Lecture plan
5.1. The classical theory of electrical conductivity of metals.
5.2. Derivation of Ohm's law and Joule-Lenz's law.
5.3. Disadvantages of the classical theory of electrical conductivity of metals.
Classical theory of electrical conductivity of metals
Any theory is considered complete only if it traces the path from the elementary mechanism of the phenomenon to the macro-relations found in it, which are used in technical practice. In this case, it was irresistible to associate the features of the ordered movement of free charges in a conductor (electrical conductivity) with the basic laws of electric current. First of all, it was necessary to clarify the nature of current carriers in metals. Rikke's experiments 1 were fundamental in this sense, in which for a long time ( ≈ year), the current was passed through three series-connected metal cylinders ( Cu, A1, Cu) of the same section with carefully ground lapped ends. A huge charge flowed through this circuit (≈ 3.5 · 10 6 C). Despite this, no (even microscopic) traces of material transfer from cylinder to cylinder were found (which was confirmed by careful weighing). From this it was concluded that in metals in the process of transferring an electric charge, some particles are involved, common (identical) for all metals.
The nature of such particles could be determined by the sign and magnitude of the specific charge (the ratio of the carrier charge to its mass) - an individual parameter for any of the microparticles known today. The idea of \u200b\u200bsuch an experiment is as follows: with a sharp deceleration of a metal conductor, current carriers weakly connected to the lattice should be displaced forward by inertia. The result of such a displacement is a current pulse, and the sign of the carriers can be determined from the direction of the current, and, knowing the dimensions and resistance of the conductor, it is possible to calculate the specific charge of the carriers. Such experiments gave values \u200b\u200bfor the ratio, which coincided with the specific charge of the electrons. Thus, it was finally proved that the carriers of electric current in metals are free electrons. In education crystal lattice metal (when isolated atoms approach each other), valence electrons weakly bound to the nuclei detach from the metal atoms, become "free" and can move throughout the volume. Thus, metal ions are located at the sites of the crystal lattice, and free electrons move randomly between them.
The founders of the classical theory of electrical conductivity of metals, Drude 2 and Lorenz 3, showed for the first time that any set of non-interacting microparticles
Ricke Karl Victor Edward (1845 - 1915), German physicist
2 Drude Paul Karl Ludwig (1863 - 1906), German physicist
3 Lorenz Hendrik Anton (1853 - 1928), Dutch theoretical physicist
particles (including free electrons in a metal) can be considered as an ideal gas, that is, all the conclusions of the molecular kinetic theory are applicable to free electrons in a metal.
Conduction electrons in their motion collide with lattice ions, as a result of which thermodynamic equilibrium is established between the ideal gas of free electrons and the lattice. The average speed of free electrons can be found in accordance with the expression for the arithmetic mean speed of chaotic thermal motion of ideal gas molecules (see formula (8.26) in Lecture 8, Part I):
which at room temperatures (T ≈ 300 K) gives<u\u003e \u003d 1.1 · 10 5 m / s.
When superimposing external electric field on the conductor, in addition to the thermal movement of electrons, their ordered movement arises, that is electricity... The average speed of the ordered motion of electrons is<v\u003e can be determined according to (4.4). At the maximum permissible current density in real conductors (≈ 10 7 A / m2), a quantitative estimate gives<v\u003e ≈ 10 3 -10 4 m / s. Thus, even in extreme cases average speed the ordered motion of electrons (causing an electric current) is much less than their speed of chaotic thermal motion (<v> << <u\u003e). Therefore, when calculating the resulting speed, we can assume that (<v> + <u>) ≈ <u\u003e. It was already noted above that the ultimate goal of the classical theory of electrical conductivity of metals is to derive the basic laws of electric current, proceeding from the considered elementary mechanism of motion of current carriers. As an example, consider how this was done when deriving Ohm's law in differential form.
5.2. Derivation of Ohm's Law and Joule-Lenz's Law
Let there be an electric field with intensity in a metal conductor. From the side of the field, the electron experiences the action of the Coulomb force F \u003d eE and gains acceleration. According to Drude's theory at the end of the free path<l\u003e the electron collides with an ion of the lattice, gives up the energy accumulated when moving in the field (the speed of its ordered motion becomes zero). Moving uniformly accelerated, the electron acquires the speed at the end of the free path 
where
Because (<v> + <u>) ≈ <u\u003e then 
and (5.1) takes the form 
... Thus, the current density, according to (4.4), can be represented as
. (5.2)
Comparing this expression with Ohm's law in differential form, you can see that these expressions are identical, provided that the conductivity
Thus, within the framework of the classical theory of electrical conductivity of metals, Ohm's law was derived in differential form.
The Joule - Lenz law was similarly derived, a quantitative relationship between specific conductivity and thermal conductivity was obtained, taking into account the fact that in metals the transfer of electricity and heat is carried out by the same particles (free electrons) and a number of other relationships.
Fundamentals of classical theoryelectrical conductivity
metals
2.11.
The main
provisions
classical
electronic theory of metal conductivity
Drude - Lorenz.
2.12. Derivation of Ohm's, Joule-Lenz's and
Wiedemann-Franz based on the theory of Drude Lorentz.
2.13.
Difficulties
classical
theory
electrical conductivity
metals.
Superconductivity
metals.
Opening
high temperature superconductivity.
2.10. The nature of current carriers in metals.
To clarify the nature of current carriers in metals, a number of experiments were performed.Rikke's experience (Riecke C., 1845-1915). In 1901. Rikke carried out an experiment in which
he passed a current through a stack of highly polished cylinders
butts Cu-Al-Cu. Before the start of the experiment, the samples were weighed with a high
degree of accuracy (Δm \u003d ± 0.03 mg). The current was passed for a year. For this
time, a charge q \u003d 3.5 ∙ 106 C passed through the cylinders.
At the end of the experiment, the cylinders were weighed again. Weighing showed that
passing the current had no effect on the weight of the cylinders. When
examination of the end surfaces under a microscope was also not
found the penetration of one metal into another. Rikke's experiment results
testified that current carriers in metals are not
atoms, and some particles that are part of all metals.
Such particles could be electrons, discovered in 1897 by Thomson
J., 1856-1940) in experiments with cathode rays. To identify carriers
current in metals with electrons, it was necessary to determine the sign and magnitude
specific
charge carriers. it
_
Cu
was implemented in
+
Tolman's experience and
Al
Stewart (Tolman R.,
Cu
1881-1948, Stewart B.,
1828-1887).
Figure 6.1. Rikke's experience. Tolman and Stewart's experience. The essence of the experiment carried out in 1916,
consisted in determining the specific charge of current carriers at a sharp
braking the conductor. The experiment used for this purpose
a coil of copper wire 500 m long, which was driven in
fast rotation (the linear speed of the turns was 300 m / s), and
then she stopped abruptly. The charge flowing through the circuit during
braking was measured using a ballistic galvanometer.
The specific charge of the current carrier found from experience q / m 1.71 1011 C / kg,
turned out to be very close to the value of the specific charge of an electron
(e / m 1.76 1011 C / kg), from which it was concluded that the current in metals
carried by electrons.
_
V
V
a 0 U 0
a
To the Tolman-Stewart experiment with electron inertia.
U
ma
d
q
2.11. The main provisions of the classical electronic theory of the conductivity of metals Drude - Lorentz.
Based on the concept of free electrons as the main current carriers in metals,Drude (P. Drude, 1863-1906) developed the classical theory of electrical conductivity of metals,
which was then improved by Lorentz (H. Lorentz, 1853-1928).
The main provisions of this theory are as follows:
1). The carriers of current in metals are electrons, the movement of which is subject to
the law of classical mechanics.
2). The behavior of electrons is similar to that of ideal gas molecules (electron
gas).
3). When electrons move in a crystal lattice, one can ignore
collisions of electrons with each other.
4). In the elastic collision of electrons with ions, the electrons completely transfer
energy accumulated in the electric field.
The average thermal velocity of the chaotic motion of electrons at T ≈ 300K is
8kT
8 1,38 10 23 300
10 5 m / s 100 km / s
.
31
m
3,14 9,1 10
When the electric field is turned on, the chaotic motion of electrons is superimposed
ordered motion (sometimes called "drift"), occurring with some
average speed u; a directed
motion
electrons - electric current.
The current density is determined by the formula
.
j ne u
Estimates show that for the maximum admissible
current density in metals j \u003d 107 A / m2
and carrier concentration 1028 - 1029m-3,
... So
way, even with very
u 10 3 m / s 1mm
/ c
high current densities, the average velocity of the ordered motion of electrons
u. Gas of free electrons in the crystal lattice of a metal. The trajectory of one of the electrons is shown
The motion of a free electron in the crystal lattice: a - chaotic motion of an electron in
crystal lattice of the metal; b - chaotic motion with a drift due to
electric field. The extent of the drift
greatly exaggerated
2.12. Derivation of Ohm's, Joule-Lenz's and Wiedemann-Franz's laws based on the Drude-Lorentz theory.
Ohm's law.Acceleration acquired by an electron in an electric field
e
On the path of free run
magnitudes
eE
a
.
m
E
λ maximum
electron speed will reach
u max
eE
m
,
where τ is the free path time: /.
Average speed of ordered
there is movement:
u
eE
u
.
2
2m
Substituting this value in the formula for the current density, we will have:
ne
j u ne
E,
2m v
max
2
The resulting formula is Ohm's law in differential form:
ne 2
j E,
2m
where σ is the specific electrical conductivity of the metal:
ne 2
ne 2
2m
2m
.Joule-Lenz law
The kinetic energy of an electron, which it has at the moment
collisions with an ion:
2
m 2
mumax
E kin
.
2
2
When colliding with an ion, the energy received by the electron in
2
electric field E mumax is completely transferred to the ion. Number
kin
1
2
collisions of one electron per unit time is
, where λ
Is the electron free path. Total collisions
per unit time per unit volume is N n
... Then
the amount of heat released per unit volume of the conductor for
the unit of time will be:
2
2
Q beats N
mumax
ne 2
E
2
2m
.
The last formula can be represented as the Joule-Lenz law in
differential form:
1
Q beats E 2 E 2
,
where ρ \u003d 1 / σ is the resistivity of the metal. Wiedemann-Franz law.
Of
experience
known
what
metals,
alongside
from
high
electrical conductivity, they also have high thermal conductivity.
Wiedemann G., 1826-1899 and Franz R.,
1853 empirical law that the attitude
coefficient
thermal conductivity
κ
to
coefficient
electrical conductivity σ for all metals is approximately the same and
changes proportionally to the absolute temperature:
.
8
2
,
3
10
T
Treating electrons as monatomic
gas, we can based on
kinetic
theory
gases
to write
for
coefficient
thermal conductivity of electron gas:
1
1
,
nm cv nk
3
2 at constant
3 k is the specific heat of a monoatomic
Where
gas
cv
volume.
2m
Dividing κ by σ, we arrive at the Wiedemann-Franz law:
.
k
3 T
e and e \u003d 1.6 10-19 C, we find that
Substituting here k \u003d 1.38 10-23 J / K
2
,
which agrees very well with
2.23 10 8 T
experimental
data.
10.2.13. Difficulties of the classical theory of electrical conductivity of metals. Superconductivity of metals. Discovery of high-temperature superconducting
2.13. Difficulties of classical theoryelectrical conductivity of metals. Superconductivity
metals. High-temperature opening
superconductivity.
Despite the successes achieved, the classical electronic theory
conductivity of metals Drude-Lorentz did not receive further
development.
This is due to two main reasons:
1) the difficulties that this theory faced in explaining
some properties of metals;
2) the creation of a more perfect quantum theory of conduction
solids, eliminating the difficulties of the classical theory and
predicted a number of new properties of metals.
11.
Let's highlight the main difficulties of the Drude-Lorentz theory:1. According to the classical theory, the dependence of the resistivity
metals on temperature ~ T, while experimentally in a wide
temperature range near T≈300K for most metals
the dependence ρ ~ T.
2. Good quantitative agreement with Wiedemann-Franz law
turned out to be somewhat accidental. In the original
version of the theory, Drude did not take into account the distribution of electrons over
speeds. Later, when Lorenz took this distribution into account, it turned out
2
what attitude will be
k
2 T
,
e
which is in much worse agreement with experiment. According to
2
quantum theory,
2 k
8
T 2.45 10 T
.
3 e
3. The theory gives an incorrect value for the heat capacity of metals. FROM
taking into account the heat capacity of the electron gas C \u003d 9 / 2R, and in practice C \u003d 3R,
which roughly corresponds to the heat capacity of dielectrics.
4. Finally, the theory was completely unable to explain
opened in 1911. Kamerligh-Onnes H., 18531926
phenomena
superconductivity
(full
disappearing
resistance) of metals at low temperatures, and
the existence of residual resistance, to a large extent
depending on the purity of the metal.
12.
12
TC
1-metal with
impurities
2-pure metal
T
Temperature dependence of the resistance of metals.
(Tk is the temperature of the transition to the superconducting state)
It is interesting to note that with regard to
low-temperature superconductors
(metals) the rule applies: metals with
higher resistivity
ρ have a higher critical
superconducting transition temperature
Tcr (see table).
.
Table. Low temperature properties
superconductors
Metal
ρ
TC, K
Titanium
1,7
0,4
Aluminum
2,5
1,2
Mercury
9,4
4,1
Lead
22
7,2
13.
Phenomenological theory of low-temperature superconductivitywas established in 1935. F. and G. London (London F., 1900-1954, London
H., 1907-1970), but only after almost half a century (in 1957) the phenomenon
superconductivity was finally explained in terms of
microscopic (quantum) theory created by J. Bardin, L.
Cooper and J. Schrieffer (Bardeen J., Cooper L., Schrieffer J.).
In 1986. J. Bednorz and K. Müller K. were
the phenomenon of high-temperature superconductivity in
ceramic metal oxides (lanthanum, barium and other elements),
which are dielectrics at room temperature. Critical
superconducting transition temperature for these
materials about 100K.
Theory of high-temperature superconductivity at present
is under development and is still far from completion.
Even the mechanism of the occurrence of high-temperature
superconductivity.
The carriers of current in metals are free electrons, that is, electrons weakly bound to the ions of the crystal lattice of the metal. This idea of \u200b\u200bthe nature of current carriers in metals is based on the electronic theory of the conductivity of metals, created by the German physicist P. Drude (1863-1906) and later developed by the Dutch physicist H. Lorentz, as well as on a number of classical experiments confirming the provisions of the electronic theory.
The first of these experiences is rikke's experience* (1901), in which, during the year, an electric current was passed through three metal cylinders (Cu, Al, Cu) of the same radius connected in series with carefully polished ends. Despite the fact that the total charge that passed through these cylinders reached an enormous value (~ 3.5 × 10 6 C), no, even microscopic, traces of the transfer of matter were found. This was an experimental proof that ions in metals do not participate in the transfer of electricity, while charge transfer in metals is carried out by particles that are common to all metals. Electrons, discovered in 1897 by the English physicist D. Thomson (1856-1940), could be such particles.
*TO. Ricke (1845-1915) - German physicist.
To prove this assumption, it was necessary to determine the sign and magnitude of the specific charge of carriers (the ratio of the charge of a carrier to its mass). The idea of \u200b\u200bsuch experiments was as follows: if there are mobile current carriers weakly connected to the lattice in the metal, then with a sharp deceleration of the conductor, these particles should be displaced forward by inertia, as passengers standing in a carriage move forward during its deceleration. The charge displacement should result in a current pulse; by the direction of the current, you can determine the sign of the current carriers, and knowing the size and resistance of the conductor, you can calculate the specific charge of the carriers. The idea of \u200b\u200bthese experiments (1913) and their qualitative implementation belong to the Russian physicists S.L. Mandelstam (1879-1944) and ND Papaleksi (1880-1947). These experiments in 1916 were improved and carried out by the American physicist R. Tolman (1881-1948) and earlier by the Scottish physicist B. Stewart (1828-1887). They experimentally proved that current carriers in metals have a negative charge, and their specific charge is approximately the same for all investigated metals. By the value of the specific charge of the carriers of electric current and by the elementary electric charge determined earlier by R. Millikan, their mass was determined. It turned out that the values \u200b\u200bof the specific charge and mass of current carriers and electrons moving in vacuum were the same. Thus, it was finally proved that the carriers of electric current in metals are free electrons.
The existence of free electrons in metals can be explained as follows: during the formation of a crystal lattice of a metal (as a result of the convergence of isolated atoms), valence electrons, relatively weakly bound to atomic nuclei, detach from metal atoms, become "free" and can move throughout the volume. Thus, metal ions are located at the nodes of the crystal lattice, and free electrons move randomly between them, forming a kind of electron gas, which, according to the electronic theory of metals, has the properties of an ideal gas.
Conduction electrons in their motion collide with lattice ions, resulting in a thermodynamic equilibrium between the electron gas and the lattice. According to the Drude-Lorentz theory, electrons have the same energy of thermal motion as molecules of a monatomic gas. Therefore, applying the conclusions of the molecular kinetic theory (see (44.3)), one can find the average velocity of the thermal motion of electrons
which for T\u003d 300 K is equal to 1.1 × 10 5 m / s. The thermal motion of electrons, being chaotic, cannot lead to the appearance of a current.
When an external electric field is applied to a metal conductor, in addition to the thermal motion of electrons, their ordered motion occurs, i.e., an electric current arises. Average speed á vñ ordered motion of electrons can be estimated according to formula (96.1) for the current density: j=neá vñ. Having chosen the permissible current density, for example, for copper wires 10 7 A / m 2, we obtain that at the concentration of current carriers n \u003d 8 × 10 28 m –3 average speed á vñ of the ordered motion of electrons is equal to 7.8 × 10 –4 m / s. Therefore, b vñ<<áuñ, that is, even at very high current densities, the average speed of the ordered motion of electrons, which determines the electric current, is much less than their speed of thermal motion. Therefore, in calculations, the resulting speed á vñ + á uñ can be replaced by the speed of thermal motion á uñ.
It would seem that the result obtained contradicts the fact of almost instantaneous transmission of electrical signals over long distances. The fact is that the closure of an electric circuit entails the propagation of an electric field with a speed from (c\u003d 3 × 10 8 m / s). Through time t=l/c (lis the length of the chain) a stationary electric field will be established along the chain and an ordered movement of electrons will begin in it. Therefore, an electric current occurs in the circuit almost simultaneously with its closure.
From the standpoint of the classical electronic theory, the high electrical conductivity of metals is due to the presence of a huge number of free electrons, the motion of which obeys the laws of classical Newtonian mechanics. In this theory, the interaction of electrons with each other is neglected, and their interaction with positive ions is reduced only to collisions. In other words, conduction electrons are considered as an electron gas similar to a monatomic ideal gas. Such an electronic gas must obey all ideal gas laws. Consequently, the average kinetic energy of the thermal motion of an electron will be equal to, where is the electron mass, is its root-mean-square velocity, k is the Boltzmann constant, T is the thermodynamic temperature. Hence, at T \u003d 300 K, the mean square velocity of the thermal motion of electrons is 10 5 m / s.
Chaotic thermal motion of electrons cannot lead to the emergence of an electric current, but under the action of an external electric field in the conductor, an ordered motion of electrons with speed arises. The value can be estimated from the previously derived relation, where j is the current density, is the concentration of electrons, and e is the electron charge. As the calculation shows, »8 × 10 -4 m / s. The extremely small value of the quantity in comparison with the quantity is explained by the very frequent collisions of electrons with lattice ions. It would seem that the result obtained for contradicts the fact that the transmission of an electrical signal over very long distances occurs almost instantly. But the fact is that the closure of an electric circuit entails the propagation of an electric field at a speed of 3 × 10 8 m / s (the speed of light). Therefore, the ordered movement of electrons with speed under the action of the field will appear almost immediately throughout the chain, which provides instant signal transmission.
On the basis of the classical electronic theory, the main laws of electric current considered above were derived - Ohm's and Joule-Lenz's laws in differential form and. In addition, the classical theory provided a qualitative explanation for the Wiedemann-Franz law. In 1853 I. Wiedemann and F. Franz established that at a certain temperature the ratio of the thermal conductivity coefficient l to the specific conductivity g is the same for all metals. Wiedemann-Franz law has the form, where b is a constant independent of the nature of the metal. The classical electronic theory also explains this pattern. Conduction electrons, moving in a metal, carry with them not only an electric charge, but also the kinetic energy of random thermal motion. Therefore, those metals that conduct electric current well are good heat conductors. The classical electronic theory has qualitatively explained the nature of the electrical resistance of metals. In an external field, the ordered motion of electrons is disturbed by their collisions with positive ions in the lattice. Between two collisions, the electron moves at an accelerated rate and acquires energy, which, during the subsequent collision, gives up to the ion. It can be considered that the motion of an electron in a metal occurs with friction similar to internal friction in gases. This friction creates the resistance of the metal.
At the same time, the classical theory met with significant difficulties. Here are some of them:
1. The discrepancy between theory and experiment arose when calculating the heat capacity of metals. According to the kinetic theory, the molar heat capacity of metals should be the sum of the heat capacity of atoms and the heat capacity of free electrons. Since atoms in a solid perform only oscillatory movements, their molar heat capacity is equal to C \u003d 3R (R \u003d 8.31 J / (mol × K) is the molar gas constant); free electrons move only translationally and their molar heat capacity is C \u003d 3 / 2R. The total heat capacity should be C »4.5R, but according to the experimental data C \u003d 3R.
The classical electronic theory of electrical conductivity of metals and its experimental substantiation. Wiedemann-Franz law.
Electric current in metals is the ordered movement of electrons under the influence of an electric field.
This assumption was experimentally confirmed in the experiment of K. Ricke (1911).
An electric current was passed through a chain of three successive cylinders - copper, aluminum and again copper - for a long time (about a year) - a total charge of 3.5 MKl passed through the cylinders. However, no traces of material transfer (copper or aluminum) were found. Hence, it followed that the electrical conductivity of metals corresponds to free charges common to all metals - only electrons were suitable for this role.
Another convincing proof of the electronic nature of the current in metals was obtained in experiments with the inertia of electrons (the experiment of Tolman and Stewart) (1916).
A coil with a large number of turns of thin wire was brought into rapid rotation around its axis. The ends of the coil were connected with flexible wires to a sensitive ballistic galvanometer. The uncoiled coil was decelerated sharply and
a short-term current appeared in the circuit due to the inertia of charge carriers. The total charge flowing through the circuit was measured with a galvanometer.
When braking a rotating coil, a braking force acts on each charge carrier e of mass m, which plays the role of an external force, i.e., a force of non-electrical origin:
External force per unit charge, by definition, is the field strength of external forces:
Therefore, in the circuit when the coil is braking, electromotive force:
During the braking of the coil by charge q will flow through the circuit, equal:
Where is the length of the coil wire, I - instantaneous value of the current in the coil, R - the total resistance of the circuit, - the initial linear speed of the wire.
The experimentally obtained value of the specific charge of current carriers in the metal turned out to be close to the specific charge of an electron 
The good electrical conductivity of metals is explained by high concentration of free electrons equal in order of magnitude the number of atoms per unit volume.
The assumption that electrons are responsible for the electric current in metals arose much earlier than the experiments of Tolman and Stewart. Back in 1900, the German scientist P. Drude, based on the hypothesis of the existence of free electrons in metals, created an electronic theory of the conductivity of metals. This theory was developed in the works of the Dutch physicist H. Lorentz and is called classical electronic theory ... According to this theory, electrons in metals behave like an electron gas, much like an ideal gas.
The electron gas fills the space between the ions that form the crystal lattice of the metal. Due to interaction with ions, electrons can leave the metal only after overcoming the so-called potential barrier ... The height of this barrier is called work exit .
At normal (room) temperatures, electrons do not have enough energy to overcome the potential barrier. According to the Drude – Lorentz theory, electrons have the same average energy of thermal motion as molecules of a monatomic ideal gas. This allows us to estimate the average speed of the thermal motion of electrons using the formulas of the molecular kinetic theory:
When an external electric field is applied in a metal conductor, in addition to the thermal motion of electrons, their ordered movement (drift) occurs, that is, an electric current. The magnitude of the drift velocity of electrons lies in the range of 0.6 - 6 mm / s. Thus, the average speed of the ordered motion of electrons in metallic conductors is many orders of magnitude less than the average speed of their thermal motion.
The low drift speed does not contradict the experimental fact that the current in the entire DC circuit is established almost instantly. Closing the circuit causes an electric field to propagate at a speed c\u003d 3 · 10 8 m / s. Through time ( l Is the length of the chain) along the chain, a stationary distribution of the electric field is established and an ordered movement of electrons begins in it.
In the classical electronic theory of metals, it is assumed that the motion of electrons obeys the laws of Newtonian mechanics. In this theory, the interaction of electrons with each other is neglected, and their interaction with positive ions is reduced only to collisions. It is also assumed that at each collision, the electron transfers to the lattice all the energy accumulated in the electric field, and therefore, after the collision, it begins to move with zero drift velocity.
Despite the fact that all these assumptions are very approximate, the classical electronic theory qualitatively explains the laws of electric current in metal conductors: Ohm's law, the Joule - Lenz law and explains the existence of electrical resistance of metals.
Ohm's law:
Electrical resistance of the conductor.