The electronic conductivity of metals was first experimentally proven by the German physicist E. Rikke in 1901. Through three polished cylinders tightly pressed against each other - copper, aluminum and again copper - an electric current was passed for a long time (during a year). The total charge that passed during this time was equal to 3.5·10 6 C. Since the masses of copper and aluminum atoms differ significantly from each other, the masses of the cylinders would have to change noticeably if the charge carriers were ions.

The results of the experiments showed that the mass of each of the cylinders remained unchanged. In the contact surfaces, only insignificant traces of mutual penetration of metals were found, which did not exceed the results of ordinary diffusion of atoms in solids. Consequently, free charge carriers in metals are not ions, but particles that are the same in both copper and aluminum. Only electrons could be such particles.

Direct and convincing proof of the validity of this assumption was obtained in the experiments set up in 1913 by L. I. Mandelstam and N. D. Papaleksi and in 1916 by T. Stuart and R. Tolman.

A wire is wound on the coil, the ends of which are soldered to two metal disks isolated from each other (Fig. 1). A galvanometer is attached to the ends of the disks using sliding contacts.

The coil is brought into rapid rotation, and then abruptly stopped. After a sharp stop of the coil, free charged particles will move along the conductor by inertia for some time, and, consequently, an electric current will appear in the coil. The current will exist for a short time, because due to the resistance of the conductor, the charged particles are slowed down and the ordered movement of the particles stops.

The direction of the current indicates that it is created by the movement of negatively charged particles. The charge transferred in this case is proportional to the ratio of the charge of the particles that create the current to their mass, i.e. . Therefore, by measuring the charge passing through the galvanometer for the entire time of the existence of the current in the circuit, it was possible to determine the ratio. It turned out to be equal to 1.8·10 11 C/kg. This value coincides with the ratio of the electron charge to its mass found earlier from other experiments.

Thus, an electric current in metals is created by the movement of negatively charged electron particles. According to the classical electronic theory of the conductivity of metals (P. Drude, 1900, H. Lorenz, 1904), a metal conductor can be considered as a physical system of a combination of two subsystems:

1. free electrons with a concentration of ~ 10 28 m -3 and
2. positively charged ions vibrating around the equilibrium position.

The appearance of free electrons in a crystal can be explained as follows.

When atoms combine into a metal crystal, the outer electrons most weakly bound to the atomic nucleus are detached from the atoms (Fig. 2). Therefore, positive ions are located at the nodes of the crystal lattice of the metal, and electrons that are not connected with the nuclei of their atoms move in the space between them. These electrons are called free or conduction electrons. They perform a chaotic movement, similar to the movement of gas molecules. Therefore, the totality of free electrons in metals is called electron gas.

If an external electric field is applied to the conductor, then a directed movement is superimposed on the random chaotic movement of free electrons under the action of the forces of the electric field, which generates an electric current. The speed of movement of the electrons themselves in the conductor is a few fractions of a millimeter per second, however, the electric field arising in the conductor propagates along the entire length of the conductor at a speed close to the speed of light in vacuum (3 10 8 m / s).

Since the electric current in metals is formed by free electrons, the conductivity of metal conductors is called electronic conductivity.

Electrons under the influence of a constant force acting from the electric field acquire a certain speed of ordered movement (it is called drift). This speed does not further increase with time, since when colliding with ions of the crystal lattice, electrons transfer the kinetic energy acquired in the electric field to the crystal lattice. In the first approximation, we can assume that over the mean free path (this is the distance that an electron travels between two successive collisions with ions), the electron moves with acceleration and its drift velocity increases linearly with time

At the moment of collision, the electron transfers kinetic energy to the crystal lattice. Then it accelerates again, and the process repeats. As a result, the average speed of the ordered movement of electrons is proportional to the electric field strength in the conductor and, consequently, the potential difference at the ends of the conductor, since , where l is the length of the conductor.

It is known that the current strength in the conductor is proportional to the speed of the ordered movement of particles

and therefore, according to the previous one, the current strength is proportional to the potential difference at the ends of the conductor: I ~ U. This is the qualitative explanation of Ohm's law based on the classical electronic theory of the conductivity of metals.

However, there are difficulties with this theory. It followed from the theory that the resistivity should be proportional to the square root of the temperature (), meanwhile, according to experience, ~ T. In addition, the heat capacity of metals, according to this theory, should be much greater than the heat capacity of monatomic crystals. In reality, the heat capacity of metals differs little from the heat capacity of non-metallic crystals. These difficulties were overcome only in quantum theory.

In 1911, the Dutch physicist G. Kamerling-Onnes, studying the change in the electrical resistance of mercury at low temperatures, found that at a temperature of about 4 K (i.e. at -269 ° C), the resistivity abruptly decreases (Fig. 3) almost down to zero. This phenomenon of turning electrical resistance to zero G. Kamerling-Onnes called superconductivity.

Later it was found that more than 25 chemical elements - metals at very low temperatures become superconductors. Each of them has its own critical transition temperature to a state with zero resistance. Its lowest value for tungsten is 0.012K, the highest for niobium is 9K.

Superconductivity is observed not only in pure metals, but also in many chemical compounds and alloys. In this case, the elements themselves, which are part of the superconducting compound, may not be superconductors. For example, NiBi, Au 2 Bi, PdTe, PtSb other.

Substances in the superconducting state have unusual properties:

1. electric current in a superconductor can exist for a long time without a current source;
2. inside a substance in a superconducting state, it is impossible to create a magnetic field:
3. the magnetic field destroys the state of superconductivity. Superconductivity is a phenomenon explained from the point of view of quantum theory. Its rather complicated description is beyond the scope of a school physics course.

Until recently, the widespread use of superconductivity was hindered by the difficulties associated with the need for cooling to ultralow temperatures, for which liquid helium was used. Nevertheless, despite the complexity of the equipment, the scarcity and high cost of helium, since the 60s of the XX century, superconducting magnets have been created without thermal losses in their windings, which made it practically possible to obtain strong magnetic fields in relatively large volumes. It is precisely such magnets that are required to create facilities for controlled thermonuclear fusion with magnetic plasma confinement, for powerful charged particle accelerators. Superconductors are used in various measuring devices, primarily in devices for measuring very weak magnetic fields with the highest accuracy.

At present, 10 - 15% of energy is spent on overcoming the resistance of wires in power lines. Superconducting lines, or at least inputs to large cities, will bring enormous savings. Another field of application of superconductivity is transport.

On the basis of superconducting films, a number of high-speed logical and memory elements for computing devices have been created. In space research, it is promising to use superconducting solenoids for radiation protection of cosmonauts, docking of ships, their deceleration and orientation, and for plasma rocket engines.

Currently, ceramic materials have been created that have superconductivity at a higher temperature - over 100K, that is, at a temperature above the boiling point of nitrogen. The ability to cool superconductors with liquid nitrogen, which has an order of magnitude higher heat of vaporization, greatly simplifies and reduces the cost of all cryogenic equipment, and promises a huge economic effect.

The substance (metal) from which the conductor is made affects the passage of electric current through it and is characterized using such a concept as electrical resistance. Electrical resistance depends on the size of the conductor, its material, temperature:

• - the longer the wire, the more often moving free electrons (current carriers) will collide on their way with atoms and molecules of matter - the resistance of the conductor increases;
• - the larger the cross section of the conductor, the more free electrons it becomes, the number of collisions decreases - the electrical resistance of the conductor decreases.

Conclusion: the longer the conductor and the smaller its cross section, the greater its resistance and vice versa - the shorter and thicker the wire, the lower its resistance ,and conductivity (the ability to pass electric current) is better.

Simplistically, the dependence of the conductor resistance on temperature can be represented as follows: electrons moving along the conductor collide with the atoms and molecules of the conductor itself and transfer their energy to them. As a result, the conductor heats up, the thermal, random movement of atoms and molecules increases. This further slows down the main flow of electrons along the conductor. This explains the increase in the resistance of the conductor to the passage of electric current during heating.

When heating or cooling conductors - metals, their resistance increases or decreases accordingly, at the rate of 0.4% for every 1 degree. This property of metals is used in the manufacture of temperature sensors.

Semiconductors and electrolytes have the opposite property than conductors - with increasing heating temperature, their resistance decreases.

The unit of measurement of electrical resistance is 1 ohm (in honor of the scientist G. Ohm). A resistance of 1 ohm is equal to a section of an electrical circuit through which a current of 1 ampere passes when a voltage of 1 volt drops across it,

Sometimes the reciprocal of the electrical resistance is used. This is electrical conductivity, denoted by the letter g or G - Siemens (in honor of the scientist E. Siemens).

Electrical conductivity is the ability of a substance to pass an electric current through itself. The greater the resistance R of the conductor, the lower its conductivity G and vice versa. 1 ohm = 1 sim

Derived units:

1Sim = 1000mSim,
1Sim = 1000000µSim.

When it is necessary to calculate the total resistance of series-connected conductors, it is more convenient to operate with Ohms. if the total resistance of parallel-connected conductors is calculated, it is more convenient to count in Sims, and then convert to Ohms.

Metals have the highest conductivity: silver, copper, aluminum, etc., as well as solutions of salts, acids, etc.
The lowest conductivity (highest resistance) for insulators: mica, glass, asbestos, ceramics, etc...

In order to make it more convenient to carry out calculations of the electrical resistance of conductors made of various metals, the concept of the specific resistance of a conductor was introduced.
The resistance of a conductor 1 meter long, 1 mm in cross section. sq. at a temperature of + 20 degrees, this will be the resistivity of the conductor p.

The specific resistances of conductors of some metals are given in the table.

From the table it can be seen: from metals, silver has the best conductivity. But it is very expensive and is used as conductors in exceptional cases.

Copper and aluminum are the most common materials in electrical engineering. Wires and cables, busbars, etc. are made of them. Tungsten, constantan, manganin are used in various heating devices, in the manufacture of wire resistors.

Using wires and cables in electrical installations, it is necessary to take into account their cross-section in order to prevent their heating and, as a rule, damage to the insulation, as well as to reduce the voltage drop and power loss during the transmission of electrical energy from the source to the consumer.

Below is a table of permissible current values ​​in the conductor, depending on its diameter (section in mm2), as well as the resistance of 1 meter of wire made of different materials.


Examples of calculation of some electrical circuits can be found here.

We assume that J diff, J conv, J term are equal to zero and J = J migr. The movement of ions in conductors of the second kind and electrons in conductors of the first kind due to the difference in electrical potentials determines their ability to pass electric current, i.e., their electrical conductivity(electrical conductivity). To quantify the ability of conductors of the first and second kind to pass electric current, two measures of electrical conductivity are used. One of them - electrical conductivityκ- is the reciprocal of the resistivity:

Resistivity is determined from the formula

where R- total resistance of the conductor, Ohm; l is the distance between two parallel planes between which the resistance is determined, m; S - cross-sectional area of ​​the conductor, m 2.

Hence

and electrical conductivity is defined as the reciprocal of the resistance of one cubic meter of a conductor with a cube edge length of one meter. Electrical conductivity unit: Sm/m. On the other hand, according to Ohm's law

where E- potential difference between given parallel planes; I - current.

Substituting this expression into the equation that determines the electrical conductivity, we get:

For S = 1 and E/l = 1 we have κ = 1. Thus, the electrical conductivity is numerically equal to the current passing through the conductor section with a surface of one square meter, with a potential gradient equal to one volt per meter.

Specific electrical conductivity characterizes the number of charge carriers per unit volume. Consequently, the electrical conductivity will depend on the concentration of the solution, and for individual substances, on their density.

The second measure of electrical conductivity is equivalentλ e (or molarλ m) electrical conductivity, equal to the product of specific electrical conductivity by the number of cubic meters, which contain one equivalent or one mole of a substance:

λ e = κφ e; λ m = κφ m

Since φ is expressed in m 3 / equiv or m 3 / mol, then the unit of λ will be Cm 2 / equiv or Cm 2 / mol.

For solutions φ = 1/С, where With- concentration, expressed in mol/m 3 . Then

λ e = κ/zC and λ m = κ/С

If With expressed in kmol / m 3, then φ e \u003d 1 / (zC ∙ 10 3); φ m \u003d 1 / (С ∙ 10 3) and

λ e \u003d κ / (zC ∙ 10 3) and λ m \u003d κ / (C ∙ 10 3)

When determining the molar conductivity of an individual substance (solid or liquid) φ m \u003d V M, but V m \u003d M / d (where V m is the molar volume; M is the molecular weight; d- density), next-

to a t e l n o

λ m = κV m = κM/d

Thus, the equivalent (or molar) electrical conductivity is the conductivity of a conductor located between two parallel planes located at a distance of one meter from each other and such an area that one equivalent (or one mole) of a substance (in the form of a solution or individual salt).

This measure of conductivity characterizes the conductivity with the same amount of substance (mole or equivalent), but contained in different volumes and, thus, reflects the influence of interaction forces between ions as a function of interionic distances.

ELECTRONIC CONDUCTIVITY

Metals characterized by a low energy of electron transition from the valence band to the conduction band already at normal temperature have a sufficient number of electrons in the conduction band to ensure high electrical conductivity. The conductivity of metals decreases with increasing temperature. This is due to the fact that with increasing temperature in metals, the effect of an increase in the vibrational energy of the ions of the crystal lattice, which resists the directed motion of electrons, prevails over the effect of an increase in the number of charge carriers in the conduction band. The resistance of chemically pure metals increases with increasing temperature, increasing by about 4 ∙ 10 -3 R 0 with an increase in temperature per degree (R 0 - resistance at 0 ° C). For most chemically pure metals, when heated, there is a linear relationship between resistance and temperature.

R = R0 (1 + αt)

where α is the temperature coefficient of resistance.

The temperature coefficients of alloys can vary over a wide range, for example, for brass α = 1.5∙10 -3, and for constantan α = 4∙10 -6.

The specific conductivity of metals and alloys lies within 10 6 - 7∙10 7 S/m. The electrical conductivity of a metal depends on the number and charge of the electrons involved in the current transfer and the average travel time between collisions. The same parameters for a given electric field strength determine the speed of the electron. Therefore, the current density in the metal can be expressed by the equation

where is the average speed of the ordered movement of charges; P is the number of electrons in the conduction band per unit volume.

Semiconductors in their conductivity occupy an intermediate position between metals and insulators. Pure semiconductor materials such as germanium and silicon are intrinsically conductive.

Rice. 5.1. Scheme of the appearance of a pair of electron conduction (1) - hole (2).

Intrinsic conductivity is due to the fact that during thermal excitation of electrons, they pass from the valence band to the conduction band. These electrons, under the action of a potential difference, move in a certain direction and provide electronic conductivity semiconductors. When an electron passes into the conduction band, a vacant place remains in the valence band - a “hole”, equivalent to the presence of a single positive charge. A hole can also move under the influence of an electric field as a result of an electron in the valence band jumping to its place, but in the direction opposite to the movement of electrons in the conduction band, providing hole conductivity semiconductor. The process of hole formation is shown in fig. 5.1.

Thus, in a semiconductor with its own conductivity, there are two types of charge carriers - electrons and holes, which provide electronic and hole conductivity of the semiconductor.

In an intrinsic semiconductor, the number of electrons in the conduction band is equal to the number of holes in the valence band. At a given temperature, there is a dynamic equilibrium between electrons and holes in a semiconductor, i.e., the rate of their formation is equal to the rate of recombination. The recombination of an electron in the conduction band with a hole in the valence band leads to the "formation" of an electron in the valence band.

The specific conductivity of a semiconductor depends on the concentration of charge carriers, i.e., on their number per unit volume. We denote the concentration of electrons n i , and the concentration of holes p i . In a semiconductor with intrinsic conductivity, n i = p i (such semiconductors are briefly called i-type semiconductors). The concentration of charge carriers, for example, in pure germanium, is equal to n i \u003d p i ≈10 19 m -3, in silicon - about 10 16 m -3 and is 10 -7 - 10 -10% with respect to the number of atoms N.

Under the action of an electric field in a semiconductor, a directed movement of electrons and holes occurs. The conduction current density is the sum of the electron i e and hole i p current densities: i = i e + i p , which, despite the equality of carrier concentrations, are not equal in magnitude, since the speeds of motion (mobility) of electrons and holes are different. The electron current density is:

The average speed of electrons is proportional to the intensity E" electric field:

Proportionality factor w e 0 characterizes the speed of the electron at a unit electric field strength and is called the absolute speed of movement. At room temperature in pure germanium w e 0 \u003d 0.36 m 2 / (V s).

From the last two equations we get:

Repeating similar reasoning for hole conductivity, we can write:

Then for the total current density:

Comparing the expression for i with Ohm's law i = κ E", at S = 1 m 2 we get:

As indicated above, for a semiconductor with intrinsic conductivity n i \u003d p i, therefore

w p 0 is always lower w e 0 , for example in germany w p 0 \u003d 0, 18 m 2 / (V ∙ s), and w e 0 \u003d 0.36 m 2 / (V s).

Thus, the electrical conductivity of a semiconductor depends on the concentration of carriers and their absolute velocities and is additively composed of two terms:

κ i = κ e + κ p

Ohm's law for semiconductors is satisfied only if the carrier concentration n i does not depend on the field strength. At high field strengths, which are called critical (for germanium E cr ' = 9∙10 4 V / m, for silicon E cr ' = 2.5 ∙ 10 4 V / m), Ohm's law is violated, which is associated with a change in the electron energy in the atom and a decrease in the energy of transfer to the conduction band, as well as with the possibility of ionization of lattice atoms. Both effects cause an increase in the concentration of charge carriers.

Electrical conductivity at high field strengths is expressed by the empirical law of Poole:

ln κ = ln κ 0 + α (E’ – E cr ’)

where κ 0 - conductivity at E ' = E cr ' .

With an increase in temperature in a semiconductor, an intense generation of charge carriers occurs, and their concentration increases faster than the absolute velocity of electrons decreases due to thermal motion. Therefore, unlike

from metals, the electrical conductivity of semiconductors increases with increasing temperature. In the first approximation, for a small temperature range, the dependence of the semiconductor conductivity on temperature can be expressed by the equation

where k- Boltzmann's constant; BUT- activation energy (the energy required to transfer an electron to the conduction band).

Near absolute zero, all semiconductors are good insulators. With an increase in temperature per degree, their conductivity increases by an average of 3 - 7%.

When impurities are introduced into a pure semiconductor, the intrinsic electrical conductivity is added to impurity electrical conductivity. If, for example, elements of group V of the periodic system (P, As, Sb) are introduced into germanium, then the latter form a lattice with germanium with the participation of four electrons, and the fifth electron, due to the low ionization energy of impurity atoms (about 1.6∙10 –21), passes from the impurity atom to the conduction band. In such a semiconductor, electronic conductivity will predominate (a semiconductor is called n-type electronic semiconductor]. If impurity atoms have a greater electron affinity than germanium, for example, group III elements (In, Ga, B, Al), then they take electrons from germanium atoms and holes are formed in the valence band. In such semiconductors, hole conductivity predominates (semiconductor p-type]. Impurity atoms providing electronic conductivity are donors electrons, and hole - acceptors).

Impurity semiconductors have a higher electrical conductivity than intrinsic semiconductors if the concentration of atoms of the donor N D or acceptor N A impurity exceeds the concentration of intrinsic charge carriers. For large values ​​of N D and N A, the concentration of intrinsic carriers can be neglected. Charge carriers, the concentration of which prevails in a semiconductor, are called basic. For example, in n-type germanium, n n ≈ 10 22 m–3, while n i ≈ 10 19 m~ 3, i.e., the concentration of main carriers is 10 3 times higher than the concentration of intrinsic carriers.

For impurity semiconductors, the relations are valid:

n n p n = n i p i = n i 2 = p i 2

n p p p = n i p i = n i 2 = p i 2

The first of these equations is written for an n-type semiconductor, and the second for a p-type semiconductor. It follows from these relations that a very small amount of impurity (about 10–4 0 /о) significantly increases the concentration of charge carriers, as a result of which the electrical conductivity increases.

If we neglect the concentration of intrinsic carriers and consider N D ≈n n for an n-type semiconductor and N A ≈ p p for a p-type semiconductor, then the electrical conductivity of the impurity semiconductor can be expressed by the equations:

When an electric field is applied in n-type semiconductors, charge transfer is carried out by electrons, and in p-type semiconductors - by holes.

Under external influences, for example, during irradiation, the concentration of charge carriers changes and can be different in different parts of the semiconductor. In this case, as in solutions, diffusion processes take place in the semiconductor. Regularities of Diffusion processes obey Fick's equations. The diffusion coefficients of charge carriers are much higher than those of ions in solution. For example, for germanium, the diffusion coefficient of electrons is 98 10 -4 m 2 / s, holes - 47 10 -4 m 2 / s. Typical semiconductors, in addition to germanium and silicon, at room temperature are a number of oxides, sulfides, selenides, telurides, etc. (for example, CdSe, GaP, ZnO, CdS, SnO 2 , In 2 O 3 , InSb).

IONIC CONDUCTIVITY

Ionic conductivity is possessed by gases, certain solid compounds (ionic crystals and glasses), molten individual salts, and solutions of compounds in water, non-aqueous solvents, and melts. The values ​​of the specific conductivity of conductors of the second kind of different classes fluctuate over a very wide range:

Substance	c∙10 3 , S/m	Substance	c∙10 3 , S/m
H 2 O	0.0044	NaOH 10% solution 30% »
C 2 H 5 OH	0.0064	KOH, 29% solution
C 3 H 7 OH	0.0009	NaCl 10% solution 25% »
CH 3 OH	0.0223	FeSO 4 , 7% solution
Acetonitrile	0.7	NiSO 4 , 19% solution
N,N-Dimethylacetamide	0.008-0.02	CuSO 4 , 15% solution
CH 3 COOH	0.0011	ZnС1 2 , 40% solution
H 2 SO 4 concentrated 10% solution 40% "		NaCl (melt, 850 °С)
HC1 40% solution 10% "		NaNO 3 (melt 500 °C)
HNO 3 concentrated 12% solution		MgCl 2 (melt, 1013 °C)
		А1С1 3 (melt, 245 °С)	0.11
		AlI 3 (melt, 270 °C)	0.74
		AgCl (melt, 800 °C)
		AgI (solid)

Note, The values ​​of the specific conductivity of solutions are given at 18 °C.

However, in all cases, the given values ​​of κ are several orders of magnitude lower than the values ​​of κ of metals (for example, the specific conductivity of silver, copper and lead is 0.67∙10 8 , 0.645∙10 8 and 0.056∙10 8 S/m, respectively).

In conductors of the second kind, all kinds of particles that have an electric charge can take part in the transfer of electricity. If the current is carried by both cations and anions, then electrolytes have bipolar conduction. If the current carries only one kind of ions - cations or anions - then there is unipolar cationic or anionic conductivity.

In the case of bipolar conduction, ions moving faster carry a larger fraction of the current than ions moving slower. The fraction of current carried by a given kind of particle is called carry number of this kind of particles (t i). With unipolar conductivity, the transfer number of the kind of ions that carry the current is equal to one, since all the current is transferred by this kind of ions. But with bipolar conductivity, the transfer number of each kind of ions is less than unity, and

moreover, the transfer number should be understood as the absolute value of the fraction of the current attributable to a given type of ions, without taking into account the fact that cations and anions carry electric current in different directions.

The transfer number of any one kind of particles (ions) with bipolar conductivity is not a constant value that characterizes only the nature of a given kind of ions, but also depends on the nature of the partner particles. For example, the transport number of chloride ions in a hydrochloric acid solution is less than in a KCl solution of the same concentration, since hydrogen ions are more mobile than potassium ions. Methods for determining transfer numbers are diverse, and their principles are outlined in the relevant laboratory workshops on theoretical electrochemistry.

Before proceeding to the consideration of the electrical conductivity of specific classes of substances, let us dwell on one general issue. Any body moves in a constant field of forces acting on it with acceleration. Meanwhile, ions in all classes of electrolytes, except for gases, move under the influence of an electric field of a given intensity at a constant speed. To explain this, let us imagine the forces acting on the ion. If the mass of the ion m and the speed of its movement w, then the Newtonian force mdw/dt will be equal to the difference between the strength of the electric field (M), which moves the ion, and the reactive force (L '), which slows down its movement, because the ion moves in a viscous medium. The reactive force is greater, the greater the speed of the ion, i.e. L' = L w(here L- coefficient of proportionality). Thus

After separating the variables, we have:

Denoting M - L w = v, we get d w= – d v/L and

or

The integration constant is determined from the boundary condition: at t = 0 w = 0, i.e. . We start counting the time from the moment the ion begins to move (the moment the current is turned on). Then:

Substituting its value for the constant, we finally get.

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1 electrical conductivity unit = 0.0001 siemens per meter [S/m]

Initial value

Converted value

siemens per meter picosiemens per meter mo per meter mo per centimeter abmo per meter abmo per centimeter staticmo per meter statmo per centimeter siemens per centimeter millisiemens per meter millisiemens per centimeter microsiemens per meter microsiemens per centimeter conventional unit of electrical conductivity conventional coefficient of electrical conductivity ppm, coefficient. recalculation of 700 ppm, coefficient. recalculation of 500 ppm, coefficient. conversion 640 TDS, ppm, coefficient conversion 640 TDS, ppm, coefficient conversion 550 TDS, ppm, coefficient conversion 500 TDS, ppm, coefficient recalculation 700

Bulk charge density

More about Electrical Conductivity

Introduction and definitions

Electrical conductivity (or electrical conductivity) is a measure of the ability of a substance to conduct an electric current or to move electric charges in it. This is the ratio of current density to electric field strength. If we consider a cube of conductive material with a side of 1 meter, then the specific conductivity will be equal to the electrical conductivity measured between two opposite sides of this cube.

Conductivity is related to conductivity by the following formula:

G = σ(A/l)

where G- electrical conductivity, σ - electrical conductivity, BUT- the cross section of the conductor, perpendicular to the direction of electric current and l- conductor length. This formula can be used with any conductor in the form of a cylinder or prism. Note that this formula can also be used for a cuboid, because it is a special case of a prism whose base is a rectangle. Recall that electrical conductivity is the reciprocal of electrical resistivity.

It can be difficult for people who are far from physics and technology to understand the difference between the conductivity of a conductor and the specific conductivity of a substance. Meanwhile, of course, these are different physical quantities. Conductivity is a property of a given conductor or device (such as a resistor or galvanic bath), while conductivity is an inherent property of the material from which that conductor or device is made. For example, the conductivity of copper is always the same, no matter how the shape and size of the copper object changes. At the same time, the conductivity of a copper wire depends on its length, diameter, mass, shape, and some other factors. Of course, similar objects made of materials with higher conductivity have higher conductivity (although not always).

In the International System of Units (SI), the unit of electrical conductivity is siemens per meter (cm/m). The unit of conductivity included in it is named after the German scientist, inventor, entrepreneur Werner von Siemens (1816–1892). Founded by him in 1847, Siemens AG (Siemens) is one of the largest companies producing electrical, electronic, energy, transport and medical equipment.

The range of electrical conductivities is very wide, from materials with high resistivity such as glass (which, by the way, conducts electricity well when heated red-hot) or polymethyl methacrylate (organic glass) to very good conductors such as silver, copper or gold. Electrical conductivity is determined by the number of charges (electrons and ions), the speed of their movement and the amount of energy they can carry. Aqueous solutions of various substances, which are used, for example, in electroplating baths, have average values ​​of specific conductivity. Another example of electrolytes with average values ​​of specific conductivity is the internal environment of the body (blood, plasma, lymph and other fluids).

The conductivity of metals, semiconductors and dielectrics is discussed in detail in the following articles of the Converter of physical quantities site:, and Electrical conductivity. In this article, we will discuss in more detail the conductivity of electrolytes, as well as methods and simple equipment for measuring it.

Electrical conductivity of electrolytes and its measurement

The specific conductivity of aqueous solutions, in which an electric current arises as a result of the movement of charged ions, is determined by the number of charge carriers (concentration of the substance in the solution), their speed of movement (the mobility of ions depends on temperature) and the charge they carry (determined by the valence of ions). Therefore, in most aqueous solutions, an increase in concentration leads to an increase in the number of ions and, consequently, to an increase in conductivity. However, after reaching a certain maximum, the specific conductivity of the solution may begin to decrease with a further increase in the concentration of the solution. Therefore, solutions with two different concentrations of the same salt can have the same conductivity.

Temperature also affects conductivity, as ions move faster as the temperature rises, resulting in an increase in conductivity. Pure water is a poor conductor of electricity. Ordinary distilled water, which contains carbon dioxide from the air in equilibrium and a total mineralization of less than 10 mg/l, has an electrical conductivity of about 20 mS/cm. The specific conductivity of various solutions is shown in the table below.

To determine the specific conductivity of a solution, a resistance meter (ohmmeter) or conductivity meter is used. These are almost the same devices, differing only in the scale. Both measure the voltage drop in the section of the circuit through which the electric current flows from the battery of the device. The measured conductivity value is manually or automatically converted into conductivity. This is done taking into account the physical characteristics of the measuring device or sensor. Conductivity sensors are simple: they are a pair (or two pairs) of electrodes immersed in an electrolyte. Conductivity sensors are characterized by conductivity sensor constant, which in the simplest case is defined as the ratio of the distance between the electrodes D to the area (electrode) perpendicular to the current flow BUT

This formula works well if the area of ​​the electrodes is much larger than the distance between them, since in this case most of the electric current flows between the electrodes. Example: for 1 cubic centimeter of liquid K=D/A= 1 cm/1 cm² = 1 cm⁻¹. Note that conductivity sensors with small electrodes spaced apart by a relatively large distance are characterized by sensor constant values ​​of 1.0 cm⁻¹ and higher. At the same time, sensors with relatively large electrodes placed close to each other have a constant of 0.1 cm⁻¹ or less. The sensor constant for measuring electrical conductivity of various devices ranges from 0.01 to 100 cm⁻¹.

Theoretical sensor constant: left - K= 0.01 cm⁻¹ , on the right - K= 1 cm⁻¹

To obtain conductivity from the measured conductivity, the following formula is used:

σ = K ∙ G

σ - specific conductivity of the solution in S/cm;

K- sensor constant in cm⁻¹;

G- conductivity of the sensor in siemens.

The sensor constant is usually not calculated from its geometrical dimensions, but is measured in a specific measuring device or in a specific measuring installation using a solution of known conductivity. This measured value is entered into the conductivity meter, which automatically calculates the conductivity from the measured conductivity or solution resistance values. Due to the fact that conductivity depends on the temperature of the solution, devices for measuring conductivity often contain a temperature sensor that measures the temperature and provides automatic temperature compensation of the measurements, i.e., bringing the results to a standard temperature of 25°C.

The easiest way to measure conductivity is to apply a voltage across two flat electrodes immersed in a solution and measure the current flowing. This method is called potentiometric. According to Ohm's law, conductivity G is the current ratio I to voltage U:

However, not everything is as simple as described above - there are many problems when measuring conductivity. If direct current is used, the ions collect at the electrode surfaces. Also, a chemical reaction can occur at the electrode surfaces. This leads to an increase in the polarization resistance on the electrode surfaces, which, in turn, leads to erroneous results. If you try to measure the resistance with a conventional tester, for example, a sodium chloride solution, you will clearly see how the readings on the display of a digital device change rather quickly in the direction of increasing resistance. To eliminate the effect of polarization, a four-electrode sensor design is often used.

Polarization can also be prevented or, in any case, reduced by using alternating current instead of direct current in the measurement, and even adjusting the frequency depending on the conductivity. Low frequencies are used to measure low conductivity where the effect of polarization is small. Higher frequencies are used to measure high conductivities. Usually, the frequency is adjusted automatically during the measurement process, taking into account the obtained values ​​of the conductivity of the solution. Modern digital two-electrode conductivity meters typically use complex AC current and temperature compensation. They are calibrated at the factory, but recalibration is often required during operation, as the constant of the measuring cell (sensor) changes over time. For example, it can change when the sensors become dirty or when the electrodes undergo physical and chemical changes.

In a traditional two-electrode conductivity meter (which is what we will use in our experiment), an alternating voltage is applied between two electrodes and the current flowing between the electrodes is measured. This simple method has one drawback - not only the resistance of the solution is measured, but also the resistance caused by the polarization of the electrodes. To minimize the influence of polarization, a four-electrode sensor design is used, as well as coating the electrodes with platinum black.

General mineralization

Devices for measuring electrical conductivity are often used to determine total mineralization or solids content(English total dissolved solids, TDS). It is a measure of the total amount of organic and inorganic substances contained in a liquid in various forms: ionized, molecular (dissolved), colloidal, and in suspension (undissolved). Solutes include any inorganic salts. These are mainly chlorides, bicarbonates and sulfates of calcium, potassium, magnesium, sodium, as well as some organic substances dissolved in water. To be considered total mineralization, the substances must be either dissolved or in the form of very fine particles that pass through filters with a pore diameter of less than 2 micrometers. Substances that are constantly in suspension in solution, but cannot pass through such a filter, are called suspended solids(English total suspended solids, TSS). Total suspended solids is usually measured to determine water quality.

There are two methods for measuring solids content: gravimetric analysis, which is the most accurate method, and conductivity measurement. The first method is the most accurate, but it requires a lot of time and the availability of laboratory equipment, since the water must be evaporated to obtain a dry residue. This is usually done at 180°C in a laboratory setting. After complete evaporation, the residue is weighed on an accurate balance.

The second method is not as accurate as gravimetric analysis. However, it is very convenient, widely used, and is the fastest method, as it is a simple measurement of conductivity and temperature, performed in a few seconds with an inexpensive measuring instrument. The method of measuring the specific electrical conductivity can be used due to the fact that the specific conductivity of water directly depends on the amount of ionized substances dissolved in it. This method is especially useful for monitoring the quality of drinking water or assessing the total amount of ions in a solution.

The measured conductivity depends on the temperature of the solution. That is, the higher the temperature, the higher the conductivity, since ions in solution move faster as the temperature rises. To obtain temperature-independent measurements, the concept of a standard (reference) temperature is used, to which the measurement results are reduced. The reference temperature allows you to compare results obtained at different temperatures. Thus, the conductivity meter can measure the actual conductivity and then use a correction function that will automatically bring the result to a reference temperature of 20 or 25°C. If very high accuracy is required, the sample can be placed in an oven, then the meter can be calibrated at the same temperature that will be used in the measurement.

Most modern conductivity meters are equipped with a built-in temperature sensor that is used for both temperature correction and temperature measurement. The most advanced instruments are capable of measuring and displaying measured values ​​in terms of conductivity, resistivity, salinity, total salinity and concentration. However, once again, we note that all these devices measure only conductivity (resistance) and temperature. All physical quantities that the display shows are calculated by the device taking into account the measured temperature, which is used for automatic temperature compensation and bringing the measured values ​​to the standard temperature.

Experiment: Total Salinity and Conductivity Measurement

Finally, we will perform some experiments to measure conductivity using an inexpensive TDS-3 total mineralization meter (also called salinometer, salinometer, or conductometer) TDS-3. The price of the "unnamed" TDS-3 device on eBay, including shipping, is less than US$3.00 at the time of writing. Exactly the same device, but with the name of the manufacturer is already 10 times more expensive. But this is for those who like to pay for the brand, although there is a very high probability that both devices will be released at the same factory. The TDS-3 performs temperature compensation and for this it is equipped with a temperature sensor located next to the electrodes. Therefore, it can also be used as a thermometer. It should be noted once again that the device actually measures not the mineralization itself, but the resistance between two wire electrodes and the temperature of the solution. Everything else it automatically calculates using calibration coefficients.

The total mineralization meter will help you determine the solids content, for example when monitoring the quality of drinking water or determining the salinity of water in an aquarium or freshwater pond. It can also be used to monitor water quality in water filtration and purification systems to know when it's time to replace a filter or membrane. The instrument is factory calibrated with 342 ppm (parts per million or mg/L) sodium chloride solution NaCl. The measuring range of the device is 0–9990 ppm or mg/l. PPM is a part per million, a dimensionless unit of measurement of relative values, equal to 1 10⁻⁶ of the base value. For example, a mass concentration of 5 mg/kg = 5 mg in 1,000,000 mg = 5 ppm or ppm. Just as a percentage is one hundredth, a millionth is one millionth. Percentages and millionths are very similar in meaning. Parts per million, unlike percentages, are convenient for indicating the concentration of very weak solutions.

The instrument measures the electrical conductivity between two electrodes (that is, the reciprocal of the resistance), then converts the result to electrical conductivity (EC is often used in English literature) using the conductivity formula above, taking into account the sensor constant K, then performs another conversion by multiplying the resulting conductivity by a conversion factor of 500. The result is a total mineralization value in parts per million (ppm). More on this below.

This total mineralization meter cannot be used to test the quality of water with a high salt content. Examples of substances with a high salt content are certain foods (common soup with a normal salt content of 10 g/l) and sea water. The maximum concentration of sodium chloride that this device can measure is 9990 ppm or about 10 g/l. This is the usual concentration of salt in foods. The salinity of seawater cannot be measured with this meter either, as it is typically 35 g/l or 35,000 ppm, which is much higher than the meter is capable of measuring. If you try to measure such a high concentration, the instrument will display an error message Err.

The TDS-3 salt meter measures conductivity and uses the so-called "500 scale" (or "NaCl scale") for calibration and conversion to concentration. This means that to obtain the concentration in parts per million, the conductivity value in mS/cm is multiplied by 500. That is, for example, 1.0 mS/cm is multiplied by 500 to get 500 ppm. Different industries use different scales. For example, three scales are used in hydroponics: 500, 640 and 700. The difference between them is only in use. The 700 scale is based on measuring the concentration of potassium chloride in a solution, and the conversion of conductivity to concentration is performed as follows:

1.0 mS/cm x 700 gives 700 ppm

The 640 scale uses a conversion factor of 640 to convert mS to ppm:

1.0 mS/cm x 640 gives 640 ppm

In our experiment, we will first measure the total mineralization of distilled water. The salt meter shows 0 ppm. The multimeter shows a resistance of 1.21 MΩ.

For the experiment, we will prepare a solution of sodium chloride NaCl with a concentration of 1000 ppm and measure the concentration using TDS-3. To prepare 100 ml of solution, we need to dissolve 100 mg of sodium chloride and add distilled water to 100 ml. Weigh 100 mg of sodium chloride and place it in a measuring cylinder, add a little distilled water and stir until the salt is completely dissolved. Then add water to the 100 ml mark and stir again.

Resistance measurement between two electrodes made of the same material and with the same dimensions as the TDS-3 electrodes; multimeter shows 2.5 kOhm

For the experimental determination of conductivity, we used two electrodes made of the same material and with the same dimensions as the TDS-3 electrodes. The measured resistance was 2.5 kOhm.

Now that we know the resistance and concentration of sodium chloride in parts per million, we can approximately calculate the measuring cell constant of the TDS-3 saline meter using the above formula:

K = σ/G= 2 mS/cm x 2.5 kΩ = 5 cm⁻¹

This value of 5 cm⁻¹ is close to the calculated value of the TDS-3 measuring cell constant with the following electrode sizes (see figure).

• D = 0.5 cm - the distance between the electrodes;
• W = 0.14 cm - electrode width
• L = 1.1 cm - electrode length

The TDS-3 sensor constant is K=D/A= 0.5/0.14x1.1 = 3.25 cm⁻¹. This is not much different from the value obtained above. Recall that the above formula allows only an approximate estimate of the sensor constant.

Do you find it difficult to translate units of measurement from one language to another? Colleagues are ready to help you. Post a question to TCTerms and within a few minutes you will receive an answer.

In this article, we will reveal the topic of electrical conductivity, recall what an electric current is, how it is related to the resistance of a conductor and, accordingly, to its electrical conductivity. We note the basic formulas for calculating these quantities, touch on the topic and its connection with the electric field strength. We will also touch on the relationship between electrical resistance and temperature.

First, let's remember what an electric current is. If you place a substance in an external electric field, then under the action of forces from this field, the movement of elementary charge carriers - ions or electrons - will begin in the substance. This will be the electric current. The current strength I is measured in amperes, and one ampere is the current at which a charge equal to one coulomb flows through the cross section of the conductor per second.

The current is constant, variable, pulsating. Direct current does not change its magnitude and direction at any given time, alternating current changes its magnitude and direction over time (alternating current generators and transformers give exactly alternating current), pulsating current changes its magnitude, but does not change direction (for example, rectified alternating current current is pulsating).

Substances have the property of conducting an electric current under the influence of an electric field, and this property is called electrical conductivity, which is different for different substances. The electrical conductivity of substances depends on the concentration of free charged particles in them, that is, ions and electrons that are not associated with either the crystal structure, or the molecules, or the atoms of the given substance. So, depending on the concentration of free charge carriers in a substance, substances are divided into: conductors, dielectrics and semiconductors according to the degree of electrical conductivity.

They have the highest electrical conductivity, and by physical nature, conductors in nature are represented by two genera: metals and electrolytes. In metals, the current is due to the movement of free electrons, that is, their conductivity is electronic, and in electrolytes (in solutions of acids, salts, alkalis) it is due to the movement of ions - parts of molecules that have a positive and negative charge, that is, the conductivity of electrolytes is ionic. Ionized vapors and gases are characterized by mixed conductivity, in which the current is due to the movement of both electrons and ions.

The electronic theory perfectly explains the high electrical conductivity of metals. The connection of valence electrons with their nuclei in metals is weak, because these electrons move freely from atom to atom throughout the volume of the conductor.

It turns out that free electrons in metals fill the space between atoms like a gas, an electron gas, and are in chaotic motion. But when a metal conductor is introduced into an electric field, free electrons will move in an orderly manner, they will move towards the positive pole, which will create a current. Thus, the ordered movement of free electrons in a metallic conductor is called electric current.

It is known that the speed of propagation of an electric field in space is approximately equal to 300,000,000 m/s, that is, the speed of light. This is the same speed at which current flows through a conductor.

What does it mean? This does not mean that each electron in the metal moves with such a huge speed, the electrons in the conductor, on the contrary, have a speed from several millimeters per second to several centimeters per second, depending on , but the speed of propagation of electric current through the conductor is just equal to the speed of light .

The thing is that each free electron finds itself in the general electron flow of that very “electron gas”, and during the passage of the current, the electric field has an effect on this entire flow, as a result, the electrons continuously transmit this field action to each other - from a neighbor to neighbor.

But electrons move in their places very slowly, despite the fact that the speed of propagation of electrical energy through the conductor is enormous. So, when a switch is turned on at a power plant, the current instantly appears in the entire network, while the electrons practically stand still.

However, when free electrons move along a conductor, they experience numerous collisions on their way, they collide with atoms, ions, molecules, transferring part of their energy to them. The energy of moving electrons overcoming such resistance is partially dissipated in the form of heat, and the conductor heats up.

These collisions serve as resistance to the movement of electrons, therefore the property of a conductor to prevent the movement of charged particles is called electrical resistance. With a low resistance of the conductor, the conductor is heated by the current weakly, with a significant one, it is much stronger, and even up to white, this effect is used in heating devices and incandescent lamps.

The unit of resistance change is Ohm. Resistance R \u003d 1 Ohm is the resistance of such a conductor, when a direct current of 1 ampere passes through it, the potential difference at the ends of the conductor is 1 volt. The resistance standard of 1 ohm is a mercury column 1063 mm high, with a cross section of 1 sq. mm at a temperature of 0 ° C.

Since conductors are characterized by electrical resistance, it can be said that, to some extent, the conductor is capable of conducting electric current. In this regard, a quantity called conductivity or electrical conductivity has been introduced. Electrical conductivity is the ability of a conductor to conduct electric current, that is, the reciprocal of electrical resistance.

The unit of measure for electrical conductivity G (conductivity) is Siemens (Sm), and 1 Sm = 1/(1 ohm). G = 1/R.

Since the atoms of different substances interfere with the passage of electric current to varying degrees, the electrical resistance of different substances is different. For this reason, the concept was introduced, the value of which "p" characterizes the conductive properties of a substance.

Electrical resistivity is measured in ohm * m, that is, the resistance of a cube of a substance with an edge of 1 meter. In the same way, the electrical conductivity of a substance is characterized by specific electrical conductivity?, measured in S / m, that is, the conductivity of a cube of a substance with an edge of 1 meter.

Today, conductive materials in electrical engineering are used mainly in the form of tapes, tires, wires, with a certain cross-sectional area and a certain length, but not in the form of meter cubes. And for more convenient calculations of electrical resistance and electrical conductivity of conductors of specific sizes, more acceptable units of measurement were introduced for both electrical resistivity and electrical conductivity. Ohm*mm2/m for resistivity, and Sm*m/mm2 for electrical conductivity.

Now we can say that electrical resistivity and electrical conductivity characterize the conductive properties of a conductor with a cross-sectional area of ​​​​1 sq. mm, a length of 1 meter at a temperature of 20 ° C, this is more convenient.

Metals such as gold, copper, silver, chromium, aluminum have the best electrical conductivity. Steel and iron conduct current worse. Pure metals always have better electrical conductivity than their alloys, so pure copper is preferable in electrical engineering. If you need a specially high resistance, then use tungsten, nichrome, constantan.

Knowing the value of electrical resistivity or electrical conductivity, one can easily calculate the resistance or electrical conductivity of a particular conductor made from a given material, taking into account the length l and cross-sectional area S of this conductor.

The electrical conductivity and electrical resistance of all materials depends on temperature., since the frequency and amplitude of thermal vibrations of the atoms of the crystal lattice also increases with increasing temperature, the resistance to electric current, to the flow of electrons, increases accordingly.

With a decrease in temperature, on the contrary, the vibrations of the atoms of the crystal lattice become smaller, the resistance decreases (electrical conductivity increases). In some substances, the dependence of resistance on temperature is less pronounced, in others it is stronger. For example, alloys such as constantan, fechral and manganin slightly change the resistivity in a certain temperature range, so they are used to make thermostable resistors.

Allows you to calculate for a particular material the increase in its resistance at a certain temperature, and numerically characterizes the relative increase in resistance with an increase in temperature by 1 °C.

Knowing the temperature coefficient of resistance and the temperature increment, one can easily calculate the resistivity of a substance at a given temperature.

We hope that our article was useful for you, and now you can easily calculate the resistance and conductivity of any wire at any temperature.