Electrical resistivity and conductivity

4087:, which causes resistance. The more regular the lattice is, the less disturbance happens and thus the less resistance. The amount of resistance is thus mainly caused by two factors. First, it is caused by the temperature and thus amount of vibration of the crystal lattice. Higher temperatures cause bigger vibrations, which act as irregularities in the lattice. Second, the purity of the metal is relevant as a mixture of different ions is also an irregularity. The small decrease in conductivity on melting of pure metals is due to the loss of long range crystalline order. The short range order remains and strong correlation between positions of ions results in coherence between waves diffracted by adjacent ions. 4581: 4546:, a real sample of a normal conductor shows some resistance. In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature. In a normal conductor, the current is driven by a voltage gradient, whereas in a superconductor, there is no voltage gradient and the current is instead related to the phase gradient of the superconducting order parameter. A consequence of this is that an electric current flowing in a loop of 3992:, an electron in an atom or crystal can only have certain precise energy levels; energies between these levels are impossible. When a large number of such allowed levels have close-spaced energy values – i.e. have energies that differ only minutely – those close energy levels in combination are called an "energy band". There can be many such energy bands in a material, depending on the atomic number of the constituent atoms and their distribution within the crystal. 4523: 3912: 546: 2998: 2000: 3380: 4032: 2722: 2532: 1721: 818:, passing current through a high-resistivity material is like pushing water through a pipe full of sand - while passing current through a low-resistivity material is like pushing water through an empty pipe. If the pipes are the same size and shape, the pipe full of sand has higher resistance to flow. Resistance, however, is not 8866: 3073: 2219: 8934:

Silver, although it is the least resistive metal known, has a high density and performs similarly to copper by this measure, but is much more expensive. Calcium and the alkali metals have the best resistivity-density products, but are rarely used for conductors due to their high reactivity with water

562:

do in fact have a uniform cross section with a uniform flow of electric current, and are made of a single material, so that this is a good model. (See the adjacent diagram.) When this is the case, the resistance of the conductor is directly proportional to its length and inversely proportional to its

4565:

in the electronic superfluid, which dissipates some of the energy carried by the current. The resistance due to this effect is tiny compared with that of non-superconducting materials, but must be taken into account in sensitive experiments. However, as the temperature decreases far enough below the

4121:

the position of the Fermi level is within the band gap, about halfway between the conduction band minimum (the bottom of the first band of unfilled electron energy levels) and the valence band maximum (the top of the band below the conduction band, of filled electron energy levels). That applies for

4008:

are free to move within the broader material structure, since the electrons can easily jump among the partially occupied states in that region. In contrast, the low energy states are completely filled with a fixed limit on the number of electrons at all times, and the high energy states are empty of

965:

If the geometry is more complicated, or if the resistivity varies from point to point within the material, the current and electric field will be functions of position. Then it is necessary to use a more general expression in which the resistivity at a particular point is defined as the ratio of the

9340:

Mr. Walsh ... has just made a curious Discovery in Electricity. You know we find that in rarify’d Air it would pass more freely, and leap thro’ greater Spaces than in dense Air; and thence it was concluded that in a perfect Vacuum it would pass any distance without the least Obstruction. But having

7001:

The effective temperature coefficient varies with temperature and purity level of the material. The 20 °C value is only an approximation when used at other temperatures. For example, the coefficient becomes lower at higher temperatures for copper, and the value 0.00427 is commonly specified at

4587:

is an example of plasma present at Earth's surface. Typically, lightning discharges 30,000 amperes at up to 100 million volts, and emits light, radio waves, and X-rays. Plasma temperatures in lightning might approach 30,000 kelvin (29,727 °C) (53,540 °F), and electron densities may exceed

7021:

The metallic substances differ from all other materials by the fact that the outer shells of their atoms are bound rather loosely, and often let one of their electrons go free. Thus the interior of a metal is filled up with a large number of unattached electrons that travel aimlessly around like a

4016:

An important part of band theory is that there may be forbidden bands of energy: energy intervals that contain no energy levels. In insulators and semiconductors, the number of electrons is just the right amount to fill a certain integer number of low energy bands, exactly to the boundary. In this

1616:

consists microscopically of a stack of sheets, and current flows very easily through each sheet, but much less easily from one sheet to the adjacent one. In such cases, the current does not flow in exactly the same direction as the electric field. Thus, the appropriate equations are generalized to

9349:

We can only assume that something was wrong with Walsh’s findings. ... Although the conductivity of a gas, as it approaches a vacuum, increases up to a point and then decreases, that point is far beyond what the technique described might have been expected to reach. Boiling replaced the air with

7387:

interactions can play a key role. At high temperatures, the resistance of a metal increases linearly with temperature. As the temperature of a metal is reduced, the temperature dependence of resistivity follows a power law function of temperature. Mathematically the temperature dependence of the

3761: 8158:

have a far more complicated temperature profile. As temperature increases starting from absolute zero they first decrease steeply in resistance as the carriers leave the donors or acceptors. After most of the donors or acceptors have lost their carriers, the resistance starts to increase again

4130:

atoms increase the majority charge carrier concentration by donating electrons to the conduction band or producing holes in the valence band. (A "hole" is a position where an electron is missing; such holes can behave in a similar way to electrons.) For both types of donor or acceptor atoms,

9511:

The conductivity of metallic silver is not significantly better than metallic copper for most practical purposes – the difference between the two can be easily compensated for by thickening the copper wire by only 3%. However silver is preferred for exposed electrical contact points because

4063:, each with an outer shell of electrons that freely dissociate from their parent atoms and travel through the lattice. This is also known as a positive ionic lattice. This 'sea' of dissociable electrons allows the metal to conduct electric current. When an electrical potential difference (a 8926:

is more important than absolute low resistivity – it is often possible to make the conductor thicker to make up for a higher resistivity; and then a low-resistivity-density-product material (or equivalently a high conductivity-to-density ratio) is desirable. For example, for long-distance

4131:

increasing dopant density reduces resistance. Hence, highly doped semiconductors behave metallically. At very high temperatures, the contribution of thermally generated carriers dominates over the contribution from dopant atoms, and the resistance decreases exponentially with temperature.

7703:. This value depends not only on the type of metal, but on its purity and thermal history. The value of the residual resistivity of a metal is decided by its impurity concentration. Some materials lose all electrical resistivity at sufficiently low temperatures, due to an effect known as 2993:{\displaystyle {\begin{bmatrix}J_{x}\\J_{y}\\J_{z}\end{bmatrix}}={\begin{bmatrix}\sigma _{xx}&\sigma _{xy}&\sigma _{xz}\\\sigma _{yx}&\sigma _{yy}&\sigma _{yz}\\\sigma _{zx}&\sigma _{zy}&\sigma _{zz}\end{bmatrix}}{\begin{bmatrix}E_{x}\\E_{y}\\E_{z}\end{bmatrix}}} 7577: 2713: 1680: 4561:, an extremely low but nonzero resistivity appears at temperatures not too far below the nominal superconducting transition when an electric current is applied in conjunction with a strong magnetic field, which may be caused by the electric current. This is due to the motion of 5049:

in the solution. Electrical conductivity of water samples is used as an indicator of how salt-free, ion-free, or impurity-free the sample is; the purer the water, the lower the conductivity (the higher the resistivity). Conductivity measurements in water are often reported as

8746: 4034: 4038: 4037: 4033: 1995:{\displaystyle {\begin{bmatrix}E_{x}\\E_{y}\\E_{z}\end{bmatrix}}={\begin{bmatrix}\rho _{xx}&\rho _{xy}&\rho _{xz}\\\rho _{yx}&\rho _{yy}&\rho _{yz}\\\rho _{zx}&\rho _{zy}&\rho _{zz}\end{bmatrix}}{\begin{bmatrix}J_{x}\\J_{y}\\J_{z}\end{bmatrix}},} 686: 1601:, which relates the electric field inside a material to the electric current flow. This equation is completely general, meaning it is valid in all cases, including those mentioned above. However, this definition is the most complicated, so it is only directly used in 8935:

and oxygen (and lack of physical strength). Aluminium is far more stable. Toxicity excludes the choice of beryllium. (Pure beryllium is also brittle.) Thus, aluminium is usually the metal of choice when the weight or cost of a conductor is the driving consideration.

4039: 4817: 1326:

This expression simplifies to the formula given above under "ideal case" when the resistivity is constant in the material and the geometry has a uniform cross-section. In this case, the electric field and current density are constant and parallel.

8159:

slightly due to the reducing mobility of carriers (much as in a metal). At higher temperatures, they behave like intrinsic semiconductors as the carriers from the donors/acceptors become insignificant compared to the thermally generated carriers.

4082:

Most metals have electrical resistance. In simpler models (non quantum mechanical models) this can be explained by replacing electrons and the crystal lattice by a wave-like structure. When the electron wave travels through the lattice, the waves

3375:{\displaystyle {\begin{aligned}J_{x}&=\sigma _{xx}E_{x}+\sigma _{xy}E_{y}+\sigma _{xz}E_{z}\\J_{y}&=\sigma _{yx}E_{x}+\sigma _{yy}E_{y}+\sigma _{yz}E_{z}\\J_{z}&=\sigma _{zx}E_{x}+\sigma _{zy}E_{y}+\sigma _{zz}E_{z}\end{aligned}}.} 4036: 3589: 802:

and does not depend on geometric properties of a material. This means that all pure copper (Cu) wires (which have not been subjected to distortion of their crystalline structure etc.), irrespective of their shape and size, have the same

7812: 4832:

It is possible to produce a plasma that is not quasineutral. An electron beam, for example, has only negative charges. The density of a non-neutral plasma must generally be very low, or it must be very small. Otherwise, the repulsive

9341:

made a perfect Vacuum by means of boil’d Mercury in a long Torricellian bent Tube, its Ends immers’d in Cups full of Mercury, he finds that the Vacuum will not conduct at all, but resists the Passage of the Electric Fluid absolutely.

4012:

Electric current consists of a flow of electrons. In metals there are many electron energy levels near the Fermi level, so there are many electrons available to move. This is what causes the high electronic conductivity of metals.

7037:

worse insulator than oven-dry. In any case, a sufficiently high voltage – such as that in lightning strikes or some high-tension power lines – can lead to insulation breakdown and electrocution risk even with apparently dry wood.

4726: 409: 7397: 2527:{\displaystyle {\begin{aligned}E_{x}&=\rho _{xx}J_{x}+\rho _{xy}J_{y}+\rho _{xz}J_{z},\\E_{y}&=\rho _{yx}J_{x}+\rho _{yy}J_{y}+\rho _{yz}J_{z},\\E_{z}&=\rho _{zx}J_{x}+\rho _{zy}J_{y}+\rho _{zz}J_{z}.\end{aligned}}} 205: 2566: 1622: 1342:

Assume the geometry has a uniform cross-section and the resistivity is constant in the material. Then the electric field and current density are constant and parallel, and by the general definition of resistivity, we obtain

3064: 2210: 8355: 9667:

The pH should be around 8.4 and the conductivity in the range of 2.5–3 mS/cm. The lower value is appropriate for freshly prepared water. The conductivity is used for the determination of TDS (total dissolved

9445:

Other relevant factors that are specifically not considered are the size of the whole crystal and external factors of the surrounding environment that modify the energy bands, such as imposed electric or magnetic

1303: 608: 4962:

Often non-Maxwellian: collisional interactions are often weak in hot plasmas and external forcing can drive the plasma far from local equilibrium and lead to a significant population of unusually fast particles.

7022:

crowd of displaced persons. When a metal wire is subjected to electric force applied on its opposite ends, these free electrons rush in the direction of the force, thus forming what we call an electric current.

10055:

When electrons are conducted through a metal, they interact with imperfections in the lattice and scatter. Thermal energy produces scattering by causing atoms to vibrate. This is the source of resistance of

7653:

as obtained from resistivity measurements and matches very closely with the values of Debye temperature obtained from specific heat measurements. n is an integer that depends upon the nature of interaction:

4383: 3999:

means that only one can exist in each such state. So the electrons "fill up" the band structure starting from the bottom. The characteristic energy level up to which the electrons have filled is called the

8739: 8125: 553:

In an ideal case, cross-section and physical composition of the examined material are uniform across the sample, and the electric field and current density are both parallel and constant everywhere. Many

613: 8038: 4122:

intrinsic (undoped) semiconductors. This means that at absolute zero temperature, there would be no free conduction electrons, and the resistance is infinite. However, the resistance decreases as the

4733: 3078: 2224: 10069: 8232: 906:(forming a cube with perfectly conductive contacts on opposite faces), then the resistance of this element in ohms is numerically equal to the resistivity of the material it is made of in Ω⋅m. 8861:{\displaystyle \mathbf {J} (\mathbf {r} )=\sigma (\mathbf {r} )\mathbf {E} (\mathbf {r} )\,\,\rightleftharpoons \,\,\mathbf {E} (\mathbf {r} )=\rho (\mathbf {r} )\mathbf {J} (\mathbf {r} ),} 1041: 4017:

case, the Fermi level falls within a band gap. Since there are no available states near the Fermi level, and the electrons are not freely movable, the electronic conductivity is very low.

4153:) traveling, each carrying an electrical charge. The resistivity of ionic solutions (electrolytes) varies tremendously with concentration – while distilled water is almost an insulator, 1525: 949: 604: 1605:

cases, where the more simple definitions cannot be applied. If the material is not anisotropic, it is safe to ignore the tensor-vector definition, and use a simpler expression instead.

1582: 872: 322: 125: 4079:

but the rapid propagation of an electric energy along a wire is not due to the mechanical forces, but the propagation of an energy-carrying electromagnetic field guided by the wire.

3426: 3582: 9345:

However, to this statement a note (based on modern knowledge) was added by the editors—at the American Philosophical Society and Yale University—of the webpage hosting the letter:

4035: 3533: 3404: 2081: 1427: 1379: 4172:

The concentration of ions in a liquid (e.g., in an aqueous solution) depends on the degree of dissociation of the dissolved substance, characterized by a dissociation coefficient

4071:

of electrons is typically small, on the order of magnitude of metres per hour. However, due to the sheer number of moving electrons, even a slow drift velocity results in a large

11189:

Mutual Impedivity Spectrometry and the Feasibility of its Incorporation into Tissue-Diagnostic Anatomical Reconstruction and Multivariate Time-Coherent Physiological Measurements

7139: 8563: 7739: 1467: 278: 4281: 11298: 8684: 4651: 7359: 2105: 2028: 7647: 8910:. In special cases, an exact or approximate solution to these equations can be worked out by hand, but for very accurate answers in complex cases, computer methods like 7734:

states that for materials where heat and charge transport is dominated by electrons, the ratio of thermal to electrical conductivity is proportional to the temperature:

3853: 3823: 3793: 3483: 822:

determined by the presence or absence of sand. It also depends on the length and width of the pipe: short or wide pipes have lower resistance than narrow or long pipes.

8472: 7222: 7608: 1076: 7922: 7834: 7332: 7312: 7291: 7269: 7161: 4506: 4303: 4190: 10475: 8530: 8499: 8425: 7249: 7195: 7033:

Wood is widely regarded as an extremely good insulator, but its resistivity is sensitively dependent on moisture content, with damp wood being a factor of at least

4486: 4459: 4432: 4237: 4004:. The position of the Fermi level with respect to the band structure is very important for electrical conduction: Only electrons in energy levels near or above the 3873: 3007: 900: 738: 8445: 2150: 1178: 1127: 9336:, that purportedly showed this astonishing fact: Although rarified air conducts electricity better than common air, a vacuum does not conduct electricity at all. 1597:

When the resistivity of a material has a directional component, the most general definition of resistivity must be used. It starts from the tensor-vector form of

11188: 4974:

Collective: waves, or organized motion of plasma, are very important because the particles can interact at long ranges through the electric and magnetic forces.

8649:

Even if the material's resistivity is known, calculating the resistance of something made from it may, in some cases, be much more complicated than the formula

8398: 8378: 7902: 7882: 7858: 4405: 4210: 1202: 1147: 1096: 764: 712: 4534:

The electrical resistivity of a metallic conductor decreases gradually as temperature is lowered. In normal (that is, non-superconducting) conductors, such as

7378: 488:) is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current. It is commonly signified by the Greek letter 9350:

mercury vapor, which as it cooled created a vacuum that could scarcely have been complete enough to decrease, let alone eliminate, the vapor’s conductivity.

7699:

As the temperature of the metal is sufficiently reduced (so as to 'freeze' all the phonons), the resistivity usually reaches a constant value, known as the

1217: 335: 9386: 4986: 4878:. Although it is closely related to the gas phase in that it also has no definite form or volume, it differs in a number of ways, including the following: 10487: 4856:. This can and does cause extremely complex behavior, such as the generation of plasma double layers, an object that separates charge over a few tens of 3756:{\displaystyle \sigma _{xx}={\frac {\rho _{xx}}{\rho _{xx}^{2}+\rho _{xy}^{2}}},\quad \sigma _{xy}={\frac {-\rho _{xy}}{\rho _{xx}^{2}+\rho _{xy}^{2}}}.} 5010:

is generally intermediate, but varies widely under different conditions, such as exposure of the material to electric fields or specific frequencies of

138: 1315: — because even a very large electric field in rubber makes almost no current flow through it. On the other hand, copper is a material with small 4047:. Like the balls in Newton's cradle, electrons in a metal quickly transfer energy from one terminal to another, despite their own negligible movement. 811:

than a thick, short copper wire. Every material has its own characteristic resistivity. For example, rubber has a far larger resistivity than copper.

4310: 8696: 8051: 7361:, and the relationship only holds in a range of temperatures around the reference. When the temperature varies over a large temperature range, the 4595:

The potential as it exists on average in the space between charged particles, independent of the question of how it can be measured, is called the

4126:(i.e., without introducing further complications, the density of electrons) in the conduction band increases. In extrinsic (doped) semiconductors, 4940:

so that they behave independently in many circumstances, with different bulk velocities and temperatures, allowing phenomena such as new types of

8257: 7692:

in the 1860s) states that the total resistance can be approximated by adding up several different terms, each with the appropriate value of

11226:. Vol. 21, January 1, 1774, through March 22, 1775. Yale University Press. pp. 147–149 – via Founders Online, National Archives. 7677:

The Bloch–Grüneisen formula is an approximation obtained assuming that the studied metal has spherical Fermi surface inscribed within the first

11328: 10021: 7973: 7572:{\displaystyle \rho (T)=\rho (0)+A\left({\frac {T}{\Theta _{R}}}\right)^{n}\int _{0}^{\Theta _{R}/T}{\frac {x^{n}}{(e^{x}-1)(1-e^{-x})}}\,dx,} 3432:

of each other. However, in the most general case, the individual matrix elements are not necessarily reciprocals of one another; for example,

4603:. If an electrode is inserted into a plasma, its potential generally lies considerably below the plasma potential, due to what is termed a 10733: 2708:{\displaystyle \rho _{xx}={\frac {E_{x}}{J_{x}}},\quad \rho _{yx}={\frac {E_{y}}{J_{x}}},{\text{ and }}\rho _{zx}={\frac {E_{z}}{J_{x}}}.} 1675:{\displaystyle \mathbf {J} ={\boldsymbol {\sigma }}\mathbf {E} \,\,\rightleftharpoons \,\,\mathbf {E} ={\boldsymbol {\rho }}\mathbf {J} ,} 9376: 8629:

An alternative description of the response to alternating currents uses a real (but frequency-dependent) conductivity, along with a real

4611:, which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma ( 874:

The resistance of a given element is proportional to the length, but inversely proportional to the cross-sectional area. For example, if

10096:"The Feynman Lectures in Physics, Vol. III, Chapter 21: The Schrödinger Equation in a Classical Context: A Seminar on Superconductivity" 8690:, where the material is inhomogeneous (different resistivity in different places), and the exact paths of current flow are not obvious. 8173: 4898:

Very low: air is an excellent insulator until it breaks down into plasma at electric field strengths above 30 kilovolts per centimetre.

9569: 4530:

showing the resistance of a mercury wire as a function of temperature. The abrupt drop in resistance is the superconducting transition.

979: 10663: 4860:. The dynamics of plasmas interacting with external and self-generated magnetic fields are studied in the academic discipline of 1484: 918: 576: 4566:

nominal superconducting transition, these vortices can become frozen so that the resistance of the material becomes truly zero.

4067:) is applied across the metal, the resulting electric field causes electrons to drift towards the positive terminal. The actual 1548: 838: 9990: 4959:: collisions usually lead to a Maxwellian velocity distribution of all gas particles, with very few relatively fast particles. 4607:. The good electrical conductivity of plasmas makes their electric fields very small. This results in the important concept of 681:{\displaystyle {\begin{aligned}R&=\rho {\frac {\ell }{A}}\\{}\Leftrightarrow \rho &=R{\frac {A}{\ell }},\end{aligned}}} 11313: 8633:. The larger the conductivity is, the more quickly the alternating-current signal is absorbed by the material (i.e., the more 11250: 10772: 10613: 10397: 10317: 10270: 10167: 10131: 10000: 9885: 9808: 9774: 9737: 525: 24: 10500: 3995:

The material's electrons seek to minimize the total energy in the material by settling into low energy states; however, the

10749: 10464: 10434: 9954: 8638: 1396: 1348: 787:(Ω⋅m) — i.e. ohms multiplied by square metres (for the cross-sectional area) then divided by metres (for the length). 10963: 798:

describe how difficult it is to make electrical current flow through a material, but unlike resistance, resistivity is an

439:. A low resistivity indicates a material that readily allows electric current. Resistivity is commonly represented by the 11291: 7062: 10715: 10522: 9798: 7610:

is the residual resistivity due to defect scattering, A is a constant that depends on the velocity of electrons at the

4956: 1436: 7374: 5026:

makes a large difference in conductivity. To a point, more doping leads to higher conductivity. The conductivity of a

4244: 11062: 10989: 10866: 10693: 10643: 10191: 10079: 9865: 9844: 9391: 4161:

is also controlled by the movement of ions, but here we are talking about molten salts rather than solvated ions. In

2536:

Since the choice of the coordinate system is free, the usual convention is to simplify the expression by choosing an

10792: 7661: = 5 implies that the resistance is due to scattering of electrons by phonons (as it is for simple metals) 7667: = 3 implies that the resistance is due to s-d electron scattering (as is the case for transition metals) 4640:

The magnitude of the potentials and electric fields must be determined by means other than simply finding the net

10848:

ASTM D5391 Standard Test Method for Electrical Conductivity and Resistivity of a Flowing High Purity Water Sample

10805:

R. M. Pashley; M. Rzechowicz; L. R. Pashley; M. J. Francis (2005). "De-Gassed Water is a Better Cleaning Agent".

9436:

The atomic number is the count of electrons in an atom that is electrically neutral – has no net electric charge.

8605:). The magnitude of impedivity is the square root of sum of squares of magnitudes of resistivity and reactivity. 8582: 8042:

An even better approximation of the temperature dependence of the resistivity of a semiconductor is given by the

4558: 3980: 294: 8687: 7314:

is different for different reference temperatures. For this reason it is usual to specify the temperature that

4812:{\displaystyle \mathbf {E} =-{\frac {k_{\text{B}}T_{\text{e}}}{e}}{\frac {\nabla n_{\text{e}}}{n_{\text{e}}}}.} 94: 8907: 3409: 1431:

Since the current density is constant, it is equal to the total current divided by the cross sectional area:

20: 11259: 10448: 3538: 11333: 9516:

silver is a tolerable conductor, but corroded copper is a fairly good insulator, like most corroded metals.

8622:. Admittivity is the sum of a real component called the conductivity and an imaginary component called the 7719: 3492: 3387: 2064: 6741: 10291: 9361: 8043: 7688:

If more than one source of scattering is simultaneously present, Matthiessen's rule (first formulated by

4848:

prevents electric fields from directly affecting the plasma over large distances, i.e., greater than the

4140: 10881:"Effect of relative humidity and sea level pressure on electrical conductivity of air over Indian Ocean" 10576: 8535: 11338: 11086: 9371: 8931:, aluminium is frequently used rather than copper (Cu) because it is lighter for the same conductance. 6949: 3966: 3924: 328: 251: 131: 11057:. James R. Chelikowsky, Steven G. Louie. Boston: Kluwer Academic Publishers. 1996. pp. 219–250. 9401: 3996: 3916: 8652: 1612:

means that the material has different properties in different directions. For example, a crystal of

11284: 11006: 8922:

In some applications where the weight of an item is very important, the product of resistivity and

4845: 1712:

are vectors. These tensors can be represented by 3×3 matrices, the vectors with 3×1 matrices, with

767: 11243:

Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics

10147: 9459:

portion of the resistivity. For example, at 30 °C (303 K), the resistivity of silver is

7337: 2088: 2011: 11219: 10384:

Douglas Giancoli (2009) . "25 Electric Currents and Resistance". In Jocelyn Phillips (ed.).

8602: 8578: 8155: 7953: 7937: 7731: 7625: 7165: 5149: 4852:. However, the existence of charged particles causes the plasma to generate, and be affected by, 4730:

Differentiating this relation provides a means to calculate the electric field from the density:

4100: 3974: 3954: 1716:

used on the right side of these equations. In matrix form, the resistivity relation is given by:

10309: 9677:

This value range is typical of high quality drinking water and not an indicator of water quality

3828: 3798: 3768: 3458: 10730: 10622: 9837:

Handbook of carbon, graphite, diamond, and fullerenes: properties, processing, and applications

9333: 8597:). Impedivity is the sum of a real component, the resistivity, and an imaginary component, the 8450: 8167: 7711: 7200: 7013:

tidily summed up the nature of the metals' dealings with electrons in his popular science book

5272: 5023: 4901:

Usually very high: for many purposes, the conductivity of a plasma may be treated as infinite.

4554: 4527: 4123: 4104: 19:

This article is about electrical conductivity in general. For other types of conductivity, see

10262: 10256: 9967: 9764: 9727: 7584: 7379:

Free electron model § Mean free dependence of the resistivity of gold, copper and silver.

1052: 10922:"What we can learn from measurements of air electric conductivity in 222Rn - rich atmosphere" 9525:

Copper is widely used in electrical equipment, building wiring, and telecommunication cables.

8911: 8897: 7925: 7907: 7819: 7317: 7297: 7276: 7254: 7146: 5123: 4996: 4633: 4491: 4288: 4175: 1713: 715: 467: 432: 10937: 10762: 10181: 10042: 9899:"Finite-difference modelling of magnetotelluric fields in two-dimensional anisotropic media" 4149:, electrical conduction happens not by band electrons or holes, but by full atomic species ( 11314:

https://edu-physics.com/2021/01/07/resistivity-of-the-material-of-a-wire-physics-practical/

11144: 11018: 10933: 10892: 10350: 8594: 8508: 8477: 8403: 7837: 7807:{\displaystyle {\kappa \over \sigma }={\pi ^{2} \over 3}\left({\frac {k}{e}}\right)^{2}T,} 7689: 7362: 7227: 7173: 7056: 5034: 4861: 4547: 4464: 4437: 4410: 4215: 3858: 885: 723: 559: 10455:. (PDF format; see page 2, table in the right lower corner). Retrieved on 2011-12-17. 8430: 7051:

The electrical resistivity of most materials changes with temperature. If the temperature

1154: 1103: 8: 10413: 9595: 9565: 9552: 9538:. The unit for expressing the conductivity of nonmagnetic materials by testing using the 9416: 9411: 8928: 8887: 7027: 7009:

The extremely low resistivity (high conductivity) of silver is characteristic of metals.

4834: 4026: 11148: 11022: 10896: 10354: 11165: 11132: 11080: 10603: 10366: 10296: 9915: 9898: 9381: 8383: 8363: 8163: 7965: 7887: 7867: 7861: 7843: 5062:

is normally used to measure conductivity in a solution. A rough summary is as follows:

4645: 4390: 4195: 4076: 4044: 1187: 1132: 1081: 799: 749: 697: 529: 521: 11272: 10655: 10502:. (Calculated as "15% conductivity of pure copper" (5.96E-7)). Retrieved on 2023-1-12. 10466:. (Calculated as "28% conductivity of pure copper" (5.96E-7)). Retrieved on 2023-1-12. 10436:. (Calculated as "56% conductivity of pure copper" (5.96E-7)). Retrieved on 2023-1-12. 10341:

Matula, R.A. (1979). "Electrical resistivity of copper, gold, palladium, and silver".

10208: 4721:{\displaystyle n_{\text{e}}\propto \exp \left(e\Phi /k_{\text{B}}T_{\text{e}}\right).} 404:{\displaystyle {\mathsf {M}}^{-1}{\mathsf {L}}^{-3}{\mathsf {T}}^{3}{\mathsf {I}}^{2}} 11246: 11170: 11068: 11058: 11034: 10985: 10862: 10839:

ASTM D1125 Standard Test Methods for Electrical Conductivity and Resistivity of Water

10822: 10768: 10711: 10689: 10639: 10609: 10558: 10393: 10323: 10313: 10266: 10187: 10163: 10127: 10075: 9996: 9881: 9861: 9840: 9804: 9770: 9733: 9329: 7961: 7715: 7704: 7650: 6185: 4517: 4084: 3989: 3920: 3429: 2142: 815: 428: 11201: 10804: 10511: 10370: 7710:

An investigation of the low-temperature resistivity of metals was the motivation to

4971:

Binary: two-particle collisions are the rule, three-body collisions extremely rare.

11160: 11152: 11133:"Stability and conductivity of self-assembled wires in a transverse electric field" 11026: 10941: 10900: 10814: 10548: 10358: 9931: 9910: 9396: 8634: 7940:

resistivity decreases with increasing temperature. The electrons are bumped to the

7673: = 2 implies that the resistance is due to electron–electron interaction. 6397: 6048: 5027: 4875: 4575: 4562: 436: 11007:"Die Abhängigkeit des elektrischen Widerstandes reiner Metalle von der Temperatur" 10095: 7383:

In general, electrical resistivity of metals increases with temperature. Electron–

4580: 200:{\displaystyle {\mathsf {M}}{\mathsf {L}}^{3}{\mathsf {T}}^{-3}{\mathsf {I}}^{-2}} 10967: 10737: 10686:

Protective coatings and thin films: synthesis, characterization, and applications

10452: 10117: 8248: 7941: 6712: 6149: 5824: 5083: 4941: 4937: 4874:

after solid, liquids and gases. It is distinct from these and other lower-energy

4870: 4592:

Plasmas are very good conductors and electric potentials play an important role.

4114: 4072: 4056: 3889: 3883: 3855:, is enough to describe the electrical resistivity. It is then written as simply 1181: 971: 830: 10984:. McGraw-Hill technical education. Maidenhead, UK: McGraw-Hill. pp. 36–40. 3965:; however, in semiconductors the bands are near enough to the Fermi level to be 10970:. US Dep. of Commerce. National Bureau of Standards Handbook. February 21, 1966 10960: 10017: 9325: 8609: 8586: 7678: 7619: 6601: 5133: 4853: 4641: 4118: 4117:(see Band Theory, above) giving rise to free conduction electrons. However, in 4068: 2214:

In either case, the resulting expression for each electric field component is:

1323: — because even a small electric field pulls a lot of current through it. 1212:

Conductivity is the inverse (reciprocal) of resistivity. Here, it is given by:

967: 954: 524:

of materials, giving the opposition of a standard cube of material to current.

513: 493: 440: 3059:{\displaystyle \mathbf {J} _{i}={\boldsymbol {\sigma }}_{ij}\mathbf {E} _{j},} 11322: 11292:

Comparison of the electrical conductivity of various elements in WolframAlpha

11038: 11030: 10562: 10389: 10305: 9638: 9366: 8939:

Resistivity, density, and resistivity-density products of selected materials

7957: 7945: 7611: 7365:

is inadequate and a more detailed analysis and understanding should be used.

5156:

Resistivity, conductivity, and temperature coefficient for several materials

5103: 5038: 5007: 4841: 4543: 4165:, currents are carried by ionic salts. Small holes in cell membranes, called 4162: 4096: 3970: 3958: 2205:{\displaystyle \mathbf {E} _{i}={\boldsymbol {\rho }}_{ij}\mathbf {J} _{j}~.} 11072: 10537:"Free-surface instabilities during electromagnetic shaping of liquid metals" 10327: 11174: 10826: 10553: 10536: 10476:

IITC – Imec Presents Copper, Cobalt and Ruthenium Interconnect Results

9539: 8883: 8630: 8566: 8502: 8350:{\displaystyle \rho (T)=\rho _{0}+aT^{2}+bT^{5}+c_{m}\ln {\frac {\mu }{T}}} 7949: 7615: 7010: 6920: 5918: 4857: 4849: 4822: 4628: 4604: 4158: 4154: 1598: 568: 447: 73: 8644: 11280: 11202:"Berryllium (Be) - Chemical properties, Health and Environmental effects" 11052: 10946: 10921: 10905: 10880: 10261:(2nd ed.). Fort Worth, Texas; London: Saunders College Pub. p. 9456: 9406: 8623: 8613: 8577:

When analyzing the response of materials to alternating electric fields (

7682: 6821: 6351: 5113: 5015: 4945: 4637:

are formed, the charge separation can extend some tens of Debye lengths.

4522: 4166: 4146: 4110: 4005: 4001: 3944: 3906: 3452: 466:

solid cube of material has sheet contacts on two opposite faces, and the

9858:

An introduction to Tensor Analysis: For Engineers and Applied Scientists

7944:

by thermal energy, where they flow freely, and in doing so leave behind

4992:

A conductor such as a metal has high conductivity and a low resistivity.

4169:, are selective to specific ions and determine the membrane resistance. 8618: 8149: 6113: 5046: 3911: 3485:

is nonzero. In the Hall effect, due to rotational invariance about the

1609: 1602: 1383:

Since the electric field is constant, it is given by the total voltage

545: 11156: 10818: 9542:

method. Generally used for temper and alloy verification of aluminium.

4542:, this decrease is limited by impurities and other defects. Even near 3584:, so the relation between resistivity and conductivity simplifies to: 1298:{\displaystyle \sigma (x)={\frac {1}{\rho (x)}}={\frac {J(x)}{E(x)}}.} 16:

Measure of a substance's ability to resist or conduct electric current

10362: 10123: 10018:"Questions & Answers – How do you explain electrical resistance?" 9587: 9177: 9149: 9123: 9097: 6541: 6511: 6279: 6250: 5984: 5651: 5347: 4914: 4584: 3940: 10160:

The Fourth State of Matter: An Introduction to the Physics of Plasma

9551:

Despite being less conductive than copper, gold is commonly used in

7392:

of a metal can be approximated through the Bloch–Grüneisen formula:

4980: 1209:

The current density is parallel to the electric field by necessity.

10148:

Flashes in the Sky: Earth's Gamma-Ray Bursts Triggered by Lightning

9642: 8162:

In non-crystalline semiconductors, conduction can occur by charges

6449: 6346: 6309: 6077: 6011: 5752: 5477: 5059: 4921: 4826: 3962: 3923:

for a certain energy in the material listed. The shade follows the

1613: 555: 549:

A piece of resistive material with electrical contacts on both ends

532:

that give the opposition of a specific object to electric current.

8608:

Conversely, in such cases the conductivity must be expressed as a

3915:

Filling of the electronic states in various types of materials at

10675:

Probably, the metal with highest value of electrical resistivity.

10636:

Schaum's outline of theory and problems of basic circuit analysis

10445: 10424:– via Internet Archive - archive.org (archived 2001-03-10). 9071: 9045: 8956: 8923: 7197:

is a fixed reference temperature (usually room temperature), and

6799: 6646: 6221: 5889: 5853: 5680: 5448: 5412: 5031: 4933: 4910: 4075:. The mechanism is similar to transfer of momentum of balls in a 4064: 234: 52: 10878: 10488:"Temperature Coefficient of Resistance | Electronics Notes" 9686:

Conductivity is lowest with monatomic gases present; changes to

512:) are sometimes used. The SI unit of electrical conductivity is 9591: 9583: 9231: 9203: 9019: 7952:, which also flow freely. The electric resistance of a typical 7384: 6899: 5615: 5578: 5275: 5236: 5200: 4929: 4644:. A common example is to assume that the electrons satisfy the 4539: 4535: 4378:{\displaystyle \sigma =q\left(b^{+}+b^{-}\right)\alpha N_{0}~,} 4127: 1697: 741: 9319: 4909:

One: all gas particles behave in a similar way, influenced by

3884:

Relation between current density and electric current velocity

2083:

is the resistivity tensor, in general a three by three matrix;

10119:

SQUIDS, the Josephson Effects and Superconducting Electronics

9616:

Nickel-iron-chromium alloy commonly used in heating elements.

8976:, i.e. cross-sectional area required to give same conductance 8734:{\displaystyle J=\sigma E\,\,\rightleftharpoons \,\,E=\rho J} 8120:{\displaystyle {\frac {1}{T}}=A+B\ln \rho +C(\ln \rho )^{3},} 7294:. Because the linear approximation is only an approximation, 6770: 5549: 5383: 5152:

of various materials at 20 °C (68 °F; 293 K).

5093: 5042: 5011: 5000: 4212:

to the concentration of molecules of the dissolved substance

4052: 3936: 784: 517: 509: 501: 459: 9287: 9259: 6970: 6682: 6480: 5948: 5716: 5513: 5311: 4060: 2141:

Equivalently, resistivity can be given in the more compact

11296: 10919: 10788: 10786: 10784: 10764:

Crystal Growth and Evaluation of Silicon for VLSI and ULSI

8240:= 2, 3, 4, depending on the dimensionality of the system. 3765:

If the electric field is parallel to the applied current,

1078:

is the resistivity of the conductor material at the point

571:) is the constant of proportionality. This is written as: 11220:"From Benjamin Franklin to Jan Ingenhousz, 18 March 1774" 8033:{\displaystyle \rho =\rho _{0}e^{\frac {E_{A}}{k_{B}T}}.} 6842: 5788: 4925: 4488:: concentration of molecules of the dissolved substance, 4150: 2107:

is the electric current density vector, with components (

780: 455: 10386:

Physics for Scientists and Engineers with Modern Physics

9702:

upon equilibration to the atmosphere due to dissolved CO

8612:(or even as a matrix of complex numbers, in the case of 8251:

are materials where the resistivity follows the formula

4631:

there can be charge imbalance. In the special case that

23:. For specific applications in electrical elements, see 10781: 9896: 8645:

Resistance versus resistivity in complicated geometries

8572: 776: 563:

cross-sectional area, where the electrical resistivity

451: 9654:

Corresponds to an average salinity of 35 g/kg at

8990: 7271:

is an empirical parameter fitted from measurement data

7030:

gives a basic description of electron flow in metals.

4461:: mobility of positively and negatively charged ions, 2941: 2788: 2731: 1940: 1787: 1730: 1335:

Derivation of the constant case from the general case

9607:

18% chromium and 8% nickel austenitic stainless steel

8749: 8699: 8655: 8538: 8511: 8480: 8453: 8433: 8406: 8386: 8366: 8260: 8176: 8166:

from one localised site to another. This is known as

8054: 7976: 7910: 7890: 7870: 7846: 7822: 7742: 7628: 7587: 7400: 7340: 7320: 7300: 7279: 7257: 7230: 7203: 7176: 7149: 7065: 4736: 4654: 4494: 4467: 4440: 4413: 4393: 4313: 4291: 4247: 4218: 4198: 4178: 3861: 3831: 3801: 3771: 3592: 3541: 3495: 3461: 3412: 3390: 3076: 3010: 2725: 2569: 2222: 2153: 2091: 2067: 2014: 1724: 1625: 1551: 1487: 1439: 1399: 1351: 1220: 1190: 1157: 1135: 1106: 1084: 1055: 982: 921: 888: 841: 752: 726: 700: 611: 579: 338: 297: 254: 141: 97: 9455:

The numbers in this column increase or decrease the

9387:

Electrical resistivities of the elements (data page)

9332:

relates an experiment by another British scientist,

7928:. The ratio on the rhs is called the Lorenz number. 4987:

Electrical resistivities of the elements (data page)

4936:

can be distinguished by the sign and value of their

4157:

is a reasonable electrical conductor. Conduction in

3878: 10601: 10043:"Electromigration : What is electromigration?" 4090: 10295: 9769:. New Delhi: Laxmi Publications. pp. 280–84. 8860: 8733: 8678: 8557: 8524: 8493: 8466: 8439: 8419: 8392: 8372: 8349: 8227:{\displaystyle \rho =A\exp \left(T^{-1/n}\right),} 8226: 8119: 8032: 7916: 7896: 7876: 7852: 7828: 7806: 7641: 7602: 7571: 7353: 7326: 7306: 7285: 7263: 7243: 7216: 7189: 7155: 7133: 4811: 4720: 4500: 4480: 4453: 4426: 4399: 4377: 4297: 4275: 4231: 4204: 4192:, which is the ratio of the concentration of ions 4184: 3867: 3847: 3817: 3787: 3755: 3576: 3527: 3477: 3420: 3398: 3374: 3058: 2992: 2707: 2526: 2204: 2099: 2075: 2022: 1994: 1674: 1576: 1519: 1461: 1421: 1373: 1297: 1196: 1172: 1141: 1121: 1090: 1070: 1035: 943: 894: 866: 758: 732: 706: 680: 598: 403: 316: 272: 199: 119: 11260:Measuring Electrical Resistivity and Conductivity 10795:. Transmission-line.net. Retrieved on 2014-02-03. 10254: 10179: 9372:Classification of materials based on permittivity 9324:In a 1774 letter to Dutch-born British scientist 8961: 8955: 8946: 8585:, it is convenient to replace resistivity with a 5189: 5176: 5163: 4981:Resistivity and conductivity of various materials 807:, but a long, thin copper wire has a much larger 11320: 11130: 10541:Proceedings in Applied Mathematics and Mechanics 10388:(4th ed.). Upper Saddle River, New Jersey: 10383: 10304:(3rd ed.). Upper Saddle River, New Jersey: 9932:"The Quantum Hall Effect: TIFR Infosys Lectures" 7714:'s experiments that led in 1911 to discovery of 5054:, relative to the conductivity of pure water at 4134: 10859:Diamond: electronic properties and applications 10684:Y. Pauleau, Péter B. Barna, P. B. Barna (1997) 10534: 10343:Journal of Physical and Chemical Reference Data 10290: 9732:. Cambridge University Press. pp. 254–55. 4550:can persist indefinitely with no power source. 2030:is the electric field vector, with components ( 11108:A. Matthiessen, Progg. Anallen, 122, 47 (1864) 11099:A. Matthiessen, Rep. Brit. Ass. 32, 144 (1862) 10740:. Kayelaby.npl.co.uk. Retrieved on 2011-12-17. 10115: 10022:Thomas Jefferson National Accelerator Facility 8917: 5018:and composition of the semiconductor material. 3875:, and this reduces to the simpler expression. 1036:{\displaystyle \rho (x)={\frac {E(x)}{J(x)}},} 10879:S. D. Pawar; P. Murugavel; D. M. Lal (2009). 10760: 10710:(3rd ed.). Academic Press. p. 561. 10705: 1307:For example, rubber is a material with large 504:) (especially in electrical engineering) and 11191:. otto-schmitt.org. Retrieved on 2011-12-17. 10535:Karcher, Ch.; Kocourek, V. (December 2007). 10416:. United States National Bureau of Standards 10286: 10284: 10282: 5684: 5655: 5619: 5582: 5553: 5517: 5481: 5452: 5416: 5351: 5279: 5240: 5204: 5003:has low conductivity and a high resistivity. 3919:. Here, height is energy while width is the 3888:Electric current is the ordered movement of 2540:-axis parallel to the current direction, so 960: 825:The above equation can be transposed to get 11240: 10597: 10595: 10071:Introduction to the Theory of Liquid Metals 9803:. Prentice Hall Professional. p. 114. 9377:Conductivity near the percolation threshold 9320:John Walsh and the conductivity of a vacuum 6189: 6153: 6117: 6081: 6052: 6015: 5952: 5923: 5893: 5857: 5828: 5792: 5756: 5720: 1520:{\displaystyle \rho ={\frac {VA}{I\ell }}.} 1387:across the conductor divided by the length 944:{\displaystyle \sigma ={\frac {1}{\rho }}.} 775:The resistivity can be expressed using the 599:{\displaystyle R\propto {\frac {\ell }{A}}} 10754: 10250: 10248: 10246: 10244: 10242: 9929: 9878:The Cambridge Handbook of Physics Formulas 6284: 6254: 6225: 5387: 4526:Original data from the 1911 experiment by 3825:are zero. When they are zero, one number, 1577:{\displaystyle \rho =R{\frac {A}{\ell }}.} 867:{\displaystyle R=\rho {\frac {\ell }{A}}.} 474:, then the resistivity of the material is 317:{\displaystyle \sigma ={\frac {1}{\rho }}} 11187:Otto H. Schmitt, University of Minnesota 11164: 11004: 10945: 10904: 10552: 10279: 10240: 10238: 10236: 10234: 10232: 10230: 10228: 10226: 10224: 10222: 9960: 9914: 9831: 9829: 9827: 8805: 8804: 8800: 8799: 8718: 8717: 8713: 8712: 7559: 7041: 6313: 3900: 3895: 1650: 1649: 1645: 1644: 974:of the current it creates at that point: 120:{\displaystyle \rho =R{\frac {A}{\ell }}} 11217: 10592: 10377: 6754: 6668: 6527: 6435: 6135: 6099: 4821:(∇ is the vector gradient operator; see 4579: 4521: 4030: 3910: 544: 520:(S/m). Resistivity and conductivity are 10920:E. Seran; M. Godefroy; E. Pili (2016). 10708:Engineering materials science, Volume 1 10608:(4th ed.). London: Prentice Hall. 10015: 9796: 9633: 9631: 7334:was measured at with a suffix, such as 7046: 6933: 6659: 6332: 6207: 6171: 5988: 5970: 5875: 5810: 5774: 5738: 5702: 5637: 5600: 5535: 5499: 5434: 5369: 5333: 5315: 5297: 5258: 5222: 4553:In a class of superconductors known as 3421:{\displaystyle {\boldsymbol {\sigma }}} 3414: 3392: 3028: 2171: 2069: 1660: 1635: 11321: 10699: 10340: 10219: 10109: 9897:Josef Pek, Tomas Verner (3 Apr 2007). 9824: 9725: 9536:International Annealed Copper Standard 8950: 7725: 6924: 6745: 6725: 6515: 6418: 6355: 6322: 6293: 6263: 6234: 6198: 6162: 6126: 6090: 6061: 6024: 5997: 5961: 5932: 5902: 5866: 5837: 5801: 5765: 5729: 5693: 5664: 5628: 5591: 5562: 5526: 5490: 5461: 5425: 5396: 5324: 5288: 5249: 5213: 4285:The specific electrical conductivity ( 3577:{\displaystyle \rho _{yx}=-\rho _{xy}} 1479:into the first expression, we obtain: 454:unit of electrical resistivity is the 390: 376: 359: 342: 183: 166: 152: 144: 11329:Electrical resistance and conductance 11213: 11211: 10605:Physics: Principles with Applications 10067: 9762: 9579: 9577: 8995: 8988: 6984: 6958: 6908: 6883: 6855: 6830: 6808: 6783: 6716: 6650: 6484: 6464: 5360: 3528:{\displaystyle \rho _{yy}=\rho _{xx}} 3399:{\displaystyle {\boldsymbol {\rho }}} 2076:{\displaystyle {\boldsymbol {\rho }}} 1592: 1422:{\displaystyle E={\frac {V}{\ell }}.} 1374:{\displaystyle \rho ={\frac {E}{J}},} 718:of a uniform specimen of the material 526:Electrical resistance and conductance 25:Electrical resistance and conductance 10979: 10206: 9988: 9758: 9756: 9641:depends strongly on the presence of 9628: 8639:Mathematical descriptions of opacity 8573:Complex resistivity and conductivity 6975: 6953: 6903: 6874: 6825: 6803: 6774: 6696: 6622: 6585: 6568: 6545: 6494: 6455: 6401: 5066:Resistivity of classes of materials 4511: 11131:Stephenson, C.; Hubler, A. (2015). 10807:The Journal of Physical Chemistry B 10638:, p. 19, McGraw-Hill Professional, 9766:Comprehensive Physics for Class XII 9555:because it does not easily corrode. 8637:the material is). For details, see 8243: 8170:and has the characteristic form of 8148:This equation is used to calibrate 7134:{\displaystyle \rho (T)=\rho _{0},} 6846: 6687: 6605: 6554: 6372: 4508:: the coefficient of dissociation. 3953:lies inside at least one band. In 2717:Conductivity is defined similarly: 1617:the three-dimensional tensor form: 1129:is the electric field at the point 13: 11234: 11208: 10045:. Middle East Technical University 9992:Electronics All-in-One For Dummies 9916:10.1111/j.1365-246X.1997.tb05314.x 9574: 8558:{\displaystyle \ln {\frac {1}{T}}} 7630: 7477: 7445: 7224:is the resistivity at temperature 5144:This table shows the resistivity ( 5045:, and other chemical species that 4780: 4682: 257: 14: 11350: 11265: 9903:Geophysical Journal International 9753: 9625:Graphite is strongly anisotropic. 9392:Electrical resistivity tomography 8693:In cases like this, the formulas 7931: 3879:Conductivity and current carriers 1462:{\displaystyle J={\frac {I}{A}}.} 1340:We will combine three equations. 913:, is the inverse of resistivity: 273:{\displaystyle \mathrm {s} ^{-1}} 11297:Partial and total conductivity. 11222:. In Willcox, William B. (ed.). 11054:Quantum theory of real materials 10731:Physical properties of sea water 10625:. hyperphysics.phy-astr.gsu.edu) 10162:, Publisher: Adam Hilger, 1989, 9694:upon complete de-gassing, or to 8886:. This equation, along with the 8848: 8840: 8832: 8815: 8807: 8792: 8784: 8776: 8759: 8751: 8156:Extrinsic (doped) semiconductors 5825:Phosphor Bronze (0.2% P / 5% Sn) 4738: 4559:high-temperature superconductors 4276:{\displaystyle N=\alpha N_{0}~.} 4091:In semiconductors and insulators 3384:Looking at the two expressions, 3043: 3013: 2186: 2156: 2093: 2016: 1665: 1652: 1640: 1627: 431:of a material that measures its 11245:(5th ed.). W. H. Freeman. 11224:The Papers of Benjamin Franklin 11194: 11181: 11124: 11111: 11102: 11093: 11045: 10998: 10973: 10954: 10913: 10885:Journal of Geophysical Research 10872: 10857:Lawrence S. Pan, Don R. Kania, 10851: 10842: 10833: 10798: 10743: 10724: 10678: 10669: 10648: 10628: 10569: 10528: 10516: 10512:Material properties of niobium. 10505: 10494: 10480: 10469: 10458: 10439: 10428: 10406: 10334: 10302:Introduction to Electrodynamics 10200: 10173: 10158:Yaffa Eliezer, Shalom Eliezer, 10152: 10140: 10088: 10061: 10035: 10009: 9982: 9948: 9680: 9671: 9661: 9648: 9619: 9610: 9601: 9558: 9545: 9528: 9519: 9505: 9502:is the temperature coefficient. 9449: 9439: 8583:electrical impedance tomography 3670: 2613: 10982:Electrical engineering science 10183:Fundamentals of Plasma Physics 10074:. Cambridge University Press. 9923: 9890: 9880:, Cambridge University Press, 9870: 9850: 9839:, p. 61, William Andrew, 1993 9790: 9719: 9430: 9012: 8999: 8973: 8908:partial differential equations 8852: 8844: 8836: 8828: 8819: 8811: 8801: 8796: 8788: 8780: 8772: 8763: 8755: 8714: 8688:spreading resistance profiling 8679:{\displaystyle R=\rho \ell /A} 8532:a lattice vibrations term and 8270: 8264: 8105: 8092: 7964:with temperature following an 7597: 7591: 7553: 7531: 7528: 7509: 7425: 7419: 7410: 7404: 7125: 7122: 7103: 7091: 7075: 7069: 1646: 1286: 1280: 1272: 1266: 1251: 1245: 1230: 1224: 1167: 1161: 1116: 1110: 1065: 1059: 1024: 1018: 1010: 1004: 992: 986: 645: 425:specific electrical resistance 1: 10751:. chemistry.stackexchange.com 9712: 6453:perpendicular to basal plane 4906:Independently acting species 4305:) of a solution is equal to: 4135:In ionic liquids/electrolytes 1529:Finally, we apply Ohm's law, 953:Conductivity has SI units of 540: 535: 11218:Franklin, Benjamin (1978) . 10602:Douglas C. Giancoli (1995). 10209:"Dielectric Strength of Air" 9968:"Current versus Drift Speed" 9800:Signal Integrity: Simplified 9598:fabricated in advanced nodes 9534:Referred to as 100% IACS or 7720:History of superconductivity 7354:{\displaystyle \alpha _{15}} 5014:, and, most important, with 4407:: module of the ion charge, 4020: 3978: 3961:the Fermi level is inside a 2100:{\displaystyle \mathbf {J} } 2023:{\displaystyle \mathbf {E} } 1331: 7: 10523:AISI 1010 Steel, cold drawn 9362:Charge transport mechanisms 9354: 8918:Resistivity-density product 8581:), in applications such as 8474:the residual resistivity, 8143:Steinhart–Hart coefficients 7642:{\displaystyle \Theta _{R}} 7622:of electrons in the metal. 7375:Bloch–Grüneisen temperature 5037:is highly dependent on its 4867:Plasma is often called the 4627:), but on the scale of the 4141:Conductivity (electrolytic) 3921:density of available states 435:or how strongly it resists 10: 11355: 10300:. In Alison Reeves (ed.). 10255:Raymond A. Serway (1998). 10180:Bittencourt, J.A. (2004). 9729:Fundamentals of Geophysics 9590:are considered to replace 9314: 7372: 7055:does not vary too much, a 7015:One, Two, Three...Infinity 4984: 4573: 4515: 4138: 4094: 4024: 3904: 3848:{\displaystyle \rho _{xx}} 3818:{\displaystyle \rho _{xz}} 3788:{\displaystyle \rho _{xy}} 3478:{\displaystyle \rho _{xy}} 3451:. This can be seen in the 1471:Plugging in the values of 470:between these contacts is 462:(Ω⋅m). For example, if a 18: 11299:"Electrical conductivity" 11273:"Electrical Conductivity" 10980:Ward, Malcolm R. (1971). 10861:, p. 140, Springer, 1994 9995:. John Wiley & Sons. 9402:SI electromagnetism units 9286: 9258: 9230: 9202: 9176: 9148: 9122: 9096: 9070: 9044: 9018: 8980: 8969: 8966: 8943: 8467:{\displaystyle \rho _{0}} 8447:are constant parameters, 7368: 7217:{\displaystyle \rho _{0}} 6969: 6948: 6919: 6898: 6871: 6841: 6820: 6798: 6769: 6740: 6711: 6681: 6645: 6600: 6565: 6540: 6510: 6479: 6448: 6396: 6345: 6308: 6278: 6249: 6220: 6184: 6148: 6112: 6076: 6046: 6010: 5983: 5947: 5917: 5888: 5852: 5823: 5787: 5751: 5715: 5679: 5650: 5614: 5577: 5548: 5512: 5476: 5447: 5411: 5382: 5346: 5310: 5271: 5235: 5199: 5194: 5160: 5132: 5122: 5112: 5102: 5092: 5082: 5073: 5070: 4569: 3997:Pauli exclusion principle 961:General scalar quantities 327: 284: 243: 233: 219: 214: 130: 84: 71: 61: 51: 39: 34: 11285:University of Nottingham 11031:10.1002/andp.19334080504 10767:. CRC Press. p. 7. 10297:"7 Electrodynamics" 9763:Kumar, Narinder (2003). 9726:Lowrie, William (2007). 9467:. This is calculated as 9423: 8972:Resistivity relative to 7884:is the electron charge, 7603:{\displaystyle \rho (0)} 4895:Electrical conductivity 4009:electrons at all times. 3988:According to elementary 3975:intrinsic semiconductors 3925:Fermi–Dirac distribution 1071:{\displaystyle \rho (x)} 10938:2017E&SS....4...91S 10926:Earth and Space Science 10793:Transmission Lines data 10186:. Springer. p. 1. 10116:John C. Gallop (1990). 9970:. The physics classroom 9930:David Tong (Jan 2016). 8912:finite element analysis 8579:dielectric spectroscopy 8044:Steinhart–Hart equation 7938:intrinsic semiconductor 7917:{\displaystyle \sigma } 7829:{\displaystyle \kappa } 7327:{\displaystyle \alpha } 7307:{\displaystyle \alpha } 7286:{\displaystyle \kappa } 7264:{\displaystyle \alpha } 7166:temperature coefficient 7156:{\displaystyle \alpha } 5150:temperature coefficient 4829:for more information.) 4555:type II superconductors 4501:{\displaystyle \alpha } 4298:{\displaystyle \sigma } 4185:{\displaystyle \alpha } 4101:Insulator (electricity) 3973:. "intrin." indicates 3935:: no state filled). In 1684:where the conductivity 482:Electrical conductivity 239:siemens per metre (S/m) 11085:: CS1 maint: others ( 11005:Grüneisen, E. (1933). 10761:Eranna, Golla (2014). 10706:Milton Ohring (1995). 10656:"Resistivity of steel" 10554:10.1002/pamm.200700645 10547:(1): 4140009–4140010. 9856:J.R. Tyldesley (1975) 9797:Bogatin, Eric (2004). 9568:with steel reinforced 9494:is the resistivity at 9352: 9343: 8967:Resistivity × density 8862: 8743:must be replaced with 8735: 8686:above. One example is 8680: 8616:materials) called the 8559: 8526: 8495: 8468: 8441: 8421: 8394: 8374: 8351: 8228: 8168:variable range hopping 8121: 8034: 7942:conduction energy band 7918: 7898: 7878: 7854: 7830: 7808: 7712:Heike Kamerlingh Onnes 7643: 7604: 7573: 7355: 7328: 7308: 7287: 7265: 7245: 7218: 7191: 7157: 7135: 7042:Temperature dependence 7026:More technically, the 7024: 5006:The conductivity of a 4953:Velocity distribution 4813: 4722: 4589: 4557:, including all known 4531: 4528:Heike Kamerlingh Onnes 4502: 4482: 4455: 4428: 4401: 4379: 4299: 4277: 4233: 4206: 4186: 4124:charge carrier density 4105:Charge carrier density 4048: 3985: 3931:: all states filled, 3901:Band theory simplified 3896:Causes of conductivity 3869: 3849: 3819: 3789: 3757: 3578: 3529: 3479: 3422: 3400: 3376: 3060: 2994: 2709: 2528: 2206: 2101: 2077: 2024: 1996: 1676: 1578: 1521: 1463: 1423: 1375: 1299: 1198: 1174: 1143: 1123: 1092: 1072: 1037: 945: 896: 868: 760: 734: 708: 682: 600: 550: 417:Electrical resistivity 405: 318: 274: 201: 121: 10634:John O'Malley (1992) 10258:Principles of Physics 9347: 9338: 8863: 8736: 8681: 8560: 8527: 8525:{\displaystyle T^{5}} 8496: 8494:{\displaystyle T^{2}} 8469: 8442: 8422: 8420:{\displaystyle c_{m}} 8395: 8375: 8352: 8229: 8122: 8035: 7926:electric conductivity 7919: 7899: 7879: 7855: 7831: 7809: 7683:Debye phonon spectrum 7644: 7605: 7574: 7356: 7329: 7309: 7288: 7266: 7246: 7244:{\displaystyle T_{0}} 7219: 7192: 7190:{\displaystyle T_{0}} 7158: 7136: 7019: 5024:semiconductors doping 4814: 4723: 4619:= ⟨Z⟩ > 4583: 4525: 4503: 4483: 4481:{\displaystyle N_{0}} 4456: 4454:{\displaystyle b^{-}} 4429: 4427:{\displaystyle b^{+}} 4402: 4380: 4300: 4278: 4234: 4232:{\displaystyle N_{0}} 4207: 4187: 4042: 3914: 3870: 3868:{\displaystyle \rho } 3850: 3820: 3790: 3758: 3579: 3530: 3480: 3423: 3401: 3377: 3061: 2995: 2710: 2529: 2207: 2102: 2078: 2025: 1997: 1714:matrix multiplication 1700:, and electric field 1677: 1579: 1522: 1464: 1424: 1376: 1300: 1199: 1175: 1144: 1124: 1093: 1073: 1038: 946: 897: 895:{\displaystyle \ell } 869: 761: 735: 733:{\displaystyle \ell } 716:electrical resistance 709: 683: 601: 548: 433:electrical resistance 406: 319: 275: 202: 122: 11241:Paul Tipler (2004). 11119:Physical Electronics 10947:10.1002/2016EA000241 10906:10.1029/2007JD009716 10688:, p. 215, Springer, 10660:The Physics Factbook 10623:Table of Resistivity 10414:"Copper wire tables" 10213:The Physics Factbook 10207:Hong, Alice (2000). 10068:Faber, T.E. (1972). 8929:overhead power lines 8747: 8697: 8653: 8595:electrical impedance 8536: 8509: 8478: 8451: 8440:{\displaystyle \mu } 8431: 8404: 8384: 8364: 8258: 8174: 8052: 7974: 7908: 7904:is temperature, and 7888: 7868: 7844: 7838:thermal conductivity 7820: 7740: 7701:residual resistivity 7690:Augustus Matthiessen 7626: 7585: 7398: 7363:linear approximation 7338: 7318: 7298: 7277: 7255: 7228: 7201: 7174: 7147: 7063: 7057:linear approximation 7047:Linear approximation 6566:Swimming pool water 5148:), conductivity and 5052:specific conductance 4862:magnetohydrodynamics 4734: 4652: 4548:superconducting wire 4492: 4465: 4438: 4411: 4391: 4311: 4289: 4245: 4216: 4196: 4176: 4163:biological membranes 3859: 3829: 3799: 3769: 3590: 3539: 3493: 3459: 3441:may not be equal to 3410: 3388: 3074: 3008: 2723: 2567: 2220: 2151: 2089: 2065: 2012: 1722: 1706:and current density 1623: 1549: 1485: 1437: 1397: 1349: 1218: 1188: 1173:{\displaystyle J(x)} 1155: 1133: 1122:{\displaystyle E(x)} 1104: 1082: 1053: 980: 919: 886: 839: 768:cross-sectional area 750: 724: 698: 609: 577: 530:extensive properties 522:intensive properties 486:specific conductance 336: 295: 252: 139: 95: 11334:Physical quantities 11149:2015NatSR...515044S 11121:, chapter 2, Pitman 11117:J. Seymour (1972) 11023:1933AnP...408..530G 10897:2009JGRD..114.2205P 10654:Glenn Elert (ed.), 10355:1979JPCRD...8.1147M 10170:, 226 pages, page 5 9989:Lowe, Doug (2012). 9637:The resistivity of 9596:integrated circuits 9566:overhead power line 9553:electrical contacts 9498:(in this case) and 9417:Dielectric strength 9412:Spitzer resistivity 8940: 8888:continuity equation 7732:Wiedemann–Franz law 7726:Wiedemann–Franz law 7495: 7059:is typically used: 7028:free electron model 5157: 5067: 4835:electrostatic force 4027:Free electron model 3967:thermally populated 3746: 3725: 3663: 3642: 3068:both resulting in: 427:) is a fundamental 11011:Annalen der Physik 10966:2010-08-21 at the 10961:Copper Wire Tables 10736:2018-01-18 at the 10451:2011-11-23 at the 10446:Physical constants 10126:. pp. 3, 20. 9564:Commonly used for 9382:Contact resistance 8981:Approx. price, at 8938: 8898:Poisson's equation 8858: 8731: 8676: 8555: 8522: 8491: 8464: 8437: 8417: 8390: 8370: 8347: 8224: 8164:quantum tunnelling 8141:are the so-called 8117: 8030: 7914: 7894: 7874: 7862:Boltzmann constant 7850: 7826: 7804: 7718:. For details see 7639: 7600: 7569: 7466: 7351: 7324: 7304: 7283: 7261: 7241: 7214: 7187: 7153: 7131: 6398:Carbon (amorphous) 5155: 5065: 4917:with one another. 4809: 4718: 4646:Boltzmann relation 4590: 4532: 4498: 4478: 4451: 4424: 4397: 4375: 4295: 4273: 4229: 4202: 4182: 4049: 3986: 3969:with electrons or 3865: 3845: 3815: 3785: 3753: 3729: 3708: 3646: 3625: 3574: 3525: 3475: 3418: 3396: 3372: 3367: 3056: 2990: 2984: 2930: 2774: 2705: 2524: 2522: 2202: 2097: 2073: 2020: 1992: 1983: 1929: 1773: 1672: 1593:Tensor resistivity 1574: 1517: 1459: 1419: 1391:of the conductor: 1371: 1295: 1194: 1170: 1139: 1119: 1088: 1068: 1033: 941: 892: 864: 800:intrinsic property 756: 730: 704: 678: 676: 596: 551: 528:are corresponding 421:volume resistivity 401: 314: 270: 197: 117: 75:SI base units 11339:Materials science 11252:978-0-7167-0810-0 11157:10.1038/srep15044 10819:10.1021/jp045975a 10774:978-1-4822-3281-3 10615:978-0-13-102153-2 10399:978-0-13-149508-1 10319:978-0-13-805326-0 10272:978-0-03-020457-9 10168:978-0-85274-164-1 10133:978-0-7503-0051-3 10002:978-0-470-14704-7 9886:978-0-521-57507-2 9835:Hugh O. Pierson, 9810:978-0-13-066946-9 9776:978-81-7008-592-8 9739:978-05-2185-902-8 9330:Benjamin Franklin 9312: 9311: 8978: 8914:may be required. 8553: 8393:{\displaystyle b} 8373:{\displaystyle a} 8345: 8063: 8024: 7897:{\displaystyle T} 7877:{\displaystyle e} 7853:{\displaystyle k} 7786: 7771: 7751: 7716:superconductivity 7705:superconductivity 7651:Debye temperature 7557: 7454: 6999: 6998: 6450:Carbon (graphite) 6347:Carbon (graphite) 5142: 5141: 4978: 4977: 4804: 4801: 4790: 4775: 4768: 4758: 4707: 4697: 4662: 4563:magnetic vortices 4518:Superconductivity 4512:Superconductivity 4400:{\displaystyle q} 4371: 4269: 4205:{\displaystyle N} 4040: 3990:quantum mechanics 3983: 3748: 3665: 2700: 2660: 2652: 2608: 2198: 2143:Einstein notation 1588: 1587: 1569: 1512: 1454: 1414: 1366: 1290: 1255: 1197:{\displaystyle x} 1142:{\displaystyle x} 1091:{\displaystyle x} 1028: 957:per metre (S/m). 936: 859: 816:hydraulic analogy 759:{\displaystyle A} 707:{\displaystyle R} 669: 637: 594: 429:specific property 414: 413: 312: 210: 209: 115: 11346: 11305: 11303: 11288: 11256: 11228: 11227: 11215: 11206: 11205: 11198: 11192: 11185: 11179: 11178: 11168: 11128: 11122: 11115: 11109: 11106: 11100: 11097: 11091: 11090: 11084: 11076: 11049: 11043: 11042: 11002: 10996: 10995: 10977: 10971: 10958: 10952: 10951: 10949: 10917: 10911: 10910: 10908: 10876: 10870: 10855: 10849: 10846: 10840: 10837: 10831: 10830: 10802: 10796: 10790: 10779: 10778: 10758: 10752: 10747: 10741: 10728: 10722: 10721: 10703: 10697: 10682: 10676: 10673: 10667: 10662:, retrieved and 10652: 10646: 10632: 10626: 10619: 10599: 10590: 10589: 10587: 10586: 10581: 10573: 10567: 10566: 10556: 10532: 10526: 10520: 10514: 10509: 10503: 10498: 10492: 10491: 10484: 10478: 10473: 10467: 10462: 10456: 10443: 10437: 10432: 10426: 10425: 10423: 10421: 10410: 10404: 10403: 10381: 10375: 10374: 10363:10.1063/1.555614 10338: 10332: 10331: 10299: 10288: 10277: 10276: 10252: 10217: 10216: 10204: 10198: 10197: 10177: 10171: 10156: 10150: 10144: 10138: 10137: 10113: 10107: 10106: 10104: 10102: 10092: 10086: 10085: 10065: 10059: 10058: 10052: 10050: 10039: 10033: 10032: 10030: 10028: 10013: 10007: 10006: 9986: 9980: 9979: 9977: 9975: 9964: 9958: 9952: 9946: 9945: 9943: 9941: 9936: 9927: 9921: 9920: 9918: 9894: 9888: 9874: 9868: 9854: 9848: 9833: 9822: 9821: 9819: 9817: 9794: 9788: 9787: 9785: 9783: 9760: 9751: 9750: 9748: 9746: 9723: 9706: 9701: 9699: 9693: 9691: 9684: 9678: 9675: 9669: 9665: 9659: 9657: 9652: 9646: 9645:in the material. 9635: 9626: 9623: 9617: 9614: 9608: 9605: 9599: 9581: 9572: 9562: 9556: 9549: 9543: 9532: 9526: 9523: 9517: 9509: 9503: 9501: 9497: 9493: 9484: 9466: 9464: 9453: 9447: 9443: 9437: 9434: 9397:Sheet resistance 9014: 9001: 8992: 8975: 8970: 8963: 8952: 8941: 8937: 8906:, form a set of 8905: 8895: 8881: 8875: 8867: 8865: 8864: 8859: 8851: 8843: 8835: 8818: 8810: 8795: 8787: 8779: 8762: 8754: 8740: 8738: 8737: 8732: 8685: 8683: 8682: 8677: 8672: 8589:quantity called 8564: 8562: 8561: 8556: 8554: 8546: 8531: 8529: 8528: 8523: 8521: 8520: 8500: 8498: 8497: 8492: 8490: 8489: 8473: 8471: 8470: 8465: 8463: 8462: 8446: 8444: 8443: 8438: 8426: 8424: 8423: 8418: 8416: 8415: 8399: 8397: 8396: 8391: 8379: 8377: 8376: 8371: 8356: 8354: 8353: 8348: 8346: 8338: 8330: 8329: 8317: 8316: 8301: 8300: 8285: 8284: 8249:Kondo insulators 8244:Kondo insulators 8239: 8233: 8231: 8230: 8225: 8220: 8216: 8215: 8211: 8140: 8136: 8132: 8126: 8124: 8123: 8118: 8113: 8112: 8064: 8056: 8039: 8037: 8036: 8031: 8026: 8025: 8023: 8019: 8018: 8008: 8007: 7998: 7992: 7991: 7923: 7921: 7920: 7915: 7903: 7901: 7900: 7895: 7883: 7881: 7880: 7875: 7859: 7857: 7856: 7851: 7835: 7833: 7832: 7827: 7813: 7811: 7810: 7805: 7797: 7796: 7791: 7787: 7779: 7772: 7767: 7766: 7757: 7752: 7744: 7695: 7672: 7666: 7660: 7648: 7646: 7645: 7640: 7638: 7637: 7609: 7607: 7606: 7601: 7578: 7576: 7575: 7570: 7558: 7556: 7552: 7551: 7521: 7520: 7507: 7506: 7497: 7494: 7490: 7485: 7484: 7474: 7465: 7464: 7459: 7455: 7453: 7452: 7440: 7391: 7360: 7358: 7357: 7352: 7350: 7349: 7333: 7331: 7330: 7325: 7313: 7311: 7310: 7305: 7293: 7292: 7290: 7289: 7284: 7270: 7268: 7267: 7262: 7251:. The parameter 7250: 7248: 7247: 7242: 7240: 7239: 7223: 7221: 7220: 7215: 7213: 7212: 7196: 7194: 7193: 7188: 7186: 7185: 7162: 7160: 7159: 7154: 7140: 7138: 7137: 7132: 7121: 7120: 7090: 7089: 7054: 7036: 7005: 6991: 6987: 6982: 6978: 6961: 6956: 6940: 6938: 6931: 6929: 6911: 6906: 6890: 6886: 6881: 6877: 6872:Wood (oven dry) 6863: 6859: 6853: 6849: 6833: 6828: 6812: 6806: 6800:Carbon (diamond) 6790: 6786: 6781: 6777: 6761: 6759: 6752: 6750: 6732: 6730: 6723: 6721: 6703: 6699: 6694: 6690: 6675: 6673: 6666: 6664: 6657: 6655: 6637: 6635: 6629: 6627: 6620: 6618: 6612: 6610: 6592: 6588: 6583: 6581: 6575: 6573: 6557: 6552: 6550: 6534: 6532: 6522: 6520: 6501: 6497: 6491: 6487: 6471: 6469: 6462: 6460: 6442: 6440: 6433: 6431: 6425: 6423: 6416: 6414: 6408: 6406: 6387: 6385: 6379: 6377: 6370: 6368: 6362: 6360: 6339: 6337: 6329: 6327: 6320: 6318: 6300: 6298: 6291: 6289: 6270: 6268: 6261: 6259: 6241: 6239: 6232: 6230: 6214: 6212: 6205: 6203: 6196: 6194: 6178: 6176: 6169: 6167: 6160: 6158: 6142: 6140: 6133: 6131: 6124: 6122: 6106: 6104: 6097: 6095: 6088: 6086: 6068: 6066: 6059: 6057: 6049:electrical steel 6040: 6038: 6031: 6029: 6022: 6020: 6004: 6002: 5995: 5993: 5977: 5975: 5968: 5966: 5959: 5957: 5939: 5937: 5930: 5928: 5909: 5907: 5900: 5898: 5882: 5880: 5873: 5871: 5864: 5862: 5844: 5842: 5835: 5833: 5817: 5815: 5808: 5806: 5799: 5797: 5781: 5779: 5772: 5770: 5763: 5761: 5745: 5743: 5736: 5734: 5727: 5725: 5709: 5707: 5700: 5698: 5691: 5689: 5671: 5669: 5662: 5660: 5644: 5642: 5635: 5633: 5626: 5624: 5607: 5605: 5598: 5596: 5589: 5587: 5569: 5567: 5560: 5558: 5542: 5540: 5533: 5531: 5524: 5522: 5506: 5504: 5497: 5495: 5488: 5486: 5468: 5466: 5459: 5457: 5441: 5439: 5432: 5430: 5423: 5421: 5403: 5401: 5394: 5392: 5376: 5374: 5367: 5365: 5358: 5356: 5340: 5338: 5331: 5329: 5322: 5320: 5304: 5302: 5295: 5293: 5286: 5284: 5265: 5263: 5256: 5254: 5247: 5245: 5229: 5227: 5220: 5218: 5211: 5209: 5192:coefficient (K) 5186: 5180: 5173: 5167: 5158: 5154: 5147: 5077: 5068: 5064: 5057: 4881: 4880: 4876:states of matter 4818: 4816: 4815: 4810: 4805: 4803: 4802: 4799: 4793: 4792: 4791: 4788: 4778: 4776: 4771: 4770: 4769: 4766: 4760: 4759: 4756: 4749: 4741: 4727: 4725: 4724: 4719: 4714: 4710: 4709: 4708: 4705: 4699: 4698: 4695: 4689: 4664: 4663: 4660: 4626: 4597:plasma potential 4576:Plasma (physics) 4507: 4505: 4504: 4499: 4487: 4485: 4484: 4479: 4477: 4476: 4460: 4458: 4457: 4452: 4450: 4449: 4433: 4431: 4430: 4425: 4423: 4422: 4406: 4404: 4403: 4398: 4384: 4382: 4381: 4376: 4369: 4368: 4367: 4355: 4351: 4350: 4349: 4337: 4336: 4304: 4302: 4301: 4296: 4282: 4280: 4279: 4274: 4267: 4266: 4265: 4238: 4236: 4235: 4230: 4228: 4227: 4211: 4209: 4208: 4203: 4191: 4189: 4188: 4183: 4043:An animation of 4041: 3979: 3890:electric charges 3874: 3872: 3871: 3866: 3854: 3852: 3851: 3846: 3844: 3843: 3824: 3822: 3821: 3816: 3814: 3813: 3794: 3792: 3791: 3786: 3784: 3783: 3762: 3760: 3759: 3754: 3749: 3747: 3745: 3740: 3724: 3719: 3706: 3705: 3704: 3688: 3683: 3682: 3666: 3664: 3662: 3657: 3641: 3636: 3623: 3622: 3610: 3605: 3604: 3583: 3581: 3580: 3575: 3573: 3572: 3554: 3553: 3534: 3532: 3531: 3526: 3524: 3523: 3508: 3507: 3488: 3484: 3482: 3481: 3476: 3474: 3473: 3450: 3440: 3427: 3425: 3424: 3419: 3417: 3405: 3403: 3402: 3397: 3395: 3381: 3379: 3378: 3373: 3368: 3364: 3363: 3354: 3353: 3338: 3337: 3328: 3327: 3312: 3311: 3302: 3301: 3282: 3281: 3268: 3267: 3258: 3257: 3242: 3241: 3232: 3231: 3216: 3215: 3206: 3205: 3186: 3185: 3172: 3171: 3162: 3161: 3146: 3145: 3136: 3135: 3120: 3119: 3110: 3109: 3090: 3089: 3065: 3063: 3062: 3057: 3052: 3051: 3046: 3040: 3039: 3031: 3022: 3021: 3016: 2999: 2997: 2996: 2991: 2989: 2988: 2981: 2980: 2967: 2966: 2953: 2952: 2935: 2934: 2927: 2926: 2912: 2911: 2897: 2896: 2880: 2879: 2865: 2864: 2850: 2849: 2833: 2832: 2818: 2817: 2803: 2802: 2779: 2778: 2771: 2770: 2757: 2756: 2743: 2742: 2714: 2712: 2711: 2706: 2701: 2699: 2698: 2689: 2688: 2679: 2674: 2673: 2661: 2658: 2653: 2651: 2650: 2641: 2640: 2631: 2626: 2625: 2609: 2607: 2606: 2597: 2596: 2587: 2582: 2581: 2560: 2539: 2533: 2531: 2530: 2525: 2523: 2516: 2515: 2506: 2505: 2490: 2489: 2480: 2479: 2464: 2463: 2454: 2453: 2434: 2433: 2417: 2416: 2407: 2406: 2391: 2390: 2381: 2380: 2365: 2364: 2355: 2354: 2335: 2334: 2318: 2317: 2308: 2307: 2292: 2291: 2282: 2281: 2266: 2265: 2256: 2255: 2236: 2235: 2211: 2209: 2208: 2203: 2196: 2195: 2194: 2189: 2183: 2182: 2174: 2165: 2164: 2159: 2135: 2106: 2104: 2103: 2098: 2096: 2082: 2080: 2079: 2074: 2072: 2058: 2029: 2027: 2026: 2021: 2019: 2001: 1999: 1998: 1993: 1988: 1987: 1980: 1979: 1966: 1965: 1952: 1951: 1934: 1933: 1926: 1925: 1911: 1910: 1896: 1895: 1879: 1878: 1864: 1863: 1849: 1848: 1832: 1831: 1817: 1816: 1802: 1801: 1778: 1777: 1770: 1769: 1756: 1755: 1742: 1741: 1711: 1705: 1695: 1690:and resistivity 1689: 1681: 1679: 1678: 1673: 1668: 1663: 1655: 1643: 1638: 1630: 1583: 1581: 1580: 1575: 1570: 1562: 1542: 1526: 1524: 1523: 1518: 1513: 1511: 1503: 1495: 1478: 1474: 1468: 1466: 1465: 1460: 1455: 1447: 1428: 1426: 1425: 1420: 1415: 1407: 1390: 1386: 1380: 1378: 1377: 1372: 1367: 1359: 1332: 1322: 1318: 1314: 1310: 1304: 1302: 1301: 1296: 1291: 1289: 1275: 1261: 1256: 1254: 1237: 1203: 1201: 1200: 1195: 1179: 1177: 1176: 1171: 1148: 1146: 1145: 1140: 1128: 1126: 1125: 1120: 1097: 1095: 1094: 1089: 1077: 1075: 1074: 1069: 1042: 1040: 1039: 1034: 1029: 1027: 1013: 999: 950: 948: 947: 942: 937: 929: 912: 905: 901: 899: 898: 893: 881: 877: 873: 871: 870: 865: 860: 852: 765: 763: 762: 757: 739: 737: 736: 731: 713: 711: 710: 705: 687: 685: 684: 679: 677: 670: 662: 644: 638: 630: 605: 603: 602: 597: 595: 587: 566: 507: 499: 491: 477: 476:1 Ω⋅m 473: 465: 445: 437:electric current 410: 408: 407: 402: 400: 399: 394: 393: 386: 385: 380: 379: 372: 371: 363: 362: 355: 354: 346: 345: 323: 321: 320: 315: 313: 305: 288:other quantities 286:Derivations from 279: 277: 276: 271: 269: 268: 260: 229: 212: 211: 206: 204: 203: 198: 196: 195: 187: 186: 179: 178: 170: 169: 162: 161: 156: 155: 148: 147: 126: 124: 123: 118: 116: 108: 88:other quantities 86:Derivations from 76: 67:s (Gaussian/ESU) 47: 32: 31: 11354: 11353: 11349: 11348: 11347: 11345: 11344: 11343: 11319: 11318: 11309: 11301: 11271: 11268: 11253: 11237: 11235:Further reading 11232: 11231: 11216: 11209: 11200: 11199: 11195: 11186: 11182: 11129: 11125: 11116: 11112: 11107: 11103: 11098: 11094: 11078: 11077: 11065: 11051: 11050: 11046: 11003: 10999: 10992: 10978: 10974: 10968:Wayback Machine 10959: 10955: 10918: 10914: 10877: 10873: 10856: 10852: 10847: 10843: 10838: 10834: 10803: 10799: 10791: 10782: 10775: 10759: 10755: 10748: 10744: 10738:Wayback Machine 10729: 10725: 10718: 10704: 10700: 10683: 10679: 10674: 10670: 10653: 10649: 10633: 10629: 10620: 10616: 10600: 10593: 10584: 10582: 10579: 10575: 10574: 10570: 10533: 10529: 10521: 10517: 10510: 10506: 10499: 10495: 10486: 10485: 10481: 10474: 10470: 10463: 10459: 10453:Wayback Machine 10444: 10440: 10433: 10429: 10419: 10417: 10412: 10411: 10407: 10400: 10392:. p. 658. 10382: 10378: 10339: 10335: 10320: 10292:David Griffiths 10289: 10280: 10273: 10253: 10220: 10205: 10201: 10194: 10178: 10174: 10157: 10153: 10145: 10141: 10134: 10114: 10110: 10100: 10098: 10094: 10093: 10089: 10082: 10066: 10062: 10048: 10046: 10041: 10040: 10036: 10026: 10024: 10014: 10010: 10003: 9987: 9983: 9973: 9971: 9966: 9965: 9961: 9953: 9949: 9939: 9937: 9934: 9928: 9924: 9895: 9891: 9876:G. Woan (2010) 9875: 9871: 9855: 9851: 9834: 9825: 9815: 9813: 9811: 9795: 9791: 9781: 9779: 9777: 9761: 9754: 9744: 9742: 9740: 9724: 9720: 9715: 9710: 9709: 9705: 9697: 9695: 9689: 9687: 9685: 9681: 9676: 9672: 9666: 9662: 9655: 9653: 9649: 9636: 9629: 9624: 9620: 9615: 9611: 9606: 9602: 9582: 9575: 9563: 9559: 9550: 9546: 9533: 9529: 9524: 9520: 9510: 9506: 9499: 9495: 9492: 9486: 9483: 9468: 9462: 9460: 9454: 9450: 9444: 9440: 9435: 9431: 9426: 9421: 9357: 9322: 9317: 9010: 9005: 8997: 8984: 8983:9 December 2018 8982: 8959: 8948: 8920: 8901: 8891: 8877: 8871: 8847: 8839: 8831: 8814: 8806: 8791: 8783: 8775: 8758: 8750: 8748: 8745: 8744: 8698: 8695: 8694: 8668: 8654: 8651: 8650: 8647: 8601:(in analogy to 8593:(in analogy to 8575: 8545: 8537: 8534: 8533: 8516: 8512: 8510: 8507: 8506: 8485: 8481: 8479: 8476: 8475: 8458: 8454: 8452: 8449: 8448: 8432: 8429: 8428: 8411: 8407: 8405: 8402: 8401: 8385: 8382: 8381: 8365: 8362: 8361: 8337: 8325: 8321: 8312: 8308: 8296: 8292: 8280: 8276: 8259: 8256: 8255: 8246: 8237: 8207: 8200: 8196: 8192: 8175: 8172: 8171: 8138: 8134: 8130: 8108: 8104: 8055: 8053: 8050: 8049: 8014: 8010: 8009: 8003: 7999: 7997: 7993: 7987: 7983: 7975: 7972: 7971: 7966:Arrhenius model 7934: 7909: 7906: 7905: 7889: 7886: 7885: 7869: 7866: 7865: 7845: 7842: 7841: 7821: 7818: 7817: 7792: 7778: 7774: 7773: 7762: 7758: 7756: 7743: 7741: 7738: 7737: 7728: 7693: 7670: 7664: 7658: 7633: 7629: 7627: 7624: 7623: 7586: 7583: 7582: 7544: 7540: 7516: 7512: 7508: 7502: 7498: 7496: 7486: 7480: 7476: 7475: 7470: 7460: 7448: 7444: 7439: 7435: 7434: 7399: 7396: 7395: 7389: 7381: 7371: 7345: 7341: 7339: 7336: 7335: 7319: 7316: 7315: 7299: 7296: 7295: 7278: 7275: 7274: 7272: 7256: 7253: 7252: 7235: 7231: 7229: 7226: 7225: 7208: 7204: 7202: 7199: 7198: 7181: 7177: 7175: 7172: 7171: 7148: 7145: 7144: 7116: 7112: 7085: 7081: 7064: 7061: 7060: 7052: 7049: 7044: 7034: 7003: 6989: 6985: 6980: 6976: 6959: 6954: 6936: 6934: 6927: 6925: 6909: 6904: 6888: 6884: 6879: 6875: 6861: 6857: 6851: 6847: 6831: 6826: 6810: 6804: 6788: 6784: 6779: 6775: 6757: 6755: 6748: 6746: 6742:Ultrapure water 6728: 6726: 6719: 6717: 6713:Deionized water 6701: 6697: 6692: 6688: 6671: 6669: 6662: 6660: 6653: 6651: 6633: 6631: 6625: 6623: 6616: 6614: 6608: 6606: 6590: 6586: 6579: 6577: 6571: 6569: 6555: 6548: 6546: 6530: 6528: 6518: 6516: 6502: 6499: 6495: 6492: 6489: 6485: 6467: 6465: 6458: 6456: 6452: 6438: 6436: 6429: 6427: 6421: 6419: 6412: 6410: 6404: 6402: 6388: 6383: 6381: 6375: 6373: 6366: 6364: 6358: 6356: 6349: 6335: 6333: 6330: 6325: 6323: 6316: 6314: 6296: 6294: 6287: 6285: 6266: 6264: 6257: 6255: 6237: 6235: 6228: 6226: 6210: 6208: 6201: 6199: 6192: 6190: 6174: 6172: 6165: 6163: 6156: 6154: 6150:Stainless steel 6138: 6136: 6129: 6127: 6120: 6118: 6102: 6100: 6093: 6091: 6084: 6082: 6064: 6062: 6055: 6053: 6047:Grain oriented 6036: 6034: 6027: 6025: 6018: 6016: 6000: 5998: 5991: 5989: 5973: 5971: 5964: 5962: 5955: 5953: 5935: 5933: 5926: 5924: 5905: 5903: 5896: 5894: 5878: 5876: 5869: 5867: 5860: 5858: 5840: 5838: 5831: 5829: 5813: 5811: 5804: 5802: 5795: 5793: 5777: 5775: 5768: 5766: 5759: 5757: 5741: 5739: 5732: 5730: 5723: 5721: 5705: 5703: 5696: 5694: 5687: 5685: 5667: 5665: 5658: 5656: 5640: 5638: 5631: 5629: 5622: 5620: 5608: 5603: 5601: 5594: 5592: 5585: 5583: 5565: 5563: 5556: 5554: 5538: 5536: 5529: 5527: 5520: 5518: 5502: 5500: 5493: 5491: 5484: 5482: 5464: 5462: 5455: 5453: 5437: 5435: 5428: 5426: 5419: 5417: 5399: 5397: 5390: 5388: 5372: 5370: 5363: 5361: 5354: 5352: 5336: 5334: 5327: 5325: 5318: 5316: 5300: 5298: 5291: 5289: 5282: 5280: 5261: 5259: 5252: 5250: 5243: 5241: 5225: 5223: 5216: 5214: 5207: 5205: 5191: 5184: 5182: 5178: 5171: 5169: 5165: 5145: 5134:Superinsulators 5084:Superconductors 5075: 5055: 4989: 4983: 4871:state of matter 4854:magnetic fields 4846:Debye screening 4837:dissipates it. 4798: 4794: 4787: 4783: 4779: 4777: 4765: 4761: 4755: 4751: 4750: 4748: 4737: 4735: 4732: 4731: 4704: 4700: 4694: 4690: 4685: 4678: 4674: 4659: 4655: 4653: 4650: 4649: 4625: 4618: 4612: 4609:quasineutrality 4601:space potential 4578: 4572: 4520: 4514: 4493: 4490: 4489: 4472: 4468: 4466: 4463: 4462: 4445: 4441: 4439: 4436: 4435: 4418: 4414: 4412: 4409: 4408: 4392: 4389: 4388: 4363: 4359: 4345: 4341: 4332: 4328: 4327: 4323: 4312: 4309: 4308: 4290: 4287: 4286: 4261: 4257: 4246: 4243: 4242: 4223: 4219: 4217: 4214: 4213: 4197: 4194: 4193: 4177: 4174: 4173: 4143: 4137: 4115:conduction band 4109:In metals, the 4107: 4095:Main articles: 4093: 4077:Newton's cradle 4073:current density 4045:Newton's cradle 4031: 4029: 4023: 3984: 3952: 3909: 3903: 3898: 3886: 3881: 3860: 3857: 3856: 3836: 3832: 3830: 3827: 3826: 3806: 3802: 3800: 3797: 3796: 3776: 3772: 3770: 3767: 3766: 3741: 3733: 3720: 3712: 3707: 3697: 3693: 3689: 3687: 3675: 3671: 3658: 3650: 3637: 3629: 3624: 3615: 3611: 3609: 3597: 3593: 3591: 3588: 3587: 3565: 3561: 3546: 3542: 3540: 3537: 3536: 3516: 3512: 3500: 3496: 3494: 3491: 3490: 3486: 3466: 3462: 3460: 3457: 3456: 3448: 3442: 3438: 3433: 3413: 3411: 3408: 3407: 3391: 3389: 3386: 3385: 3366: 3365: 3359: 3355: 3346: 3342: 3333: 3329: 3320: 3316: 3307: 3303: 3294: 3290: 3283: 3277: 3273: 3270: 3269: 3263: 3259: 3250: 3246: 3237: 3233: 3224: 3220: 3211: 3207: 3198: 3194: 3187: 3181: 3177: 3174: 3173: 3167: 3163: 3154: 3150: 3141: 3137: 3128: 3124: 3115: 3111: 3102: 3098: 3091: 3085: 3081: 3077: 3075: 3072: 3071: 3047: 3042: 3041: 3032: 3027: 3026: 3017: 3012: 3011: 3009: 3006: 3005: 2983: 2982: 2976: 2972: 2969: 2968: 2962: 2958: 2955: 2954: 2948: 2944: 2937: 2936: 2929: 2928: 2919: 2915: 2913: 2904: 2900: 2898: 2889: 2885: 2882: 2881: 2872: 2868: 2866: 2857: 2853: 2851: 2842: 2838: 2835: 2834: 2825: 2821: 2819: 2810: 2806: 2804: 2795: 2791: 2784: 2783: 2773: 2772: 2766: 2762: 2759: 2758: 2752: 2748: 2745: 2744: 2738: 2734: 2727: 2726: 2724: 2721: 2720: 2694: 2690: 2684: 2680: 2678: 2666: 2662: 2659: and 2657: 2646: 2642: 2636: 2632: 2630: 2618: 2614: 2602: 2598: 2592: 2588: 2586: 2574: 2570: 2568: 2565: 2564: 2561:. This leaves: 2558: 2549: 2541: 2537: 2521: 2520: 2511: 2507: 2498: 2494: 2485: 2481: 2472: 2468: 2459: 2455: 2446: 2442: 2435: 2429: 2425: 2422: 2421: 2412: 2408: 2399: 2395: 2386: 2382: 2373: 2369: 2360: 2356: 2347: 2343: 2336: 2330: 2326: 2323: 2322: 2313: 2309: 2300: 2296: 2287: 2283: 2274: 2270: 2261: 2257: 2248: 2244: 2237: 2231: 2227: 2223: 2221: 2218: 2217: 2190: 2185: 2184: 2175: 2170: 2169: 2160: 2155: 2154: 2152: 2149: 2148: 2139: 2134: 2125: 2116: 2108: 2092: 2090: 2087: 2086: 2068: 2066: 2063: 2062: 2057: 2048: 2039: 2031: 2015: 2013: 2010: 2009: 1982: 1981: 1975: 1971: 1968: 1967: 1961: 1957: 1954: 1953: 1947: 1943: 1936: 1935: 1928: 1927: 1918: 1914: 1912: 1903: 1899: 1897: 1888: 1884: 1881: 1880: 1871: 1867: 1865: 1856: 1852: 1850: 1841: 1837: 1834: 1833: 1824: 1820: 1818: 1809: 1805: 1803: 1794: 1790: 1783: 1782: 1772: 1771: 1765: 1761: 1758: 1757: 1751: 1747: 1744: 1743: 1737: 1733: 1726: 1725: 1723: 1720: 1719: 1707: 1701: 1691: 1685: 1664: 1659: 1651: 1639: 1634: 1626: 1624: 1621: 1620: 1595: 1561: 1550: 1547: 1546: 1530: 1504: 1496: 1494: 1486: 1483: 1482: 1476: 1472: 1446: 1438: 1435: 1434: 1406: 1398: 1395: 1394: 1388: 1384: 1358: 1350: 1347: 1346: 1320: 1316: 1312: 1308: 1276: 1262: 1260: 1241: 1236: 1219: 1216: 1215: 1207: 1189: 1186: 1185: 1182:current density 1156: 1153: 1152: 1134: 1131: 1130: 1105: 1102: 1101: 1083: 1080: 1079: 1054: 1051: 1050: 1014: 1000: 998: 981: 978: 977: 963: 928: 920: 917: 916: 910: 903: 887: 884: 883: 879: 875: 851: 840: 837: 836: 831:Claude Pouillet 773: 770:of the specimen 751: 748: 747: 744:of the specimen 725: 722: 721: 699: 696: 695: 675: 674: 661: 651: 643: 640: 639: 629: 619: 612: 610: 607: 606: 586: 578: 575: 574: 564: 543: 538: 505: 497: 489: 475: 471: 463: 443: 395: 389: 388: 387: 381: 375: 374: 373: 364: 358: 357: 356: 347: 341: 340: 339: 337: 334: 333: 304: 296: 293: 292: 289: 287: 261: 256: 255: 253: 250: 249: 246: 225: 222: 188: 182: 181: 180: 171: 165: 164: 163: 157: 151: 150: 149: 143: 142: 140: 137: 136: 107: 96: 93: 92: 89: 87: 74: 64: 57:ohm metre (Ω⋅m) 45: 42: 28: 17: 12: 11: 5: 11352: 11342: 11341: 11336: 11331: 11317: 11316: 11307: 11306: 11294: 11289: 11267: 11266:External links 11264: 11263: 11262: 11257: 11251: 11236: 11233: 11230: 11229: 11207: 11193: 11180: 11123: 11110: 11101: 11092: 11063: 11044: 11017:(5): 530–540. 10997: 10990: 10972: 10953: 10912: 10891:(D2): D02205. 10871: 10850: 10841: 10832: 10797: 10780: 10773: 10753: 10742: 10723: 10717:978-0125249959 10716: 10698: 10677: 10668: 10647: 10627: 10614: 10591: 10568: 10527: 10515: 10504: 10493: 10479: 10468: 10457: 10438: 10427: 10405: 10398: 10376: 10333: 10318: 10278: 10271: 10218: 10199: 10192: 10172: 10151: 10139: 10132: 10108: 10087: 10080: 10060: 10034: 10008: 10001: 9981: 9959: 9947: 9922: 9909:(3): 505–521. 9889: 9869: 9849: 9823: 9809: 9789: 9775: 9752: 9738: 9717: 9716: 9714: 9711: 9708: 9707: 9703: 9679: 9670: 9660: 9647: 9639:semiconductors 9627: 9618: 9609: 9600: 9573: 9557: 9544: 9527: 9518: 9504: 9490: 9481: 9448: 9438: 9428: 9427: 9425: 9422: 9420: 9419: 9414: 9409: 9404: 9399: 9394: 9389: 9384: 9379: 9374: 9369: 9364: 9358: 9356: 9353: 9326:Jan Ingenhousz 9321: 9318: 9316: 9313: 9310: 9309: 9307: 9305: 9302: 9299: 9296: 9293: 9290: 9284: 9283: 9280: 9277: 9274: 9271: 9268: 9265: 9262: 9256: 9255: 9252: 9249: 9246: 9243: 9240: 9237: 9234: 9228: 9227: 9224: 9221: 9218: 9215: 9212: 9209: 9206: 9200: 9199: 9197: 9195: 9192: 9189: 9186: 9183: 9180: 9174: 9173: 9170: 9167: 9164: 9161: 9158: 9155: 9152: 9146: 9145: 9143: 9141: 9138: 9135: 9132: 9129: 9126: 9120: 9119: 9117: 9115: 9112: 9109: 9106: 9103: 9100: 9094: 9093: 9091: 9089: 9086: 9083: 9080: 9077: 9074: 9068: 9067: 9065: 9063: 9060: 9057: 9054: 9051: 9048: 9042: 9041: 9039: 9037: 9034: 9031: 9028: 9025: 9022: 9016: 9015: 9007: 9002: 8994: 8986: 8985: 8979: 8968: 8965: 8954: 8945: 8919: 8916: 8857: 8854: 8850: 8846: 8842: 8838: 8834: 8830: 8827: 8824: 8821: 8817: 8813: 8809: 8803: 8798: 8794: 8790: 8786: 8782: 8778: 8774: 8771: 8768: 8765: 8761: 8757: 8753: 8730: 8727: 8724: 8721: 8716: 8711: 8708: 8705: 8702: 8675: 8671: 8667: 8664: 8661: 8658: 8646: 8643: 8610:complex number 8574: 8571: 8552: 8549: 8544: 8541: 8519: 8515: 8505:contribution, 8488: 8484: 8461: 8457: 8436: 8414: 8410: 8389: 8369: 8358: 8357: 8344: 8341: 8336: 8333: 8328: 8324: 8320: 8315: 8311: 8307: 8304: 8299: 8295: 8291: 8288: 8283: 8279: 8275: 8272: 8269: 8266: 8263: 8245: 8242: 8223: 8219: 8214: 8210: 8206: 8203: 8199: 8195: 8191: 8188: 8185: 8182: 8179: 8116: 8111: 8107: 8103: 8100: 8097: 8094: 8091: 8088: 8085: 8082: 8079: 8076: 8073: 8070: 8067: 8062: 8059: 8029: 8022: 8017: 8013: 8006: 8002: 7996: 7990: 7986: 7982: 7979: 7933: 7932:Semiconductors 7930: 7913: 7893: 7873: 7849: 7825: 7803: 7800: 7795: 7790: 7785: 7782: 7777: 7770: 7765: 7761: 7755: 7750: 7747: 7727: 7724: 7679:Brillouin zone 7675: 7674: 7668: 7662: 7636: 7632: 7620:number density 7599: 7596: 7593: 7590: 7568: 7565: 7562: 7555: 7550: 7547: 7543: 7539: 7536: 7533: 7530: 7527: 7524: 7519: 7515: 7511: 7505: 7501: 7493: 7489: 7483: 7479: 7473: 7469: 7463: 7458: 7451: 7447: 7443: 7438: 7433: 7430: 7427: 7424: 7421: 7418: 7415: 7412: 7409: 7406: 7403: 7370: 7367: 7348: 7344: 7323: 7303: 7282: 7260: 7238: 7234: 7211: 7207: 7184: 7180: 7168:of resistivity 7163:is called the 7152: 7130: 7127: 7124: 7119: 7115: 7111: 7108: 7105: 7102: 7099: 7096: 7093: 7088: 7084: 7080: 7077: 7074: 7071: 7068: 7048: 7045: 7043: 7040: 6997: 6996: 6994: 6992: 6983: 6974: 6967: 6966: 6964: 6962: 6957: 6952: 6946: 6945: 6943: 6941: 6932: 6923: 6917: 6916: 6914: 6912: 6907: 6902: 6896: 6895: 6893: 6891: 6882: 6873: 6869: 6868: 6866: 6864: 6854: 6845: 6839: 6838: 6836: 6834: 6829: 6824: 6818: 6817: 6815: 6813: 6807: 6802: 6796: 6795: 6793: 6791: 6782: 6773: 6767: 6766: 6764: 6762: 6753: 6744: 6738: 6737: 6735: 6733: 6724: 6715: 6709: 6708: 6706: 6704: 6695: 6686: 6679: 6678: 6676: 6667: 6658: 6649: 6643: 6642: 6640: 6638: 6621: 6604: 6602:Drinking water 6598: 6597: 6595: 6593: 6584: 6567: 6563: 6562: 6560: 6558: 6553: 6544: 6538: 6537: 6535: 6526: 6523: 6514: 6508: 6507: 6505: 6503: 6493: 6483: 6477: 6476: 6474: 6472: 6463: 6454: 6446: 6445: 6443: 6434: 6417: 6400: 6394: 6393: 6391: 6389: 6371: 6354: 6343: 6342: 6340: 6331: 6321: 6312: 6306: 6305: 6303: 6301: 6292: 6283: 6276: 6275: 6273: 6271: 6262: 6253: 6247: 6246: 6244: 6242: 6233: 6224: 6218: 6217: 6215: 6206: 6197: 6188: 6182: 6181: 6179: 6170: 6161: 6152: 6146: 6145: 6143: 6134: 6125: 6116: 6110: 6109: 6107: 6098: 6089: 6080: 6074: 6073: 6071: 6069: 6060: 6051: 6044: 6043: 6041: 6032: 6023: 6014: 6008: 6007: 6005: 5996: 5987: 5981: 5980: 5978: 5969: 5960: 5951: 5945: 5944: 5942: 5940: 5931: 5922: 5915: 5914: 5912: 5910: 5901: 5892: 5886: 5885: 5883: 5874: 5865: 5856: 5850: 5849: 5847: 5845: 5836: 5827: 5821: 5820: 5818: 5809: 5800: 5791: 5785: 5784: 5782: 5773: 5764: 5755: 5749: 5748: 5746: 5737: 5728: 5719: 5713: 5712: 5710: 5701: 5692: 5683: 5677: 5676: 5674: 5672: 5663: 5654: 5648: 5647: 5645: 5636: 5627: 5618: 5612: 5611: 5609: 5599: 5590: 5581: 5575: 5574: 5572: 5570: 5561: 5552: 5550:Brass (30% Zn) 5546: 5545: 5543: 5534: 5525: 5516: 5510: 5509: 5507: 5498: 5489: 5480: 5474: 5473: 5471: 5469: 5460: 5451: 5445: 5444: 5442: 5433: 5424: 5415: 5409: 5408: 5406: 5404: 5395: 5386: 5380: 5379: 5377: 5368: 5359: 5350: 5344: 5343: 5341: 5332: 5323: 5314: 5308: 5307: 5305: 5296: 5287: 5278: 5269: 5268: 5266: 5257: 5248: 5239: 5233: 5232: 5230: 5221: 5212: 5203: 5197: 5196: 5193: 5188: 5177:Conductivity, 5175: 5162: 5140: 5139: 5136: 5130: 5129: 5126: 5120: 5119: 5116: 5110: 5109: 5106: 5104:Semiconductors 5100: 5099: 5096: 5090: 5089: 5086: 5080: 5079: 5072: 5022:The degree of 5020: 5019: 5004: 4993: 4985:Main article: 4982: 4979: 4976: 4975: 4972: 4969: 4965: 4964: 4960: 4954: 4950: 4949: 4920:Two or three: 4918: 4907: 4903: 4902: 4899: 4896: 4892: 4891: 4888: 4885: 4808: 4797: 4786: 4782: 4774: 4764: 4754: 4747: 4744: 4740: 4717: 4713: 4703: 4693: 4688: 4684: 4681: 4677: 4673: 4670: 4667: 4658: 4642:charge density 4623: 4616: 4574:Main article: 4571: 4568: 4516:Main article: 4513: 4510: 4497: 4475: 4471: 4448: 4444: 4421: 4417: 4396: 4374: 4366: 4362: 4358: 4354: 4348: 4344: 4340: 4335: 4331: 4326: 4322: 4319: 4316: 4294: 4272: 4264: 4260: 4256: 4253: 4250: 4226: 4222: 4201: 4181: 4139:Main article: 4136: 4133: 4119:semiconductors 4092: 4089: 4069:drift velocity 4055:consists of a 4025:Main article: 4022: 4019: 3959:semiconductors 3950: 3902: 3899: 3897: 3894: 3885: 3882: 3880: 3877: 3864: 3842: 3839: 3835: 3812: 3809: 3805: 3782: 3779: 3775: 3752: 3744: 3739: 3736: 3732: 3728: 3723: 3718: 3715: 3711: 3703: 3700: 3696: 3692: 3686: 3681: 3678: 3674: 3669: 3661: 3656: 3653: 3649: 3645: 3640: 3635: 3632: 3628: 3621: 3618: 3614: 3608: 3603: 3600: 3596: 3571: 3568: 3564: 3560: 3557: 3552: 3549: 3545: 3522: 3519: 3515: 3511: 3506: 3503: 3499: 3472: 3469: 3465: 3446: 3436: 3430:matrix inverse 3416: 3394: 3371: 3362: 3358: 3352: 3349: 3345: 3341: 3336: 3332: 3326: 3323: 3319: 3315: 3310: 3306: 3300: 3297: 3293: 3289: 3286: 3284: 3280: 3276: 3272: 3271: 3266: 3262: 3256: 3253: 3249: 3245: 3240: 3236: 3230: 3227: 3223: 3219: 3214: 3210: 3204: 3201: 3197: 3193: 3190: 3188: 3184: 3180: 3176: 3175: 3170: 3166: 3160: 3157: 3153: 3149: 3144: 3140: 3134: 3131: 3127: 3123: 3118: 3114: 3108: 3105: 3101: 3097: 3094: 3092: 3088: 3084: 3080: 3079: 3055: 3050: 3045: 3038: 3035: 3030: 3025: 3020: 3015: 2987: 2979: 2975: 2971: 2970: 2965: 2961: 2957: 2956: 2951: 2947: 2943: 2942: 2940: 2933: 2925: 2922: 2918: 2914: 2910: 2907: 2903: 2899: 2895: 2892: 2888: 2884: 2883: 2878: 2875: 2871: 2867: 2863: 2860: 2856: 2852: 2848: 2845: 2841: 2837: 2836: 2831: 2828: 2824: 2820: 2816: 2813: 2809: 2805: 2801: 2798: 2794: 2790: 2789: 2787: 2782: 2777: 2769: 2765: 2761: 2760: 2755: 2751: 2747: 2746: 2741: 2737: 2733: 2732: 2730: 2704: 2697: 2693: 2687: 2683: 2677: 2672: 2669: 2665: 2656: 2649: 2645: 2639: 2635: 2629: 2624: 2621: 2617: 2612: 2605: 2601: 2595: 2591: 2585: 2580: 2577: 2573: 2554: 2545: 2519: 2514: 2510: 2504: 2501: 2497: 2493: 2488: 2484: 2478: 2475: 2471: 2467: 2462: 2458: 2452: 2449: 2445: 2441: 2438: 2436: 2432: 2428: 2424: 2423: 2420: 2415: 2411: 2405: 2402: 2398: 2394: 2389: 2385: 2379: 2376: 2372: 2368: 2363: 2359: 2353: 2350: 2346: 2342: 2339: 2337: 2333: 2329: 2325: 2324: 2321: 2316: 2312: 2306: 2303: 2299: 2295: 2290: 2286: 2280: 2277: 2273: 2269: 2264: 2260: 2254: 2251: 2247: 2243: 2240: 2238: 2234: 2230: 2226: 2225: 2201: 2193: 2188: 2181: 2178: 2173: 2168: 2163: 2158: 2138: 2137: 2130: 2121: 2112: 2095: 2084: 2071: 2060: 2053: 2044: 2035: 2018: 2006: 1991: 1986: 1978: 1974: 1970: 1969: 1964: 1960: 1956: 1955: 1950: 1946: 1942: 1941: 1939: 1932: 1924: 1921: 1917: 1913: 1909: 1906: 1902: 1898: 1894: 1891: 1887: 1883: 1882: 1877: 1874: 1870: 1866: 1862: 1859: 1855: 1851: 1847: 1844: 1840: 1836: 1835: 1830: 1827: 1823: 1819: 1815: 1812: 1808: 1804: 1800: 1797: 1793: 1789: 1788: 1786: 1781: 1776: 1768: 1764: 1760: 1759: 1754: 1750: 1746: 1745: 1740: 1736: 1732: 1731: 1729: 1671: 1667: 1662: 1658: 1654: 1648: 1642: 1637: 1633: 1629: 1594: 1591: 1590: 1589: 1586: 1585: 1573: 1568: 1565: 1560: 1557: 1554: 1516: 1510: 1507: 1502: 1499: 1493: 1490: 1458: 1453: 1450: 1445: 1442: 1418: 1413: 1410: 1405: 1402: 1370: 1365: 1362: 1357: 1354: 1337: 1336: 1294: 1288: 1285: 1282: 1279: 1274: 1271: 1268: 1265: 1259: 1253: 1250: 1247: 1244: 1240: 1235: 1232: 1229: 1226: 1223: 1206: 1205: 1193: 1169: 1166: 1163: 1160: 1150: 1138: 1118: 1115: 1112: 1109: 1099: 1087: 1067: 1064: 1061: 1058: 1047: 1032: 1026: 1023: 1020: 1017: 1012: 1009: 1006: 1003: 997: 994: 991: 988: 985: 968:electric field 962: 959: 940: 935: 932: 927: 924: 909:Conductivity, 891: 863: 858: 855: 850: 847: 844: 827:Pouillet's law 821: 810: 806: 772: 771: 755: 745: 729: 719: 703: 692: 673: 668: 665: 660: 657: 654: 652: 650: 647: 642: 641: 636: 633: 628: 625: 622: 620: 618: 615: 614: 593: 590: 585: 582: 567: (Greek: 542: 539: 537: 534: 412: 411: 398: 392: 384: 378: 370: 367: 361: 353: 350: 344: 331: 325: 324: 311: 308: 303: 300: 290: 285: 282: 281: 280:(Gaussian/ESU) 267: 264: 259: 247: 244: 241: 240: 237: 231: 230: 223: 221:Common symbols 220: 217: 216: 208: 207: 194: 191: 185: 177: 174: 168: 160: 154: 146: 134: 128: 127: 114: 111: 106: 103: 100: 90: 85: 82: 81: 78: 69: 68: 65: 62: 59: 58: 55: 49: 48: 43: 41:Common symbols 40: 37: 36: 15: 9: 6: 4: 3: 2: 11351: 11340: 11337: 11335: 11332: 11330: 11327: 11326: 11324: 11315: 11312: 11311: 11310: 11300: 11295: 11293: 11290: 11286: 11282: 11278: 11277:Sixty Symbols 11274: 11270: 11269: 11261: 11258: 11254: 11248: 11244: 11239: 11238: 11225: 11221: 11214: 11212: 11203: 11197: 11190: 11184: 11176: 11172: 11167: 11162: 11158: 11154: 11150: 11146: 11142: 11138: 11134: 11127: 11120: 11114: 11105: 11096: 11088: 11082: 11074: 11070: 11066: 11064:0-7923-9666-9 11060: 11056: 11055: 11048: 11040: 11036: 11032: 11028: 11024: 11020: 11016: 11012: 11008: 11001: 10993: 10991:9780070942554 10987: 10983: 10976: 10969: 10965: 10962: 10957: 10948: 10943: 10939: 10935: 10932:(2): 91–106. 10931: 10927: 10923: 10916: 10907: 10902: 10898: 10894: 10890: 10886: 10882: 10875: 10868: 10867:0-7923-9524-7 10864: 10860: 10854: 10845: 10836: 10828: 10824: 10820: 10816: 10813:(3): 1231–8. 10812: 10808: 10801: 10794: 10789: 10787: 10785: 10776: 10770: 10766: 10765: 10757: 10750: 10746: 10739: 10735: 10732: 10727: 10719: 10713: 10709: 10702: 10695: 10694:0-7923-4380-8 10691: 10687: 10681: 10672: 10666:16 June 2011. 10665: 10661: 10657: 10651: 10645: 10644:0-07-047824-4 10641: 10637: 10631: 10624: 10617: 10611: 10607: 10606: 10598: 10596: 10578: 10572: 10564: 10560: 10555: 10550: 10546: 10542: 10538: 10531: 10524: 10519: 10513: 10508: 10501: 10497: 10489: 10483: 10477: 10472: 10465: 10461: 10454: 10450: 10447: 10442: 10435: 10431: 10415: 10409: 10401: 10395: 10391: 10390:Prentice Hall 10387: 10380: 10372: 10368: 10364: 10360: 10356: 10352: 10348: 10344: 10337: 10329: 10325: 10321: 10315: 10311: 10307: 10306:Prentice Hall 10303: 10298: 10293: 10287: 10285: 10283: 10274: 10268: 10264: 10260: 10259: 10251: 10249: 10247: 10245: 10243: 10241: 10239: 10237: 10235: 10233: 10231: 10229: 10227: 10225: 10223: 10214: 10210: 10203: 10195: 10193:9780387209753 10189: 10185: 10184: 10176: 10169: 10165: 10161: 10155: 10149: 10143: 10135: 10129: 10125: 10121: 10120: 10112: 10097: 10091: 10083: 10081:9780521154499 10077: 10073: 10072: 10064: 10057: 10044: 10038: 10023: 10019: 10016:Keith Welch. 10012: 10004: 9998: 9994: 9993: 9985: 9969: 9963: 9956: 9951: 9933: 9926: 9917: 9912: 9908: 9904: 9900: 9893: 9887: 9883: 9879: 9873: 9867: 9866:0-582-44355-5 9863: 9859: 9853: 9846: 9845:0-8155-1339-9 9842: 9838: 9832: 9830: 9828: 9812: 9806: 9802: 9801: 9793: 9778: 9772: 9768: 9767: 9759: 9757: 9741: 9735: 9731: 9730: 9722: 9718: 9683: 9674: 9664: 9651: 9644: 9640: 9634: 9632: 9622: 9613: 9604: 9597: 9593: 9589: 9585: 9580: 9578: 9571: 9567: 9561: 9554: 9548: 9541: 9537: 9531: 9522: 9515: 9508: 9489: 9480: 9476: 9472: 9458: 9452: 9442: 9433: 9429: 9418: 9415: 9413: 9410: 9408: 9405: 9403: 9400: 9398: 9395: 9393: 9390: 9388: 9385: 9383: 9380: 9378: 9375: 9373: 9370: 9368: 9367:Chemiresistor 9365: 9363: 9360: 9359: 9351: 9346: 9342: 9337: 9335: 9331: 9327: 9308: 9306: 9303: 9300: 9297: 9294: 9291: 9289: 9285: 9281: 9278: 9275: 9272: 9269: 9266: 9263: 9261: 9257: 9253: 9250: 9247: 9244: 9241: 9238: 9235: 9233: 9229: 9225: 9222: 9219: 9216: 9213: 9210: 9207: 9205: 9201: 9198: 9196: 9193: 9190: 9187: 9184: 9181: 9179: 9175: 9171: 9168: 9165: 9162: 9159: 9156: 9153: 9151: 9147: 9144: 9142: 9139: 9136: 9133: 9130: 9127: 9125: 9121: 9118: 9116: 9113: 9110: 9107: 9104: 9101: 9099: 9095: 9092: 9090: 9087: 9084: 9081: 9078: 9075: 9073: 9069: 9066: 9064: 9061: 9058: 9055: 9052: 9049: 9047: 9043: 9040: 9038: 9035: 9032: 9029: 9026: 9023: 9021: 9017: 9008: 9003: 8987: 8977: 8958: 8942: 8936: 8932: 8930: 8925: 8915: 8913: 8909: 8904: 8899: 8894: 8889: 8885: 8884:vector fields 8880: 8874: 8868: 8855: 8825: 8822: 8769: 8766: 8741: 8728: 8725: 8722: 8719: 8709: 8706: 8703: 8700: 8691: 8689: 8673: 8669: 8665: 8662: 8659: 8656: 8642: 8640: 8636: 8632: 8627: 8625: 8621: 8620: 8615: 8611: 8606: 8604: 8600: 8596: 8592: 8588: 8584: 8580: 8570: 8568: 8550: 8547: 8542: 8539: 8517: 8513: 8504: 8486: 8482: 8459: 8455: 8434: 8412: 8408: 8387: 8367: 8342: 8339: 8334: 8331: 8326: 8322: 8318: 8313: 8309: 8305: 8302: 8297: 8293: 8289: 8286: 8281: 8277: 8273: 8267: 8261: 8254: 8253: 8252: 8250: 8241: 8234: 8221: 8217: 8212: 8208: 8204: 8201: 8197: 8193: 8189: 8186: 8183: 8180: 8177: 8169: 8165: 8160: 8157: 8153: 8151: 8146: 8144: 8127: 8114: 8109: 8101: 8098: 8095: 8089: 8086: 8083: 8080: 8077: 8074: 8071: 8068: 8065: 8060: 8057: 8047: 8045: 8040: 8027: 8020: 8015: 8011: 8004: 8000: 7994: 7988: 7984: 7980: 7977: 7969: 7967: 7963: 7962:exponentially 7959: 7958:semiconductor 7955: 7951: 7947: 7943: 7939: 7929: 7927: 7911: 7891: 7871: 7863: 7847: 7839: 7823: 7814: 7801: 7798: 7793: 7788: 7783: 7780: 7775: 7768: 7763: 7759: 7753: 7748: 7745: 7735: 7733: 7723: 7721: 7717: 7713: 7708: 7706: 7702: 7697: 7691: 7686: 7684: 7680: 7669: 7663: 7657: 7656: 7655: 7652: 7634: 7621: 7617: 7613: 7612:Fermi surface 7594: 7588: 7579: 7566: 7563: 7560: 7548: 7545: 7541: 7537: 7534: 7525: 7522: 7517: 7513: 7503: 7499: 7491: 7487: 7481: 7471: 7467: 7461: 7456: 7449: 7441: 7436: 7431: 7428: 7422: 7416: 7413: 7407: 7401: 7393: 7386: 7380: 7376: 7366: 7364: 7346: 7342: 7321: 7301: 7280: 7273:, equal to 1/ 7258: 7236: 7232: 7209: 7205: 7182: 7178: 7169: 7167: 7150: 7141: 7128: 7117: 7113: 7109: 7106: 7100: 7097: 7094: 7086: 7082: 7078: 7072: 7066: 7058: 7039: 7031: 7029: 7023: 7018: 7016: 7012: 7007: 6995: 6993: 6972: 6968: 6965: 6963: 6951: 6947: 6944: 6942: 6922: 6918: 6915: 6913: 6901: 6897: 6894: 6892: 6870: 6867: 6865: 6844: 6840: 6837: 6835: 6823: 6819: 6816: 6814: 6801: 6797: 6794: 6792: 6772: 6768: 6765: 6763: 6743: 6739: 6736: 6734: 6714: 6710: 6707: 6705: 6684: 6680: 6677: 6648: 6644: 6641: 6639: 6603: 6599: 6596: 6594: 6564: 6561: 6559: 6543: 6539: 6536: 6524: 6513: 6509: 6506: 6504: 6482: 6478: 6475: 6473: 6451: 6447: 6444: 6399: 6395: 6392: 6390: 6353: 6348: 6344: 6341: 6311: 6307: 6304: 6302: 6281: 6277: 6274: 6272: 6252: 6248: 6245: 6243: 6223: 6219: 6216: 6187: 6183: 6180: 6151: 6147: 6144: 6115: 6111: 6108: 6079: 6075: 6072: 6070: 6050: 6045: 6042: 6033: 6013: 6009: 6006: 5986: 5982: 5979: 5950: 5946: 5943: 5941: 5920: 5916: 5913: 5911: 5891: 5887: 5884: 5855: 5851: 5848: 5846: 5826: 5822: 5819: 5790: 5786: 5783: 5754: 5750: 5747: 5718: 5714: 5711: 5682: 5678: 5675: 5673: 5653: 5649: 5646: 5617: 5613: 5610: 5580: 5576: 5573: 5571: 5551: 5547: 5544: 5515: 5511: 5508: 5479: 5475: 5472: 5470: 5450: 5446: 5443: 5414: 5410: 5407: 5405: 5385: 5384:Brass (5% Zn) 5381: 5378: 5349: 5345: 5342: 5313: 5309: 5306: 5277: 5274: 5270: 5267: 5238: 5234: 5231: 5202: 5198: 5164:Resistivity, 5159: 5153: 5151: 5137: 5135: 5131: 5127: 5125: 5121: 5117: 5115: 5111: 5107: 5105: 5101: 5097: 5095: 5091: 5087: 5085: 5081: 5074:Resistivity, 5069: 5063: 5061: 5053: 5048: 5044: 5041:of dissolved 5040: 5039:concentration 5036: 5033: 5029: 5025: 5017: 5013: 5009: 5008:semiconductor 5005: 5002: 4998: 4994: 4991: 4990: 4988: 4973: 4970: 4968:Interactions 4967: 4966: 4961: 4958: 4955: 4952: 4951: 4947: 4946:instabilities 4943: 4939: 4935: 4931: 4927: 4923: 4919: 4916: 4912: 4908: 4905: 4904: 4900: 4897: 4894: 4893: 4889: 4886: 4883: 4882: 4879: 4877: 4873: 4872: 4865: 4863: 4859: 4858:Debye lengths 4855: 4851: 4847: 4843: 4842:astrophysical 4838: 4836: 4830: 4828: 4824: 4819: 4806: 4795: 4784: 4772: 4762: 4752: 4745: 4742: 4728: 4715: 4711: 4701: 4691: 4686: 4679: 4675: 4671: 4668: 4665: 4656: 4647: 4643: 4638: 4636: 4635: 4634:double layers 4630: 4622: 4615: 4610: 4606: 4602: 4598: 4593: 4586: 4582: 4577: 4567: 4564: 4560: 4556: 4551: 4549: 4545: 4544:absolute zero 4541: 4537: 4529: 4524: 4519: 4509: 4495: 4473: 4469: 4446: 4442: 4419: 4415: 4394: 4385: 4372: 4364: 4360: 4356: 4352: 4346: 4342: 4338: 4333: 4329: 4324: 4320: 4317: 4314: 4306: 4292: 4283: 4270: 4262: 4258: 4254: 4251: 4248: 4240: 4224: 4220: 4199: 4179: 4170: 4168: 4164: 4160: 4159:ionic liquids 4156: 4152: 4148: 4142: 4132: 4129: 4125: 4120: 4116: 4112: 4106: 4102: 4098: 4097:Semiconductor 4088: 4086: 4080: 4078: 4074: 4070: 4066: 4062: 4058: 4054: 4046: 4028: 4018: 4014: 4010: 4007: 4003: 3998: 3993: 3991: 3982: 3976: 3972: 3968: 3964: 3960: 3956: 3949: 3946: 3942: 3938: 3934: 3930: 3926: 3922: 3918: 3913: 3908: 3893: 3891: 3876: 3862: 3840: 3837: 3833: 3810: 3807: 3803: 3780: 3777: 3773: 3763: 3750: 3742: 3737: 3734: 3730: 3726: 3721: 3716: 3713: 3709: 3701: 3698: 3694: 3690: 3684: 3679: 3676: 3672: 3667: 3659: 3654: 3651: 3647: 3643: 3638: 3633: 3630: 3626: 3619: 3616: 3612: 3606: 3601: 3598: 3594: 3585: 3569: 3566: 3562: 3558: 3555: 3550: 3547: 3543: 3520: 3517: 3513: 3509: 3504: 3501: 3497: 3470: 3467: 3463: 3454: 3449: 3439: 3431: 3382: 3369: 3360: 3356: 3350: 3347: 3343: 3339: 3334: 3330: 3324: 3321: 3317: 3313: 3308: 3304: 3298: 3295: 3291: 3287: 3285: 3278: 3274: 3264: 3260: 3254: 3251: 3247: 3243: 3238: 3234: 3228: 3225: 3221: 3217: 3212: 3208: 3202: 3199: 3195: 3191: 3189: 3182: 3178: 3168: 3164: 3158: 3155: 3151: 3147: 3142: 3138: 3132: 3129: 3125: 3121: 3116: 3112: 3106: 3103: 3099: 3095: 3093: 3086: 3082: 3069: 3066: 3053: 3048: 3036: 3033: 3023: 3018: 3003: 3000: 2985: 2977: 2973: 2963: 2959: 2949: 2945: 2938: 2931: 2923: 2920: 2916: 2908: 2905: 2901: 2893: 2890: 2886: 2876: 2873: 2869: 2861: 2858: 2854: 2846: 2843: 2839: 2829: 2826: 2822: 2814: 2811: 2807: 2799: 2796: 2792: 2785: 2780: 2775: 2767: 2763: 2753: 2749: 2739: 2735: 2728: 2718: 2715: 2702: 2695: 2691: 2685: 2681: 2675: 2670: 2667: 2663: 2654: 2647: 2643: 2637: 2633: 2627: 2622: 2619: 2615: 2610: 2603: 2599: 2593: 2589: 2583: 2578: 2575: 2571: 2562: 2557: 2553: 2548: 2544: 2534: 2517: 2512: 2508: 2502: 2499: 2495: 2491: 2486: 2482: 2476: 2473: 2469: 2465: 2460: 2456: 2450: 2447: 2443: 2439: 2437: 2430: 2426: 2418: 2413: 2409: 2403: 2400: 2396: 2392: 2387: 2383: 2377: 2374: 2370: 2366: 2361: 2357: 2351: 2348: 2344: 2340: 2338: 2331: 2327: 2319: 2314: 2310: 2304: 2301: 2297: 2293: 2288: 2284: 2278: 2275: 2271: 2267: 2262: 2258: 2252: 2249: 2245: 2241: 2239: 2232: 2228: 2215: 2212: 2199: 2191: 2179: 2176: 2166: 2161: 2146: 2144: 2133: 2129: 2124: 2120: 2115: 2111: 2085: 2061: 2056: 2052: 2047: 2043: 2038: 2034: 2008: 2007: 2005: 2002: 1989: 1984: 1976: 1972: 1962: 1958: 1948: 1944: 1937: 1930: 1922: 1919: 1915: 1907: 1904: 1900: 1892: 1889: 1885: 1875: 1872: 1868: 1860: 1857: 1853: 1845: 1842: 1838: 1828: 1825: 1821: 1813: 1810: 1806: 1798: 1795: 1791: 1784: 1779: 1774: 1766: 1762: 1752: 1748: 1738: 1734: 1727: 1717: 1715: 1710: 1704: 1699: 1694: 1688: 1682: 1669: 1656: 1631: 1618: 1615: 1611: 1606: 1604: 1600: 1584: 1571: 1566: 1563: 1558: 1555: 1552: 1544: 1541: 1537: 1533: 1527: 1514: 1508: 1505: 1500: 1497: 1491: 1488: 1480: 1469: 1456: 1451: 1448: 1443: 1440: 1432: 1429: 1416: 1411: 1408: 1403: 1400: 1392: 1381: 1368: 1363: 1360: 1355: 1352: 1344: 1339: 1338: 1334: 1333: 1330: 1329: 1328: 1324: 1305: 1292: 1283: 1277: 1269: 1263: 1257: 1248: 1242: 1238: 1233: 1227: 1221: 1213: 1210: 1191: 1184:at the point 1183: 1164: 1158: 1151: 1136: 1113: 1107: 1100: 1085: 1062: 1056: 1049: 1048: 1046: 1043: 1030: 1021: 1015: 1007: 1001: 995: 989: 983: 975: 973: 969: 958: 956: 951: 938: 933: 930: 925: 922: 914: 907: 889: 861: 856: 853: 848: 845: 842: 834: 832: 829:(named after 828: 823: 819: 817: 812: 808: 804: 801: 797: 793: 788: 786: 782: 778: 769: 753: 746: 743: 727: 720: 717: 701: 694: 693: 691: 688: 671: 666: 663: 658: 655: 653: 648: 634: 631: 626: 623: 621: 616: 591: 588: 583: 580: 572: 570: 561: 557: 547: 533: 531: 527: 523: 519: 515: 511: 503: 495: 487: 483: 479: 469: 461: 457: 453: 449: 442: 438: 434: 430: 426: 422: 419:(also called 418: 396: 382: 368: 365: 351: 348: 332: 330: 326: 309: 306: 301: 298: 291: 283: 265: 262: 248: 242: 238: 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11155:: 11147:: 11141:5 11089:) 11075:. 11041:. 11029:: 11021:: 10994:. 10950:. 10944:: 10936:: 10930:4 10909:. 10903:: 10895:: 10869:. 10829:. 10817:: 10777:. 10720:. 10696:. 10618:. 10588:. 10565:. 10551:: 10545:7 10490:. 10402:. 10373:. 10361:: 10353:: 10347:8 10330:. 10275:. 10215:. 10196:. 10136:. 10105:. 10084:. 10031:. 10005:. 9978:. 9944:. 9919:. 9913:: 9847:. 9820:. 9786:. 9749:. 9704:2 9698:× 9690:× 9658:. 9500:α 9491:0 9488:ρ 9482:0 9477:Δ 9475:α 9471:ρ 9469:Δ 9463:× 8989:( 8960:( 8949:( 8903:E 8893:J 8879:J 8873:E 8856:, 8853:) 8849:r 8845:( 8841:J 8837:) 8833:r 8829:( 8823:= 8820:) 8816:r 8812:( 8808:E 8797:) 8793:r 8789:( 8785:E 8781:) 8777:r 8773:( 8767:= 8764:) 8760:r 8756:( 8752:J 8729:J 8723:= 8720:E 8710:E 8704:= 8701:J 8674:A 8670:/ 8660:= 8657:R 8551:T 8548:1 8518:5 8514:T 8487:2 8483:T 8460:0 8413:m 8409:c 8388:b 8368:a 8343:T 8327:m 8323:c 8319:+ 8314:5 8310:T 8306:b 8303:+ 8298:2 8294:T 8290:a 8287:+ 8282:0 8274:= 8271:) 8268:T 8265:( 8238:n 8222:, 8218:) 8213:n 8209:/ 8205:1 8198:T 8194:( 8184:A 8181:= 8139:C 8135:B 8131:A 8115:, 8110:3 8106:) 8093:( 8090:C 8087:+ 8075:B 8072:+ 8069:A 8066:= 8061:T 8058:1 8028:. 8021:T 8016:B 8012:k 8005:A 8001:E 7995:e 7989:0 7981:= 7892:T 7872:e 7848:k 7802:, 7799:T 7794:2 7789:) 7784:e 7781:k 7776:( 7769:3 7764:2 7754:= 7694:n 7671:n 7665:n 7659:n 7635:R 7598:) 7595:0 7592:( 7567:, 7564:x 7561:d 7554:) 7549:x 7542:e 7535:1 7532:( 7529:) 7526:1 7518:x 7514:e 7510:( 7504:n 7500:x 7492:T 7488:/ 7482:R 7472:0 7462:n 7457:) 7450:R 7442:T 7437:( 7432:A 7429:+ 7426:) 7423:0 7420:( 7414:= 7411:) 7408:T 7405:( 7390:ρ 7237:0 7233:T 7210:0 7183:0 7179:T 7129:, 7126:] 7123:) 7118:0 7114:T 7107:T 7104:( 7098:+ 7095:1 7092:[ 7087:0 7079:= 7076:) 7073:T 7070:( 7053:T 6937:× 6928:× 6856:~ 6809:~ 6758:× 6749:× 6729:× 6720:× 6672:× 6663:× 6654:× 6634:× 6632:5 6626:× 6624:5 6617:× 6615:2 6609:× 6607:2 6580:× 6572:× 6549:× 6531:× 6519:× 6468:× 6459:× 6439:× 6430:× 6422:× 6413:× 6405:× 6384:× 6382:3 6376:× 6374:2 6367:× 6359:× 6336:× 6326:× 6317:× 6297:× 6288:× 6267:× 6258:× 6238:× 6229:× 6211:× 6202:× 6193:× 6175:× 6166:× 6157:× 6139:× 6130:× 6121:× 6103:× 6094:× 6085:× 6065:× 6056:× 6037:× 6028:× 6019:× 6001:× 5992:× 5974:× 5965:× 5956:× 5936:× 5927:× 5906:× 5897:× 5879:× 5870:× 5861:× 5841:× 5832:× 5814:× 5805:× 5796:× 5778:× 5769:× 5760:× 5742:× 5733:× 5724:× 5706:× 5697:× 5688:× 5668:× 5659:× 5641:× 5632:× 5623:× 5604:× 5595:× 5586:× 5566:× 5557:× 5539:× 5530:× 5521:× 5503:× 5494:× 5485:× 5465:× 5456:× 5438:× 5429:× 5420:× 5400:× 5391:× 5373:× 5364:× 5355:× 5337:× 5328:× 5319:× 5301:× 5292:× 5283:× 5262:× 5253:× 5244:× 5226:× 5217:× 5208:× 5179:σ 5166:ρ 5146:ρ 5076:ρ 5030:/ 4807:. 4800:e 4796:n 4789:e 4785:n 4773:e 4767:e 4763:T 4757:B 4753:k 4743:= 4739:E 4716:. 4712:) 4706:e 4702:T 4696:B 4692:k 4687:/ 4680:e 4676:( 4661:e 4657:n 4624:i 4621:n 4617:e 4614:n 4474:0 4470:N 4443:b 4420:+ 4416:b 4395:q 4373:, 4365:0 4361:N 4353:) 4343:b 4339:+ 4334:+ 4330:b 4325:( 4321:q 4318:= 4271:. 4263:0 4259:N 4252:= 4249:N 4225:0 4221:N 4200:N 3951:F 3948:E 3927:( 3841:x 3838:x 3811:z 3808:x 3781:y 3778:x 3751:. 3743:2 3738:y 3735:x 3727:+ 3722:2 3717:x 3714:x 3702:y 3699:x 3685:= 3680:y 3677:x 3668:, 3660:2 3655:y 3652:x 3644:+ 3639:2 3634:x 3631:x 3620:x 3617:x 3607:= 3602:x 3599:x 3570:y 3567:x 3556:= 3551:x 3548:y 3521:x 3518:x 3510:= 3505:y 3502:y 3487:z 3471:y 3468:x 3445:ρ 3435:σ 3370:. 3361:z 3357:E 3351:z 3348:z 3340:+ 3335:y 3331:E 3325:y 3322:z 3314:+ 3309:x 3305:E 3299:x 3296:z 3288:= 3279:z 3275:J 3265:z 3261:E 3255:z 3252:y 3244:+ 3239:y 3235:E 3229:y 3226:y 3218:+ 3213:x 3209:E 3203:x 3200:y 3192:= 3183:y 3179:J 3169:z 3165:E 3159:z 3156:x 3148:+ 3143:y 3139:E 3133:y 3130:x 3122:+ 3117:x 3113:E 3107:x 3104:x 3096:= 3087:x 3083:J 3054:, 3049:j 3044:E 3037:j 3034:i 3024:= 3019:i 3014:J 2986:] 2978:z 2974:E 2964:y 2960:E 2950:x 2946:E 2939:[ 2932:] 2924:z 2921:z 2909:y 2906:z 2894:x 2891:z 2877:z 2874:y 2862:y 2859:y 2847:x 2844:y 2830:z 2827:x 2815:y 2812:x 2800:x 2797:x 2786:[ 2781:= 2776:] 2768:z 2764:J 2754:y 2750:J 2740:x 2736:J 2729:[ 2703:. 2696:x 2692:J 2686:z 2682:E 2676:= 2671:x 2668:z 2655:, 2648:x 2644:J 2638:y 2634:E 2628:= 2623:x 2620:y 2611:, 2604:x 2600:J 2594:x 2590:E 2584:= 2579:x 2576:x 2556:z 2552:J 2547:y 2543:J 2538:x 2518:. 2513:z 2509:J 2503:z 2500:z 2492:+ 2487:y 2483:J 2477:y 2474:z 2466:+ 2461:x 2457:J 2451:x 2448:z 2440:= 2431:z 2427:E 2419:, 2414:z 2410:J 2404:z 2401:y 2393:+ 2388:y 2384:J 2378:y 2375:y 2367:+ 2362:x 2358:J 2352:x 2349:y 2341:= 2332:y 2328:E 2320:, 2315:z 2311:J 2305:z 2302:x 2294:+ 2289:y 2285:J 2279:y 2276:x 2268:+ 2263:x 2259:J 2253:x 2250:x 2242:= 2233:x 2229:E 2200:. 2192:j 2187:J 2180:j 2177:i 2167:= 2162:i 2157:E 2132:z 2128:J 2123:y 2119:J 2114:x 2110:J 2094:J 2055:z 2051:E 2046:y 2042:E 2037:x 2033:E 2017:E 1990:, 1985:] 1977:z 1973:J 1963:y 1959:J 1949:x 1945:J 1938:[ 1931:] 1923:z 1920:z 1908:y 1905:z 1893:x 1890:z 1876:z 1873:y 1861:y 1858:y 1846:x 1843:y 1829:z 1826:x 1814:y 1811:x 1799:x 1796:x 1785:[ 1780:= 1775:] 1767:z 1763:E 1753:y 1749:E 1739:x 1735:E 1728:[ 1709:J 1703:E 1693:ρ 1687:σ 1670:, 1666:J 1657:= 1653:E 1641:E 1632:= 1628:J 1572:. 1564:A 1559:R 1556:= 1540:R 1536:I 1534:/ 1532:V 1515:. 1506:I 1501:A 1498:V 1492:= 1477:J 1473:E 1457:. 1452:A 1449:I 1444:= 1441:J 1417:. 1409:V 1404:= 1401:E 1389:ℓ 1385:V 1369:, 1364:J 1361:E 1356:= 1321:σ 1317:ρ 1313:σ 1309:ρ 1293:. 1287:) 1284:x 1281:( 1278:E 1273:) 1270:x 1267:( 1264:J 1258:= 1252:) 1249:x 1246:( 1239:1 1234:= 1231:) 1228:x 1225:( 1204:. 1192:x 1168:) 1165:x 1162:( 1159:J 1149:, 1137:x 1117:) 1114:x 1111:( 1108:E 1098:, 1086:x 1066:) 1063:x 1060:( 1031:, 1025:) 1022:x 1019:( 1016:J 1011:) 1008:x 1005:( 1002:E 996:= 993:) 990:x 987:( 939:. 931:1 926:= 911:σ 876:A 862:. 857:A 846:= 843:R 754:A 702:R 672:, 664:A 659:R 656:= 635:A 624:= 617:R 592:A 581:R 565:ρ 506:γ 498:κ 490:σ 458:- 444:ρ 397:2 391:I 383:3 377:T 369:3 360:L 352:1 343:M 307:1 302:= 266:1 258:s 193:2 184:I 176:3 167:T 159:3 153:L 145:M 110:A 105:R 102:= 46:ρ 27:.

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Knowledge

Electrical resistivity and conductivity

Index