cadmium and copper (probably the residual resistance of impurities), manganin and constantan have still a sufficient temperature coefficient to be of use in resistance thermometers for very low temperatures. It was possible to send through a super-conducting mercury wire a current of 1200 amperes per mm², through a lead wire 560 amperes without that Joule heat developed . (Crommelin)

Electrolytic and metallic conduction

For certain substances, the conductivity rises or falls with the temperature. If you subdivide them into two groups, you find in the first group those, which electric current decomposes, predominantly acids, bases and salts dissolved in water. They are called electrolytes. The second group comprises metallic conducting substances which are not decomposed by current. Experience shows: At rising temperatures, the conductivity of metallic conducting substances falls, of electrolytes rises. Note: Ohm's law is also valid for eletrolytes.

Electrolytes also include certain substances which current does no as definitely change as the acids, bases and salts in watery solutions; this applies to glass and porcelain. They insulate well at ordinary and conduct well at high temperatures. Above all, this applies to the oxides of rare earths. At ordinary temperatures, they are insulators, in glowing heat, good conductors, so good that they are used in certain cases where only a conductor can be used, for example, in the form of sticks as replacement of the threads of incandescent lamps (Nernst). Especially strange is the behaviour of the metallized* carbon filament (incandescent lamp): Initially, its conductivity rises (as that of the ordinary filament) with rising temperature to a certain temperature after which it drops quickly.

* It has this name because it behaves like a metal filament, it is a thread of a special kind of carbon (General. Electric. Company, Schenectady)

Apart from heat, other physical processes affect conductivity; for example, a transition to another aggregate state frequently changes conductivity abruptly. Thus, all substances in a gaseous and vapour state conduct very badly, also the gases of metals, relatively best the vapours of mercury and tin.

In the field of a magnet, the conductivity of iron, nickel, cobalt rises or falls depending on their position with respect to the lines of force. - Selenium behaves very strangely; its all over very low conductivity can rise to ten- to twenty-fold values under strong lighting. The behaviour of dry, coarse, loosely accumulated metal powder (granules, filings) is similar (Branly 1890): Between two metal electrodes E₁ and E₂ (in a glass tube), it has normally almost infinite resistance, but if it is irradiated by electric waves, its resistance drops to several thousand (at times, a few hundred) Ohm and remains like this also after irradiation. In this state, it closes the circuit. If the tube is shaken, the initial state is reinstalled. Telegraphy has employed this gadget - coherer ( Lodge) - for many years as wave indicator (detector) (Fig. 470). Most surprisingly changes the conductivity of a substance, dissolved in water. Distilled water is an almost perfect insulator (a column of 1 mm height has as much resistance as 40·10⁶ km of copper wire with the same diameter, and salts are similar and by themselves non-conductors. However, if a salt, for example chlorine calcium, is dissolved in water - that is, the non-conducting solid salt in the non-conducting distilled water - there arises a solution which conducts current. In general, the conductivity depends on the concentration of the solution.

Conductivity depending on current direction (electric valves)

Conductivity can depend on the direction of the current, that is, the same body can let the current pass and stop the current . Such a system is called an electric valve; depending on the given conditions, it is open or shut, that is, electricity passes or not (strictly speaking: as well as not). For example, if you make a solution of boric potassium part of a circuit (Fig. 490) - A out of aluminium and B out of a lead sheet - and link to the aluminium the negative pole of a battery, the circuit conducts well. If you connect the positive pole to the aluminium, it does not work at all (electro-chemical processes cover the aluminium with a skin of gas which isolates it completely from the fluid). Hence the circuit is a conductor only in one direction, an insulator in the other direction. The circuit of Fig. 471 acts similarly: A wire K, glowing in a vacuum, sends out electrons and is faced by an ordinary electrode A (this is what you call the current loaders A and B in Fig. 490 and the corresponding ones in Fig. 471). If you connect to the heated electrode K the negative pole of a battery, the device is a conductor, but with the +pole it is a complete insulator. (The reason: The electrons are negative elementary particles and emit only from the heated electrode. If you connect A to the positive pole, the electric field inside the tube acts in the direction A to K, that is, a force towards A acts on the negatively charged particles, whence they move from K up to A and current flows through the tube. In contrast, if A is made into the negative pole, the field inside the tube is directed from K to A. Hence there acts on the negatively charged particles a force from A to K, the particles are driven back to the incandescent filament and cannot reach A, so that the circuit remains open.) Hence a high vacuum tube with an incandescent electrode is an electric valve, it is a conductor in the one and an insulator in the other direction.

We will mention only among the numerous kinds of electric valves the one which Braun introduced into spark telegraphy. It is a combination of a small plate made out of lead glance with a small, pointed graphite rod touching it: The resistance at the point of contact is very much larger for the passage of current in one direction than in the other direction. - Electric valves serve mainly practical purposes, especially the transformation of alternating current into direct current; moreover, they are important in wireless telegraphy as detectors of electric waves.

The electrons which an incandescent filament emits were already previously present in it. Movable between the atoms of the metal, they move also under the influence of an electric field, which is generated along the filament by an imposed potential difference. It is suspected that the current in metals consists altogether of motion of electrons. In a high vacuum tube with a heating cathode, the electrons are obviously the carriers of the current, its valve action is thereby explained.

The uniformity of the electrons - all of them are negative - allows us now to make the valve steadily controllable by a simple trick, to open it steadily more or less and close it; you place between the incandescent cathode K and the anode A an electrode and connect to this electrode G - the lattice (wires stretched over a glass frame) - a potential. If you make it positive (negative) towards K, it supports (weakens) the current in the circuit, the anode current. The characteristic voltage in the electron flow between K and A causes then already at very small changes of the lattice potential a very large change of the current intensity. Even minimal vibrations of the lattice potential cause therefore comparatively strong oscillations of the anode current (and thereby, for example, amplification of induction action ). Moreover, the lack of inertia of the electrons causes an immediate reaction of the electrons to very small changes of potential, that is, an immediate change of the current intensity. For example, on this rests the immense amplification of the current, caused by the electron valve, in its in the anode circuit lying telephone. In wireless telegraphy and telephony, the high vacuum tube with an incandescent cathode and the lattice electrode as amplifier tube (electron relays)are most important. Radio owes it its existence to it. (Technical employment of the amplification principle for the generation of electric oscillation is discussed later on ).

In order to supply large regions with electric energy, power stations transform alternating current of low voltage (because it is less dangerous) into high tension, conduct it through thin (and therefore cheap) cables to the consumer and transform it there back to low voltage. (You cannot transform direct current in this manner.) However, certain tasks can only be undertaken with direct current (operation of accumulators, electrolytic baths, mercury lamps). Hence you must convert alternating current at the user into direct current. You can pass it for this purpose through an alternating current motor and let the motor operate a direct current generator. However, this is not economical; there exists a simpler process. If alternating current flows through an electric valve, the valve only lets pass that half of the period, for which it is a conductor, and suppresses the other half, that is, it converts the wave formed alternating current into a pulsating direct current (Fig, 473 (1)). If you pass the current through two valves v₁ and v₂ (Fig. 473 (2), you can make use of its two directions; there arises in the cable (CD) a current of the form Fig. 473 (3) (the weakly drawn curve). The throttle coil r prevents the current from stopping, whence there arises in the cable the direct (strongly drawn) current (3), which is sufficient for most purposes.

An alternating current rectifier (Fig. 474 (4)) is a combination of two valves (Cooper Hewitt). The valve action occurs at the border between the hot metal and the cold (relatively cold!) surrounding space. Two electrodes, used as anodes, made out of iron (or graphite) and one, used as cathode and made out of mercury, in a high vacuum vessel (glass) form the two valves. The special ignition component z heats the mercury and causes an escape of electrons and initiates current to flow from the anodes to the cathode. (As a consequence of the very high temperature, the mercury evaporates violently, it condenses on the very large surface of the glass vessel and returns to the cathode.) The throttle coil in the direct current circuit (Weintraub) is indispensable; if the current drops (from one anode to the cathode) only for a very small fraction of a second below 2.5 Amp, the mercury vapour arc vanishes and does not restart on its own. The throttle prevents the sinking of the current intensity. The Hg-rectifier is one of the most important tools of the alternating current industry.

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