This site could not do without an article about resistance. Well, no way! There is the most fundamental concept in electronics, which is also physical property. You probably already know these friends:
Resistance is the ability of a material to interfere with the flow of electrons. The material seems to resist, impede this flow, like the sails of a frigate against a strong wind!
In the world, almost everything has the ability to resist: air resists the flow of electrons, water also resists the flow of electrons, but they still slip through. Copper wires also resist the flow of electrons, but lazily. So they handle this kind of flow very well.
Only superconductors have no resistance, but that’s another story, since since they have no resistance, we are not interested in them today.
By the way, the flow of electrons is electricity. The formal definition is more pedantic, so look for it yourself in the same dry book.
And yes, electrons interact with each other. The strength of such interaction is measured in Volts and is called voltage. Can you tell me what sounds strange? Nothing strange. The electrons are strained and move other electrons with force. A little rustic, but the basic principle is clear.
It remains to mention power. Power is when current, voltage and resistance come together at one table and start working. Then power appears - the energy that electrons lose when passing through resistance. By the way:
I = U/R P = U * I
For example, you have a 60W light bulb with a wire. You plug it into a 220V socket. What's next? The light bulb provides some resistance to the flow of electrons with a potential of 220V. If there is too little resistance, boom, it burns out. If it is too large, the filament will glow very faintly, if at all. But if it is “just right,” then the light bulb will consume 60W and turn this energy into light and heat.
It's warm by-effect and is called “loss” of energy, since instead of shining brighter, the light bulb spends energy on heating. Use energy-saving lamps! By the way, the wire also has resistance and if the flow of electrons is too large, it will also heat up to a noticeable temperature. Here you can suggest reading a note about why high-voltage lines are used
I'm sure you understand more about resistance now. At the same time, we did not fall into details like the resistivity of the material and formulas like
where ρ - resistivity conductor substances, Ohm m, l— conductor length, m, a S— cross-sectional area, m².
A few animations to complete the picture
And it is clear how the flow of electrons varies depending on the temperature of the conductor and its thickness
 |
 |
 |
Concept of electrical resistance and conductivity
Any body through which electric current flows exhibits a certain resistance to it. The property of a conductor material to prevent electric current from passing through it is called electrical resistance.
Electronic theory This explains the essence of the electrical resistance of metal conductors. Free electrons, when moving along a conductor, encounter atoms and other electrons on their way countless times and, interacting with them, inevitably lose part of their energy. Electrons experience a kind of resistance to their movement. Various metal conductors having different atomic structure, have different resistance to electric current.
The same thing explains the resistance of liquid conductors and gases to the passage of electric current. However, we should not forget that in these substances it is not electrons, but charged particles of molecules that encounter resistance during their movement.
Resistance is denoted by the Latin letters R or r.
The unit of electrical resistance is the ohm.
Ohm is the resistance of a column of mercury 106.3 cm high with a cross section of 1 mm2 at a temperature of 0° C.
If, for example, the electrical resistance of a conductor is 4 ohms, then it is written like this: R = 4 ohms or r = 4 ohms.
For measuring resistance large size The unit adopted is called the megom.
One megohm is equal to one million ohms.
The greater the resistance of a conductor, the worse it conducts electric current, and, conversely, the less less resistance conductor, the easier it is for electric current to pass through that conductor.
Consequently, to characterize a conductor (from the point of view of the passage of electric current through it), one can consider not only its resistance, but also the reciprocal of the resistance and called conductivity.
Electrical conductivity is the ability of a material to pass electric current through itself.
Since conductivity is the reciprocal of resistance, it is expressed as 1/R, denoted conductivity Latin letter g.
The influence of 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 electrical resistance various materials introduced the concept of the so-called resistivity.
Resistivity is called the resistance of a conductor with a length of 1 m and area cross section 1 mm2. Resistivity is denoted by the letter p of the Greek alphabet. Each material from which a conductor is made has its own resistivity.
For example, the resistivity of copper is 0.017, i.e. a copper conductor 1 m long and 1 mm2 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, i.e. the longer the conductor, the greater its electrical resistance.
The resistance of a conductor is inversely proportional to its cross-sectional area, i.e. the thicker the conductor, the lower 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 transfer to the other vessel through a thick tube will occur much faster than through a thin tube, i.e., a thick tube will have less resistance to the flow of water. In the same way, it is easier for electric current to pass through a thick conductor than through a thin one, i.e., the first offers it less resistance than the second.
Electrical resistance of a conductor is equal to the resistivity of the material from which the conductor is made, multiplied by the length of the conductor and divided by the area of the cross-sectional area of the conductor:
R = р l/S,
Where - R is the resistance of the conductor, ohm, l is the length of the conductor in m, S is the cross-sectional area of the conductor, mm 2.
Cross-sectional area of a round conductor calculated by the formula:
S = π d 2 / 4
Where π - constant, equal to 3.14; d is the diameter of the conductor.
And this is how 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 the conductor, then the formula takes the following form:
S = р 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 must be used in cases where the resistance and dimensions of the conductor are known, but its material is unknown and, moreover, difficult to determine by appearance. To do this, you need 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 with decreasing temperature it decreases. 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 carbon decreases with increasing temperature.
The electronic theory of the structure of matter provides the following explanation for the increase in resistance of metal conductors with increasing temperature. When heated, the conductor receives thermal energy, which is inevitably transmitted to all atoms of the substance, as a result of which the intensity of their movement increases. The increased movement of atoms creates greater resistance to the directional movement of free electrons, which is why the resistance of the conductor increases. With a decrease in temperature, Better conditions for the directional movement of electrons, and the resistance of the conductor decreases. This explains interesting phenomenon - superconductivity of metals.
Superconductivity, i.e., a decrease in the resistance of metals to zero, occurs at a huge negative temperature - 273 ° C, called absolute zero. At a temperature absolute zero the metal atoms seem to freeze in place, without at all interfering with the movement of electrons.
Ohm's law is the fundamental law of electrical circuits. At the same time, it allows us to explain many natural phenomena. For example, you can understand why electricity does not “hit” birds that are sitting on 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 meaning
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 denoted as V) supplied to the element in question, we will monitor the change in the current strength (I) passing through it. As a result, we obtain a dependence of the form I = I (U), which is called the “volt-ampere characteristic of the element” and is a direct indicator of its electrical properties.
The current-voltage characteristic may look different for various elements. Its simplest form is obtained by examining a metal conductor, which is what Georg Ohm (1789 - 1854) did.
The current-voltage characteristic is linear dependence. Therefore, its graph is a straight line.
Law in simple form
Ohm's studies 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 became known as “conductor resistance”, and the unit of measurement of electrical resistance is Ohm or V/A.
Another thing worth noting is this. Ohm's law is often used to calculate resistance in circuits.
Statement of the law
Ohm's law says that the current strength (I) of a single section of a 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.
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 a conductor with a voltage of 1 V at its ends is capable of passing an electric current of 1 A.
Electrical resistivity
Experimental method It was found that the resistance of the electric current of a 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 = p*l/S.
If in this formula we put s = 1 m 2 and l = 1 m, then R will be numerically equal to p. From here the unit of measurement for the conductor resistivity coefficient in SI is calculated - this is Ohm*m.
In the resistivity formula, p is the resistance coefficient determined by chemical properties the material from which the conductor is made.
To consider the differential form of Ohm's law, it is necessary to consider several more concepts.
As is known, electric current is a strictly ordered movement of any charged particles. For example, in metals the current carriers are electrons, and in conducting gases they are ions.
Let's take a trivial case when all current carriers are homogeneous - a metal conductor. Let us mentally select an infinitesimal volume in this conductor and denote by u the average (drift, ordered) speed of electrons in this volume. Next, let n denote the concentration of current carriers per unit volume.
Now let's spend endlessly small area dS is perpendicular to the vector u and construct an infinitesimal cylinder along the velocity with a height u*dt, where dt denotes the time during which all current velocity carriers contained in the volume under consideration will pass through the area dS.
In this case, the electrons will transfer a charge through the area equal to q = n*e*u*dS*dt, 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 differential definition Ohm's law is that you can often do without calculating resistance.
Electric charge. Electric field strength
Field strength, along with electric charge, is a fundamental parameter in the theory of electricity. Moreover, a quantitative idea of them can be obtained from simple experiments available to schoolchildren.
For simplicity of reasoning, we will consider the electrostatic field. This is an electric field that does not change over time. Such a field can be created by stationary electric charges.
A test charge is also necessary for our purposes. We will use a charged body as it - so small that it is not capable of causing any disturbances (redistribution of charges) in surrounding objects.
Let us consider in turn two taken test charges, sequentially placed at one point in space under the influence electrostatic field. It turns out that the charges will be subject to constant influence on his part over time. Let F 1 and F 2 be the forces acting on the charges.
As a result of generalization of experimental data, it was found that the forces F 1 and F 2 are directed either in one or in opposite sides, 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 in any way on the field.
Opening this fact made it possible to characterize the electrification of bodies and was later called an electric charge. Thus, by definition, it turns out q 1 /q 2 = F 1 /F 2, 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 similar considerations, the charges of various particles were experimentally established. By conditionally putting one of the test charges into the ratio equal to one, you can calculate the magnitude of the other charge by measuring the ratio F 1 / F 2 .
Any electric field can be characterized through a known charge. Thus, the force acting on a unit test charge at rest is called tension electric field and is denoted by E. From the definition of charge we find that the intensity vector has next view: E = F/q.
Relationship between vectors j and E. Another form of Ohm's law
Also note that the definition of cylinder resistivity can be generalized to wires consisting 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.
- an electrical quantity that characterizes the property of a material to prevent the flow of electric current. Depending on the type of material, the resistance can tend to zero - be minimal (miles/micro ohms - conductors, metals), or be very large (giga ohms - insulation, dielectrics). The reciprocal of electrical resistance is .
Unit electrical resistance - Ohm. It is designated by the letter R. The dependence of resistance on current in a closed circuit is determined.
Ohmmeter- a device for direct measurement circuit resistance. Depending on the range of the measured value, they are divided into gigaohmmeters (for large resistances - when measuring insulation), and micro/miliohmmeters (for small resistances - when measuring transition resistances of contacts, motor windings, etc.).
There is a wide variety of ohmmeters by design from different manufacturers, from electromechanical to microelectronic. It is worth noting that a classic ohmmeter measures the active part of the resistance (so-called ohms).
Any resistance (metal or semiconductor) in the circuit alternating current has an active and reactive component. The sum of active and reactive resistance is AC circuit impedance and is calculated by the formula:
where, Z is the total resistance of the alternating current circuit;
R is the active resistance of the alternating current circuit;
Xc is the capacitive reactance of the alternating current circuit; 
(C - capacity, w - angular velocity alternating current)
Xl is the inductive reactance of the alternating current circuit; 
(L is inductance, w is the angular velocity of alternating current).
Active resistance- this is part of the total resistance of an electrical circuit, the energy of which is completely converted into other types of energy (mechanical, chemical, thermal). Distinctive property the active component is the complete consumption of all electricity (energy is not returned to the network), and the reactance returns part of the energy back to the network ( negative property reactive component).
The physical meaning of active resistance
Each environment where electric charges pass creates obstacles in their path (it is believed that these are nodes of the crystal lattice), into which they seem to hit and lose their energy, which is released in the form of heat.
Thus, a fall occurs (loss electrical energy), part of which is lost due to the internal resistance of the conducting medium.
The numerical value characterizing the ability of a material to prevent the passage of charges is called resistance. It is measured in Ohms (Ohm) and is inversely proportional to electrical conductivity.
Miscellaneous elements periodic table Mendeleev have different electrical resistivities (p), for example, the smallest. Silver (0.016 Ohm*mm2/m), copper (0.0175 Ohm*mm2/m), gold (0.023) and aluminum (0.029) have resistance. They are used in industry as the main materials on which all electrical engineering and energy are built. Dielectrics, on the contrary, have a high shock value. resistance and are used for insulation.
The resistance of the conductive medium can vary significantly depending on the cross-section, temperature, magnitude and frequency of the current. In addition, different environments have different charge carriers (free electrons in metals, ions in electrolytes, “holes” in semiconductors), which are the determining factors of resistance.
Physical meaning of reactance
In coils and capacitors, when applied, energy accumulates in the form of magnetic and electric fields, which takes some time.
Magnetic fields in alternating current networks change following the changing direction of movement of charges, while providing additional resistance.
In addition, a stable phase and current shift occurs, and this leads to additional electricity losses.
Resistivity
How can we find out the resistance of a material if there is no flow through it and we do not have an ohmmeter? There is a special value for this - electrical resistivity of the material V
(these are tabular values that are determined empirically for most metals). Using this value and the physical quantities of the material, we can calculate the resistance using the formula:
Where, p— resistivity (units ohm*m/mm2);
l—conductor length (m);
S - cross section (mm 2).
Having collected electrical circuit, consisting of a current source, resistor, ammeter, voltmeter, switch, it can be shown that current strength (I ) flowing through the resistor is directly proportional to the voltage ( U ) at its ends: I-U . Voltage to current ratio U/I - there is a quantity constant.
Therefore there is physical quantity, characterizing the properties of a conductor (resistor) through which electric current flows. This quantity is called electrical resistance conductor, or simply resistance. Resistance is indicated by the letter R .
(R) is a physical quantity, equal to the ratio voltage ( U ) at the ends of the conductor to the current strength ( I ) in him. R = U/I . Resistance unit – Ohm (1 ohm).
One Ohm- the resistance of a conductor in which the current is 1A with a voltage at its ends of 1V: 1 Ohm = 1 V / 1 A.
The reason that a conductor has resistance is that the directional movement electric charges in him prevent ions crystal lattice making erratic movements. Accordingly, the speed of directional movement of charges decreases.
Electrical resistivity
R ) is directly proportional to the length of the conductor ( l ), inversely proportional to its cross-sectional area ( S ) and depends on the conductor material. This dependence is expressed by the formula: R = p*l/SR - this is a quantity characterizing the material from which the conductor is made. It is called conductor resistivity, its value is equal to the resistance of a conductor of length 1m and cross-sectional area 1 m2.
The unit of conductor resistivity is: [p] = 1 0m 1 m 2 / 1 m. Often the cross-sectional area is measured in mm 2, therefore, in reference books the conductor resistivity values are given as in Ohm m so in Ohm mm2/m.
By changing the length of the conductor, and therefore its resistance, you can regulate the current in the circuit. The device with which this can be done is called rheostat.
