What is ohm resistance. Electrical resistance - Knowledge Hypermarket

Conductor resistance - the ability of a material to resist flow electric current. Including the case of the skin effect of alternating high-frequency voltages.

Physical definitions

Materials are divided into classes according to resistivity. The value under consideration - resistance - is considered the key one, it will allow to perform the gradation of all substances found in nature:

Conductors - materials with resistivity up to 10 μΩ m. Applies to most metals, graphite.
Dielectrics - resistivity 100 MΩ m - 10 PΩ m. The prefix Peta is used in the context of the fifteenth degree of ten.
Semiconductors are a group of electrical materials with resistivity ranging from conductors to dielectrics.

Resistivity is called, allowing you to characterize the parameters of a wire cut 1 meter long, area 1 square meter. Most of the time it's hard to use numbers. The cross section of a real cable is much smaller. For example, for PV-3, the area is tens of millimeters. The calculation is simplified if you use the units of Ohm sq. mm / m (see Fig.).

Resistivity of metals

Resistivity is denoted Greek letter"ro", to obtain a resistance index, multiply the value by the length, dividing by the area of \u200b\u200bthe sample. The conversion between standard units of measurement Ohm m more often used for calculation shows: the relationship is established through the sixth power of ten. Sometimes it will be possible to find information regarding the resistivity of copper among the tabular values:

168 μΩ m;
0.00175 ohm sq. mmm.

It is easy to make sure that the numbers differ by about 4%, make sure by casting the units. This means that the figures are given for the grade of copper. If exact calculations are needed, the question is specified additionally, separately. Information about the resistivity of the sample is obtained purely empirically. A piece of wire with a known cross section, length is connected to the contacts of the multimeter. To get an answer, you need to divide the readings by the length of the sample, multiply by the cross-sectional area. In tests, it is supposed to choose a sample that is more authentic, minimizing the error. A significant part of the testers is endowed with insufficient accuracy to obtain valid values.

So, it is inconvenient for those who are afraid of physicists, who are desperate to master Chinese multimeters, to work with resistivity. It is much easier to take a finished cut (of greater length), evaluate the parameter of a full piece. In practice, Ohm's fractions play a small role, these actions are performed to estimate losses. Directly determined by the active resistance of the circuit section and quadratically depend on the current. Given the above, we note: conductors in electrical engineering are usually divided into two categories according to applicability:

Materials of high conductivity, high resistance. The former are used to create cables, the latter - resistances (resistors). There is no clear distinction in the tables, practicality is taken into account. Silver with low resistance is not used at all to create wires, rarely for device contacts. For obvious reasons.
Alloys with high elasticity are used to create flexible current-carrying parts: springs, working parts of contactors. Resistance should usually be kept to a minimum. It is clear that ordinary copper, which has a high degree of plasticity, is fundamentally unsuitable for these purposes.
Alloys with high or low thermal expansion coefficient. The former serve as the basis for the creation of bimetallic plates that structurally serve as the basis. The latter form a group of invar alloys. Often required where important geometric shape. At filament holders (replacing expensive tungsten) and vacuum-tight junctions at the junction with glass. But even more often, Invar alloys have nothing to do with electricity, they are used as part of machine tools and devices.

The formula for relating resistivity to ohmic

Physical basis of electrical conductivity

The resistance of the conductor is recognized as the inverse of electrical conductivity. In modern theory, it has not been thoroughly established how the process of current generation occurs. Physicists often hit a wall, observing a phenomenon that could not be explained in any way from the standpoint of previously put forward concepts. Today, the band theory is considered to be dominant. It is required to give a brief excursion into the development of ideas about the structure of matter.

Initially, it was assumed that the substance is represented by a positively charged substance, electrons float in it. So thought the notorious Lord Kelvin (nee Thomson), after whom the unit of measurement of absolute temperature is named. For the first time made an assumption about the planetary structure of atoms Rutherford. The theory, put forward in 1911, was built on the fact that alpha radiation was deflected by substances with large dispersion (individual particles changed the flight angle by a very significant amount). Based on the existing prerequisites, the author concluded that the positive charge of the atom is concentrated inside a small region of space, which is called the nucleus. The fact of individual cases of a strong deviation of the flight angle is due to the fact that the path of the particle ran in the immediate vicinity of the nucleus.

So the limits of geometric dimensions are set individual elements and for different substances. We concluded that the diameter of the gold core fits in the region of 3 pm (pico is a prefix to the negative twelfth power of ten). Further development The theory of the structure of substances was carried out by Bohr in 1913. Based on the observation of the behavior of hydrogen ions, he concluded that the charge of an atom is unity, and the mass was determined to be approximately one sixteenth of the weight of oxygen. Bohr suggested that the electron is held by the forces of attraction determined by Coulomb. Therefore, something keeps from falling on the core. Bohr suggested that the centrifugal force arising from the rotation of the particle in orbit is to blame.

An important amendment to the layout was made by Sommerfeld. Allowed the ellipticity of the orbits, introduced two quantum numbers describing the trajectory – n and k. Bohr noticed that Maxwell's theory for the model is failing. A moving particle must generate a magnetic field in space, then the electron would gradually fall on the nucleus. Therefore, we have to admit: there are orbits on which the radiation of energy into space does not occur. It is easy to see: the assumptions contradict each other, once again reminding: the resistance of the conductor, as physical quantity, physicists today are unable to explain.

Why? The zone theory has chosen Bohr's postulates as a basis, which say: the positions of the orbits are discrete, they are calculated in advance, the geometric parameters are connected by some relations. The conclusions of the scientist had to be supplemented by wave mechanics, since the mathematical models were powerless to explain some phenomena. Modern theory says: for each substance there are three zones in the state of electrons:

The valence band of electrons strongly bonded to atoms. It takes a lot of energy to break the bond. Electrons of the valence band do not participate in conduction.
The conduction band, electrons, when a field strength occurs in a substance, form an electric current (an ordered movement of charge carriers).
The forbidden zone is the region of energy states where electrons cannot be under normal conditions.

Jung's inexplicable experience

According to the band theory, the conduction band of a conductor overlaps with the valence band. An electron cloud is formed, easily carried away by tension electric field, forming a current. For this reason, the resistance of the conductor is so small. Moreover, scientists are making futile efforts to explain what an electron is. It is only known that an elementary particle exhibits wave and corpuscular properties. The Heisenberg uncertainty principle puts the facts in place: it is impossible with 100% probability to simultaneously determine the location of an electron and energy.

As for the empirical part, scientists have noticed that Young's experiment with electrons gives an interesting result. The scientist passed a stream of photons through two close slits of the shield, an interference pattern was obtained, composed by a series of fringes. They suggested doing a test with electrons, a collapse happened:

If electrons pass in a beam, bypassing two slits, an interference pattern is formed. It's like photons are moving.
If the electrons are fired one at a time, nothing changes. Therefore... one particle is reflected from itself, exists at once in several places?
Then they began to try to fix the moment when the electron passed through the plane of the shield. And… the interference pattern disappeared. There were two spots opposite the cracks.

The effect is powerless to explain with scientific point vision. It turns out that the electrons "guess" about the ongoing observation, cease to exhibit wave properties. Shows the limitations of modern ideas of physics. It would be nice if you could enjoy it! Another man of science proposed to observe the particles when they had already passed through the gap (flying in a certain direction). And what? Again, the electrons no longer exhibit wave properties.

It turns out, elementary particles went back in time. At the moment when they passed the gap. Penetrated into the mystery of the future, knowing whether there will be surveillance. Behavior was adjusted depending on the fact. Clearly, the answer cannot be a hit on the bull's-eye. The mystery is still waiting to be solved. By the way, Einstein's theory, put forward at the beginning of the 20th century, has now been refuted: particles have been found whose speed exceeds the speed of light.

How is the resistance of conductors formed?

Modern views say: free electrons move along the conductor at a speed of about 100 km / s. Under the action of the field that arises inside, the drift is ordered. The speed of movement of carriers along the lines of tension is small, a few centimeters per minute. In the course of movement, electrons collide with atoms of the crystal lattice, a certain amount of energy is converted into heat. And the measure of this transformation is usually called the resistance of the conductor. The higher the more electrical energy turns into heat. This is the principle of operation of heaters.

Parallel to the context is the numerical expression of the conductivity of the material, which can be seen in the figure. To obtain resistance, it is necessary to divide the unit by the specified number. The course of further transformations is discussed above. It can be seen that the resistance depends on the parameters - the temperature motion of electrons and the length of their free path, which directly leads to the structure crystal lattice substances. Explanation - the resistance of the conductors is different. Copper has less aluminum.

§ fifteen. Electrical resistance

The directed movement of electric charges in any conductor is hindered by the molecules and atoms of this conductor. Therefore, both the external section of the circuit and the internal one (inside the energy source itself) interfere with the passage of current. The value characterizing the resistance of an electric circuit to the passage of electric current is called electrical resistance.
The source of electrical energy, included in a closed electrical circuit, consumes energy to overcome the resistance of the external and internal circuits.
Electrical resistance is denoted by the letter r and is depicted in the diagrams as shown in Fig. 14, a.

The unit of resistance is the ohm. Ohm called the electrical resistance of such a linear conductor in which, with a constant potential difference of one volt, a current of one ampere flows, i.e.

When measuring high resistances, units of a thousand and a million times more ohms are used. They are called kiloohm ( com) and megohm ( Mom), 1 com = 1000 ohm; 1 Mom = 1 000 000 ohm.
AT various substances contains a different number of free electrons, and the atoms between which these electrons move have a different arrangement. Therefore, the resistance of conductors to electric current depends on the material from which they are made, on the length and area. cross section conductor. If two conductors of the same material are compared, then the longer conductor has more resistance at equal areas cross sections, and a conductor with a large cross section has less resistance at equal lengths.
For a relative assessment of the electrical properties of the conductor material, its resistivity serves. Resistivity is the resistance of a metal conductor with a length of 1 m and cross-sectional area 1 mm 2; denoted by the letter ρ, and is measured in
If a conductor made of a material with resistivity ρ has a length l meters and cross-sectional area q square millimeters, then the resistance of this conductor

Formula (18) shows that the resistance of the conductor is directly proportional to the resistivity of the material from which it is made, as well as its length, and inversely proportional to the cross-sectional area.
The resistance of conductors depends on temperature. The resistance of metal conductors increases with increasing temperature. This dependence is quite complicated, but within a relatively narrow range of temperature changes (up to about 200 ° C), we can assume that for each metal there is a certain, so-called temperature, resistance coefficient (alpha), which expresses the increase in the resistance of the conductor Δ r when the temperature changes by 1 ° C, referred to 1 ohm initial resistance.
Thus, the temperature coefficient of resistance

and increase in resistance

Δ r = r 2 - r 1 = α r 2 (T 2 - T 1) (20)

where r 1 - conductor resistance at temperature T 1 ;
r 2 - resistance of the same conductor at a temperature T 2 .
Let us explain the expression for the temperature coefficient of resistance with an example. Let us assume that a copper linear wire at a temperature T 1 = 15° has resistance r 1 = 50 ohm, and at a temperature T 2 = 75° - r 2 - 62 ohm. Therefore, the increase in resistance when the temperature changes by 75 - 15 \u003d 60 ° is 62 - 50 \u003d 12 ohm. Thus, the increase in resistance corresponding to a change in temperature by 1 ° is equal to:

The temperature coefficient of resistance for copper is equal to the increase in resistance divided by 1 ohm initial resistance, i.e. divided by 50:

Based on formula (20), it is possible to establish the relationship between the resistances r 2 and r 1:

(21)

It should be borne in mind that this formula is only an approximate expression of the dependence of resistance on temperature and cannot be used for measuring resistances at temperatures exceeding 100 ° C.
Adjustable resistances are called rheostats(Fig. 14, b). Rheostats are made of wire with high resistivity, such as nichrome. The resistance of rheostats can vary evenly or in steps. Liquid rheostats are also used, which are a metal vessel filled with some kind of solution that conducts electric current, for example, a solution of soda in water.
The ability of a conductor to pass electric current is characterized by conductivity, which is the reciprocal of resistance, and is indicated by the letter g. The SI unit for conductivity is (siemens).

Thus, the relationship between the resistance and conductivity of a conductor is as follows.

Electrical resistance is understood as any resistance that detects current when passing through a closed circuit, weakening or inhibiting the free flow of electrical charges.

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Measuring resistance with a multimeter

The physical concept of resistance

Electrons, when passing current, circulate in a conductor in an organized manner according to the resistance they encounter along the way. The lower this resistance, the greater the existing order in the microcosm of electrons. But when the resistance is high, they begin to collide with each other and secrete thermal energy. In this regard, the temperature of the conductor always rises slightly, by a larger amount, the higher the electrons find resistance to their movement.

Materials used

All known metals are more or less resistant to the passage of current, including the best conductors. Gold and silver have the least resistance, but they are expensive, so the most commonly used material is copper, which has a high electrical conductivity. Aluminum is used on a smaller scale.

Nichrome wire has the highest resistance to the passage of current (an alloy of nickel (80%) and chromium (20%)). It is widely used in resistors.

Another widely used resistor material is carbon. From it, fixed resistances and rheostats are made for use in electronic circuits. Fixed resistors and potentiometers are used to control current and voltage values, for example, when controlling the volume and tone of audio amplifiers.

Resistance calculation

To calculate the value of the load resistance, the formula derived from Ohm's law is used as the main one if the values of current and voltage are known:

The unit of measure is Ohm.

For serial connection resistors, the total resistance is found by summing the individual values:

R = R1 + R2 + R3 + …..

At parallel connection expression is used:

1/R = 1/R1 + 1/R2 + 1/R3 + …

And how to find the electrical resistance for a wire, given its parameters and material of manufacture? There is another resistance formula for this:

R \u003d ρ x l / S, where:

l is the length of the wire,
S are the dimensions of its cross section,
ρ is the specific volume resistance of the wire material.

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Resistance Formula

The geometric dimensions of the wire can be measured. But in order to calculate the resistance using this formula, you need to know the coefficient ρ.

Important! beat values volume resistance has already been calculated for different materials and summarized in special tables.

The value of the coefficient allows you to compare the resistance different types conductors at a given temperature in accordance with their physical properties regardless of size. This can be illustrated with examples.

Example of electrical resistance calculation copper wire, 500 m long:

If the dimensions of the wire section are unknown, you can measure its diameter with a caliper. Let's say it's 1.6mm;
When calculating the cross-sectional area, the formula is used:

Then S = 3.14 x (1.6 / 2)² = 2 mm²;

According to the table, we found the value of ρ for copper, equal to 0.0172 Ohm x m / mm²;
Now the electrical resistance of the calculated conductor will be:

R \u003d ρ x l / S \u003d 0.0172 x 500/2 \u003d 4.3 ohms.

Another example– nichrome wire with a cross section of 0.1 mm², length 1 m:

The ρ index for nichrome is 1.1 Ohm x m / mm²;
R \u003d ρ x l / S \u003d 1.1 x 1 / 0.1 \u003d 11 ohms.

Two examples clearly show that a meter-long nichrome wire with a cross section 20 times smaller has an electrical resistance 2.5 times greater than 500 meters of copper wire.

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Resistivity of some metals

Important! The resistance is influenced by temperature, with the increase of which it increases and, conversely, decreases with a decrease.

Impedance

Impedance is a more general term for resistance that takes into account a reactive load. Loop resistance calculation alternating current is to calculate the impedance.

While a resistor provides resistance for a specific purpose, reactive is an unfortunate by-product of some electrical circuit components.

Two types of reactance:

Inductive. Created by coils. Calculation formula:

X (L) = 2π x f x L, where:

f is the current frequency (Hz),
L - inductance (H);

Capacitive. Created by capacitors. Calculated according to the formula:

X (C) = 1/(2π x f x C),

where C is the capacitance (F).

Like its active counterpart, reactance is expressed in ohms and also limits the flow of current through the loop. If there is both a capacitance and an inductor in the circuit, then the total resistance is:

X = X (L) - X (C).

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Active, inductive and capacitive reactance

Important! From the reactive load formulas follow interesting features. With an increase in the frequency of the alternating current and inductance, X (L) increases. Conversely, the higher the frequency and capacitance, the smaller X (C).

Finding the impedance (Z) is not a simple addition of the active and reactive components:

Z = √ (R² + X²).

Example 1

A coil in a circuit with a power frequency current has an active resistance of 25 Ohms and an inductance of 0.7 H. You can calculate the impedance:

X (L) \u003d 2π x f x L \u003d 2 x 3.14 x 50 x 0.7 \u003d 218.45 ohms;
Z = √ (R² + X (L)²) = √ (25² + 218.45²) = 219.9 ohms.

tg φ \u003d X (L) / R \u003d 218.45 / 25 \u003d 8.7.

The angle φ is approximately equal to 83 degrees.

Example 2

There is a capacitor with a capacity of 100 microfarads and an internal resistance of 12 ohms. You can calculate the impedance:

X (C) \u003d 1 / (2π x f x C) \u003d 1 / 2 x 3.14 x 50 x 0, 0001 \u003d 31.8 ohms;
Z \u003d √ (R² + X (C)²) \u003d √ (12² + 31.8²) \u003d 34 ohms.

On the Internet, you can find an online calculator to simplify the calculation of the resistance and impedance of the entire electrical circuit or its sections. There you just need to keep your calculated data and record the results of the calculation.

Video

The concept of electrical resistance and conductivity

Any body through which an electric current flows, has a certain resistance to it. The property of a conductor material to prevent the passage of electric current through it is called electrical resistance.

Electronic theory explains the essence of the electrical resistance of metal conductors in this way. When moving along a conductor, free electrons encounter atoms and other electrons countless times on their way and, interacting with them, inevitably lose part of their energy. The electrons experience, as it were, resistance to their movement. Various metal conductors having different atomic structure, have different resistance to electric current.

Exactly the same explains the resistance of liquid conductors and gases to the passage of electric current. However, one should not forget that in these substances, not electrons, but charged particles of molecules meet resistance during their movement.

Resistance is indicated by Latin letters R or r.

The ohm is taken as the unit of electrical resistance.

Ohm is the resistance of a mercury column 106.3 cm high with a cross section of 1 mm2 at a temperature of 0 ° C.

If, for example, the electrical resistance of the conductor is 4 ohms, then it is written as follows: R \u003d 4 ohms or r \u003d 4 ohms.

To measure the resistance of a large value, a unit called megohm is adopted.

One meg is equal to one million ohms.

The greater the resistance of the conductor, the worse it conducts electric current, and, conversely, the lower the resistance of the conductor, the easier it is for the electric current to pass through this conductor.

Therefore, to characterize the conductor (in terms of the passage of electric current through it), one can consider not only its resistance, but also the reciprocal of the resistance and is called conductivity.

electrical conductivity The ability of a material to pass an electric current through itself is called.

Since conductivity is the reciprocal of resistance, it is expressed as 1 / R, the conductivity is denoted Latin letter g.

The influence of the conductor material, its dimensions and ambient temperature on the value of electrical resistance

The resistance of various conductors depends on the material from which they are made. To characterize the electrical resistance various materials introduced the concept of the so-called resistivity.

Resistivity is the resistance of a conductor 1 m long and with a cross-sectional area of 1 mm2. Resistivity is denoted by the Greek letter p. Each material from which the conductor is made has its own resistivity.

For example, the resistivity of copper is 0.017, that is, a copper conductor 1 m long and 1 mm2 in cross section has a resistance of 0.017 ohms. The resistivity of aluminum is 0.03, the resistivity of iron is 0.12, the resistivity of constantan is 0.48, the resistivity of nichrome is 1-1.1.

The resistance of a conductor is directly proportional to its length, that is, the longer the conductor, the greater its electrical resistance.

The resistance of a conductor is inversely proportional to its cross-sectional area, that is, the thicker the conductor, the less its resistance, and, conversely, the thinner the conductor, the greater its resistance.

To better understand this relationship, imagine two pairs of communicating vessels, with one pair of vessels having a thin connecting tube and the other having a thick one. It is clear that when one of the vessels (each pair) is filled with water, its transition to another vessel through a thick tube will occur much faster than through a thin one, i.e., a thick tube will offer less resistance to the flow of water. In the same way, it is easier for an electric current to pass through a thick conductor than through a thin one, that is, the first one offers him less resistance than the second.

The electrical resistance of a conductor is equal to the specific resistance of the material from which this conductor is made, multiplied by the length of the conductor and divided by the area of the cross-sectional area of the conductor:

R = R l / S,

Where - R - conductor resistance, ohm, l - conductor length in m, S - conductor cross-sectional area, mm 2.

Cross-sectional area of a round conductor calculated by the formula:

S = π d 2 / 4

Where π - constant value equal to 3.14; d is the diameter of the conductor.

And so the length of the conductor is determined:

l = S R / p ,

This formula makes it possible to determine the length of the conductor, its cross section and resistivity, if the other quantities included in the formula are known.

If it is necessary to determine the cross-sectional area of \u200b\u200bthe conductor, then the formula is reduced to the following form:

S = R l / R

Transforming the same formula and solving the equality with respect to p, we find the resistivity of the conductor:

R = R S / l

The last formula has to be used in cases where the resistance and dimensions of the conductor are known, and its material is unknown and, moreover, it is difficult to determine by appearance. To do this, it is necessary to determine the resistivity of the conductor and, using the table, find a material that has such a resistivity.

Another reason that affects the resistance of conductors is temperature.

It has been established that with increasing temperature, the resistance of metal conductors increases, and decreases with decreasing. This increase or decrease in resistance for pure metal conductors is almost the same and averages 0.4% per 1°C. The resistance of liquid conductors and coal decreases with increasing temperature.

The electronic theory of the structure of matter gives the following explanation for the increase in the resistance of metallic conductors with increasing temperature. When heated, the conductor receives thermal energy, which is inevitably transferred to all atoms of the substance, as a result of which the intensity of their movement increases. The increased movement of atoms creates more resistance to the directed movement of free electrons, which is why the resistance of the conductor increases. As the temperature decreases, there are Better conditions for the directed movement of electrons, and the resistance of the conductor decreases. This explains an interesting phenomenon - superconductivity of metals.

Superconductivity, i.e., a decrease in the resistance of metals to zero, occurs with a huge negative temperature- 273° C, called absolute zero. At a temperature of absolute zero, the metal atoms seem to freeze in place, without impeding the movement of electrons at all.

Ohm's law is the basic law of electrical circuits. At the same time, it allows us to explain many natural phenomena. For example, one can understand why electricity does not "beat" the birds that sit on the wires. For physics, Ohm's law is extremely significant. Without his knowledge, it would be impossible to create stable electrical circuits or there would be no electronics at all.

Dependence I = I(U) and its value

The history of the discovery of the resistance of materials is directly related to the current-voltage characteristic. What it is? Let's take a circuit with a constant electric current and consider any of its elements: a lamp, a gas tube, a metal conductor, an electrolyte flask, etc.

By changing the voltage U (often referred to as V) applied to the element in question, we will track the change in the current strength (I) passing through it. As a result, we will get a dependence of the form I \u003d I (U), which is called the "voltage characteristic of the element" and is a direct indicator of its electrical properties.

The volt-ampere characteristic may look different for different elements. Its simplest form is obtained by considering a metal conductor, which was done by Georg Ohm (1789 - 1854).

The current-voltage characteristic is a linear relationship. Therefore, its graph is a straight line.

Law in its simplest form

Ohm's research on the current-voltage characteristics of conductors showed that the current strength inside a metal conductor is proportional to the potential difference at its ends (I ~ U) and inversely proportional to a certain coefficient, that is, I ~ 1/R. This coefficient began to be called "conductor resistance", and the unit of measurement of electrical resistance was Ohm or V/A.

It is worth noting one more thing. Ohm's law is often used to calculate resistance in circuits.

The wording of the law

Ohm's law says that the current strength (I) of a single section of the circuit is proportional to the voltage in this section and inversely proportional to its resistance.

It should be noted that in this form the law remains true only for a homogeneous section of the chain. Homogeneous is that part of the electrical circuit that does not contain a current source. How to use Ohm's law in an inhomogeneous circuit will be discussed below.

Later, it was experimentally established that the law remains valid for electrolyte solutions in an electrical circuit.

The physical meaning of resistance

Resistance is the property of materials, substances or media to prevent the passage of electric current. Quantitatively, a resistance of 1 ohm means that an electric current of 1 A can pass in a conductor at a voltage of 1 V at its ends.

Specific electrical resistance

It was experimentally established that the resistance of the electric current of the conductor depends on its dimensions: length, width, height. And also on its shape (sphere, cylinder) and the material from which it is made. Thus, the formula for resistivity, for example, of a homogeneous cylindrical conductor will be: R \u003d p * l / S.

If we put s \u003d 1 m 2 and l \u003d 1 m in this formula, then R will be numerically equal to p. From here, the unit of measurement for the coefficient of resistivity of the conductor in SI is calculated - this is Ohm * m.

In the resistivity formula, p is the drag coefficient given by chemical properties material from which the conductor is made.

To consider the differential form of Ohm's law, it is necessary to consider a few more concepts.

As you know, electric current is a strictly ordered movement of any charged particles. For example, in metals, current carriers are electrons, and in conducting gases, ions.

Let's take a trivial case when all current carriers are homogeneous - a metal conductor. Let us mentally single out an infinitely small volume in this conductor and denote by u the average (drift, ordered) velocity of electrons in the given volume. Further, let n denote the concentration of current carriers per unit volume.

Now let's draw an infinitesimal area dS perpendicular to the vector u and construct along the velocity an infinitesimal cylinder with a height u*dt, where dt denotes the time it takes for all current velocity carriers contained in the volume under consideration to pass through the area dS.

In this case, the charge equal to q \u003d n * e * u * dS * dt will be transferred by electrons through the area, where e is the charge of the electron. Thus, the electric current density is a vector j = n * e * u, denoting the amount of charge transferred per unit time through a unit area.

One of the advantages of differential definition of Ohm's law is that you can often get by without calculating the resistance.

Electric charge. Electric field strength

The field strength along with electric charge is a fundamental parameter in the theory of electricity. At the same time, a quantitative representation of them can be obtained from simple experiments available to students.

For simplicity of reasoning, we will consider an electrostatic field. it electric field, which does not change with time. Such a field can be created by stationary electric charges.

Also, for our purposes, a test charge is needed. In its capacity we will use a charged body - so small that it is not capable of causing any disturbances (redistribution of charges) in the surrounding objects.

Consider in turn two test charges taken, successively placed at one point in space, which is under the influence of an electrostatic field. It turns out that the charges will be subjected to time-invariant influence on his part. Let F 1 and F 2 be the forces acting on the charges.

As a result of the generalization of experimental data, it was found that the forces F 1 and F 2 are directed either in one or in opposite directions, and their ratio F 1 /F 2 is independent of the point in space where the test charges were alternately placed. Consequently, the ratio F 1 /F 2 is a characteristic exclusively of the charges themselves, and does not depend on the field in any way.

Opening this fact made it possible to characterize the electrification of bodies and was later called electric charge. Thus, by definition, q 1 / q 2 \u003d F 1 / F 2 is obtained, where q 1 and q 2 are the magnitude of the charges placed at one point of the field, and F 1 and F 2 are the forces acting on the charges from the field.

From such considerations, the magnitudes of the charges of various particles were experimentally established. Conditionally putting in the ratio one of the test charges equal to one, you can calculate the value of another charge by measuring the ratio F 1 /F 2 .

Any electric field can be characterized in terms of a known charge. Thus, the force acting on a unit test charge at rest is called the electric field strength and is denoted by E. From the definition of the charge, we obtain that the strength vector has the following form: E = F/q.

Connection of vectors j and E. Another form of Ohm's law

Also note that the definition of cylinder resistivity can be generalized to wires made of the same material. In this case, the cross-sectional area from the resistivity formula will be equal to the cross section of the wire, and l - its length.