When closed electrical circuit, at the terminals of which there is a potential difference, a electricity. Free electrons under the influence electrical forces fields move along the conductor. In their movement, electrons collide with the atoms of the conductor and give them a supply of their kinetic energy. The speed of electrons continuously changes: when electrons collide with atoms, molecules and other electrons, it decreases, then under the influence electric field increases and decreases again with a new collision. As a result, a uniform flow of electrons is established in the conductor at a speed of several fractions of a centimeter per second. Consequently, electrons passing through a conductor always encounter resistance to their movement from its side. When electric current passes through a conductor, the latter heats up.
Electrical resistance
The electrical resistance of a conductor, which is denoted by a Latin letter r, is the property of a body or medium to transform electrical energy into heat when an electric current passes through it.
In the diagrams, electrical resistance is indicated as shown in Figure 1, A.
Variable electrical resistance, which serves to change the current in a circuit, is called rheostat. In the diagrams, rheostats are designated as shown in Figure 1, b. IN general view A rheostat is made from a wire of one resistance or another, wound on an insulating base. The slider or rheostat lever is placed in a certain position, as a result of which the required resistance is introduced into the circuit.
Long conductor small cross section creates high resistance to current. Short conductors with a large cross-section offer little resistance to current.
If we take two conductors from different materials, but the same length and cross-section, then the conductors will conduct current differently. This shows that the resistance of a conductor depends on the material of the conductor itself.
The temperature of the conductor also affects its resistance. As temperature increases, the resistance of metals increases, and the resistance of liquids and coal decreases. Only some special metal alloys (manganin, constantan, nickel and others) hardly change their resistance with increasing temperature.
So, we see that the electrical resistance of a conductor depends on: 1) the length of the conductor, 2) the cross-section of the conductor, 3) the material of the conductor, 4) the temperature of the conductor.
The unit of resistance is one ohm. Om is often denoted in Greek capital letterΩ (omega). Therefore, instead of writing “The conductor resistance is 15 ohms,” you can simply write: r= 15 Ω.
1,000 ohms is called 1 kiloohm(1kOhm, or 1kΩ),
1,000,000 ohms is called 1 megaohm(1mOhm, or 1MΩ).
When comparing the resistance of conductors from various materials It is necessary to take a certain length and cross-section for each sample. Then we will be able to judge which material conducts electric current better or worse.
Video 1. Conductor resistance
Electrical resistivity
The resistance in ohms of a conductor 1 m long, with a cross section of 1 mm² is called resistivity and is denoted by the Greek letter ρ (ro).
Table 1 shows the resistivities of some conductors.
Table 1
Resistivities of various conductors
The table shows that an iron wire with a length of 1 m and a cross-section of 1 mm² has a resistance of 0.13 Ohm. To get 1 Ohm of resistance you need to take 7.7 m of such wire. Silver has the lowest resistivity. 1 Ohm of resistance can be obtained by taking 62.5 m of silver wire with a cross section of 1 mm². Silver is the best conductor, but the cost of silver excludes the possibility of its mass use. After silver in the table comes copper: 1 m of copper wire with a cross section of 1 mm² has a resistance of 0.0175 Ohm. To get a resistance of 1 ohm, you need to take 57 m of such wire.
Chemically pure copper obtained by refining has found widespread use in electrical engineering for the manufacture of wires, cables, and windings. electric machines and devices. Aluminum and iron are also widely used as conductors.
The conductor resistance can be determined by the formula:
Where r– conductor resistance in ohms; ρ – resistivity conductor; l– conductor length in m; S– conductor cross-section in mm².
Example 1. Determine the resistance of 200 m of iron wire with a cross section of 5 mm².
Example 2. Calculate the resistance of 2 km of aluminum wire with a cross section of 2.5 mm².
From the resistance formula you can easily determine the length, resistivity and cross-section of the conductor.
Example 3. For a radio receiver, it is necessary to wind a 30 Ohm resistance from nickel wire with a cross section of 0.21 mm². Determine the required wire length.
Example 4. Determine cross section 20 m nichrome wire, if its resistance is 25 Ohms.
Example 5. A wire with a cross section of 0.5 mm² and a length of 40 m has a resistance of 16 Ohms. Determine the wire material.
The material of the conductor characterizes its resistivity.
Based on the resistivity table, we find that lead has this resistance.
It was stated above that the resistance of conductors depends on temperature. Let's do the following experiment. Let's wind several meters of thin metal wire in the form of a spiral and connect this spiral to the battery circuit. To measure current, we connect an ammeter to the circuit. When the coil is heated in the burner flame, you will notice that the ammeter readings will decrease. This shows that the resistance of a metal wire increases with heating.
For some metals, when heated by 100°, the resistance increases by 40–50%. There are alloys that change their resistance slightly with heating. Some special alloys show virtually no change in resistance when temperature changes. The resistance of metal conductors increases with increasing temperature, the resistance of electrolytes (liquid conductors), coal and some solids, on the contrary, decreases.
The ability of metals to change their resistance with changes in temperature is used to construct resistance thermometers. This thermometer is a platinum wire wound on a mica frame. By placing a thermometer, for example, in a furnace and measuring the resistance of the platinum wire before and after heating, the temperature in the furnace can be determined.
The change in the resistance of a conductor when it is heated per 1 ohm of initial resistance and per 1° temperature is called temperature coefficient of resistance and is denoted by the letter α.
If at temperature t 0 conductor resistance is r 0 , and at temperature t equals r t, then the temperature coefficient of resistance
Note. Calculation using this formula can only be done in a certain temperature range (up to approximately 200°C).
We present the values of the temperature coefficient of resistance α for some metals (Table 2).
table 2
Temperature coefficient values for some metals
From the formula for the temperature coefficient of resistance we determine r t:
r t = r 0 .
Example 6. Determine the resistance of an iron wire heated to 200°C if its resistance at 0°C was 100 Ohms.
r t = r 0 = 100 (1 + 0.0066 × 200) = 232 ohms.
Example 7. A resistance thermometer made of platinum wire had a resistance of 20 ohms in a room at 15°C. The thermometer was placed in the oven and after some time its resistance was measured. It turned out to be equal to 29.6 Ohms. Determine the temperature in the oven.
Electrical conductivity
So far, we have considered the resistance of a conductor as the obstacle that the conductor provides to the electric current. But still, current flows through the conductor. Therefore, in addition to resistance (obstacle), the conductor also has the ability to conduct electric current, that is, conductivity.
The more resistance a conductor has, the less conductivity it has, the worse it conducts electric current, and, conversely, the lower the resistance of a conductor, the more conductivity it has, the easier it is for current to pass through the conductor. Therefore, the resistance and conductivity of a conductor are reciprocal quantities.
From mathematics it is known that the inverse of 5 is 1/5 and, conversely, the inverse of 1/7 is 7. Therefore, if the resistance of a conductor is denoted by the letter r, then the conductivity is defined as 1/ r. Conductivity is usually symbolized by the letter g.
Electrical conductivity is measured in (1/Ohm) or in siemens.
Example 8. The conductor resistance is 20 ohms. Determine its conductivity.
If r= 20 Ohm, then
Example 9. The conductivity of the conductor is 0.1 (1/Ohm). Determine its resistance
If g = 0.1 (1/Ohm), then r= 1 / 0.1 = 10 (Ohm)
Most laws of physics are based on experiments. The names of the experimenters are immortalized in the names of these laws. One of them was Georg Ohm.
Georg Ohm's experiments
During experiments on the interaction of electricity with various substances, including metals, he established a fundamental relationship between density, electric field strength and the property of a substance, which was called “specific conductivity”. The formula corresponding to this pattern, called “Ohm’s Law,” is as follows:
j= λE , wherein
- j— electric current density;
- λ — specific conductivity, also called “electrical conductivity”;
- E – electric field strength.
In some cases, a different letter of the Greek alphabet is used to indicate conductivity - σ . Specific conductivity depends on certain parameters of the substance. Its value is influenced by temperature, substances, pressure, if it is a gas, and most importantly, the structure of this substance. Ohm's law is observed only for homogeneous substances.
For more convenient calculations the reciprocal of specific conductivity is used. It is called “resistivity”, which is also associated with the properties of the substance in which the electric current flows, denoted by the Greek letter ρ and has the dimension Ohm*m. But since for different physical phenomena Different theoretical justifications apply; alternative formulas can be used for resistivity. They are a reflection of the classical electronic theory of metals, as well as quantum theory.
Formulas
In these formulas, which are tedious for ordinary readers, factors such as Boltzmann's constant, Avogadro's constant and Planck's constant appear. These constants are used for calculations that take into account the free path of electrons in a conductor, their speed during thermal motion, the degree of ionization, the concentration and density of the substance. In short, everything is quite complicated for a non-specialist. In order not to be unfounded, below you can familiarize yourself with how everything actually looks:
Features of metals
Since the movement of electrons depends on the homogeneity of the substance, the current in a metal conductor flows according to its structure, which affects the distribution of electrons in the conductor, taking into account its heterogeneity. It is determined not only by the presence of impurity inclusions, but also by physical defects - cracks, voids, etc. The heterogeneity of the conductor increases its resistivity, which is determined by Matthiesen's rule.
This easy-to-understand rule essentially says that several separate resistivities can be distinguished in a current-carrying conductor. And the resulting value will be their sum. The terms will be the resistivity crystal lattice metal, impurities and conductor defects. Since this parameter depends on the nature of the substance, corresponding laws have been defined to calculate it, including for mixed substances.
Despite the fact that alloys are also metals, they are considered as solutions with a chaotic structure, and for calculating the resistivity, it matters which metals are included in the alloy. Basically, most alloys of two components that do not belong to transition metals, as well as rare earth metals, fall under the description of Nodheim's law.
The resistivity of metal thin films is considered as a separate topic. It is quite logical to assume that its value should be greater than that of a bulk conductor made of the same metal. But at the same time, a special empirical Fuchs formula is introduced for the film, which describes the interdependence of resistivity and film thickness. It turns out that metals in films exhibit semiconductor properties.
And the process of charge transfer is influenced by electrons, which move in the direction of the film thickness and interfere with the movement of “longitudinal” charges. At the same time, they are reflected from the surface of the film conductor, and thus one electron oscillates between its two surfaces for quite a long time. Another significant factor in increasing resistivity is the temperature of the conductor. The higher the temperature, the greater the resistance. Conversely, the lower the temperature, the lower the resistance.
Metals are the substances with the lowest resistivity at so-called “room” temperature. The only non-metal that justifies its use as a conductor is carbon. Graphite, which is one of its varieties, is widely used for making sliding contacts. He has a very good combination properties such as resistivity and sliding friction coefficient. Therefore, graphite is an indispensable material for electric motor brushes and other sliding contacts. The resistivity values of the main substances used for industrial purposes are given in the table below.
Superconductivity
At temperatures corresponding to the liquefaction of gases, that is, up to the temperature of liquid helium, which is equal to -273 degrees Celsius, the resistivity decreases almost to complete disappearance. And not just good metal conductors such as silver, copper and aluminum. Almost all metals. Under such conditions, which are called superconductivity, the structure of the metal has no inhibitory effect on the movement of charges under the influence of an electric field. Therefore, mercury and most metals become superconductors.
But, as it turned out, relatively recently in the 80s of the 20th century, some types of ceramics are also capable of superconductivity. Moreover, you do not need to use liquid helium for this. Such materials were called high-temperature superconductors. However, several decades have already passed, and the range of high-temperature conductors has expanded significantly. But mass use no such high-temperature superconducting elements have been observed. In some countries, single installations have been made with the replacement of conventional copper conductors with high-temperature superconductors. To maintain the normal regime of high-temperature superconductivity, liquid nitrogen is required. And this turns out to be a too expensive technical solution.
Therefore, the low resistivity value given by Nature to copper and aluminum still makes them irreplaceable materials for the manufacture of various electrical conductors.
As we know from Ohm’s law, the current in a section of the circuit is in the following relationship: I=U/R. The law was derived through a series of experiments by the German physicist Georg Ohm in the 19th century. He noticed a pattern: the current strength in any section of the circuit directly depends on the voltage that is applied to this section, and inversely on its resistance.
Later it was found that the resistance of a section depends on its geometric characteristics in the following way: R=ρl/S,
where l is the length of the conductor, S is its cross-sectional area, and ρ is a certain proportionality coefficient.
Thus, the resistance is determined by the geometry of the conductor, as well as by such a parameter as specific resistance (hereinafter referred to as resistivity) - this is how this coefficient is called. If you take two conductors with the same cross-section and length and place them in a circuit one by one, then by measuring the current and resistance, you can see that in the two cases these indicators will be different. Thus, the specific electrical resistance- this is a characteristic of the material from which the conductor is made, or, to be even more precise, the substance.
Conductivity and resistance
U.S. shows the ability of a substance to prevent the passage of current. But in physics there is also an inverse quantity - conductivity. It shows the ability to conduct electric current. It looks like this:
σ=1/ρ, where ρ is the resistivity of the substance.
If we talk about conductivity, it is determined by the characteristics of charge carriers in this substance. So, metals have free electrons. There are no more than three of them on the outer shell, and it is more profitable for the atom to “give them away,” which is what happens when chemical reactions with substances from the right side of the periodic table. In a situation where we have a pure metal, it has a crystalline structure in which these outer electrons are shared. They are the ones that transfer charge if an electric field is applied to the metal.
In solutions, charge carriers are ions.
If we talk about substances such as silicon, then in its properties it is semiconductor and it works on a slightly different principle, but more on that later. In the meantime, let’s figure out how these classes of substances differ:
- Conductors;
- Semiconductors;
- Dielectrics.
Conductors and dielectrics
There are substances that almost do not conduct current. They are called dielectrics. Such substances are capable of polarization in electric field, that is, their molecules can rotate in this field depending on how they are distributed in them electrons. But since these electrons are not free, but serve for communication between atoms, they do not conduct current.
The conductivity of dielectrics is almost zero, although there are no ideal ones among them (this is the same abstraction as an absolutely black body or an ideal gas).
The conventional boundary of the concept of “conductor” is ρ<10^-5 Ом, а нижний порог такового у диэлектрика - 10^8 Ом.
In between these two classes there are substances called semiconductors. But their separation into a separate group of substances is associated not so much with their intermediate state in the “conductivity - resistance” line, but with the features of this conductivity under different conditions.
Dependence on environmental factors
Conductivity is not a completely constant value. The data in the tables from which ρ is taken for calculations exists for normal environmental conditions, that is, for a temperature of 20 degrees. In reality, it is difficult to find such ideal conditions for the operation of a circuit; actually US (and therefore conductivity) depend on the following factors:
- temperature;
- pressure;
- presence of magnetic fields;
- light;
- state of aggregation.
Different substances have their own schedule for changing this parameter under different conditions. Thus, ferromagnets (iron and nickel) increase it when the direction of the current coincides with the direction of the magnetic field lines. As for temperature, the dependence here is almost linear (there is even a concept of temperature coefficient of resistance, and this is also a tabular value). But the direction of this dependence is different: for metals it increases with increasing temperature, and for rare earth elements and electrolyte solutions it increases - and this is within the same state of aggregation.
For semiconductors, the dependence on temperature is not linear, but hyperbolic and inverse: with increasing temperature, their conductivity increases. This qualitatively distinguishes conductors from semiconductors. This is what the dependence of ρ on temperature for conductors looks like:
The resistivities of copper, platinum and iron are shown here. Some metals, for example, mercury, have a slightly different graph - when the temperature drops to 4 K, it loses it almost completely (this phenomenon is called superconductivity).
And for semiconductors this dependence will be something like this:
Upon transition to the liquid state, the ρ of the metal increases, but then they all behave differently. For example, for molten bismuth it is lower than for room temperature, and for copper - 10 times higher than normal. Nickel leaves the linear graph at another 400 degrees, after which ρ falls.
But tungsten has such a high temperature dependence that it causes incandescent lamps to burn out. When turned on, the current heats the coil, and its resistance increases several times.
Also y. With. alloys depends on the technology of their production. So, if we are dealing with a simple mechanical mixture, then the resistance of such a substance can be calculated using the average, but for a substitution alloy (this is when two or more elements are combined into one crystal lattice) it will be different, as a rule, much greater. For example, nichrome, from which spirals for electric stoves are made, has such a value for this parameter that when connected to the circuit, this conductor heats up to the point of redness (which is why, in fact, it is used).
Here is the characteristic ρ of carbon steels:
As can be seen, as it approaches the melting temperature, it stabilizes.
Resistivity of various conductors
Be that as it may, in the calculations ρ is used precisely under normal conditions. Here is a table by which you can compare this characteristic of different metals:
As can be seen from the table, the best conductor is silver. And only its cost prevents its widespread use in cable production. U.S. aluminum is also small, but less than gold. From the table it becomes clear why the wiring in houses is either copper or aluminum.
The table does not include nickel, which, as we have already said, has a slightly unusual graph of y. With. on temperature. The resistivity of nickel after increasing the temperature to 400 degrees begins not to increase, but to fall. It also behaves interestingly in other substitution alloys. This is how an alloy of copper and nickel behaves, depending on the percentage of both:
And this interesting graph shows the resistance of Zinc - magnesium alloys:
High-resistivity alloys are used as materials for the manufacture of rheostats, here are their characteristics:
These are complex alloys consisting of iron, aluminum, chromium, manganese, and nickel.
As for carbon steels, it is approximately 1.7*10^-7 Ohm m.
The difference between y. With. The different conductors are determined by their application. Thus, copper and aluminum are widely used in the production of cables, and gold and silver are used as contacts in a number of radio engineering products. High-resistance conductors have found their place among manufacturers of electrical appliances (more precisely, they were created for this purpose).
The variability of this parameter depending on environmental conditions formed the basis for such devices as magnetic field sensors, thermistors, strain gauges, and photoresistors.
It has been experimentally established that resistance R metal conductor is directly proportional to its length L and inversely proportional to its cross-sectional area A:
R = ρ L/ A (26.4)
where is the coefficient ρ is called resistivity and serves as a characteristic of the substance from which the conductor is made. This is common sense: a thick wire should have less resistance than a thin wire because electrons can move over a larger area in a thick wire. And we can expect an increase in resistance with increasing length of the conductor, as the number of obstacles to the flow of electrons increases.
Typical values ρ for different materials are given in the first column of the table. 26.2. (Actual values vary depending on purity, heat treatment, temperature and other factors.)
|
Table 26.2. Specific resistance and temperature coefficient of resistance (TCR) (at 20 °C) |
||
| Substance | ρ ,Ohm m | TKS α ,°C -1 |
| Conductors | ||
| Silver | 1.59·10 -8 | 0,0061 |
| Copper | 1.68·10 -8 | 0,0068 |
| Aluminum | 2.65·10 -8 | 0,00429 |
| Tungsten | 5.6·10 -8 | 0,0045 |
| Iron | 9.71·10 -8 | 0,00651 |
| Platinum | 10.6·10 -8 | 0,003927 |
| Mercury | 98·10 -8 | 0,0009 |
| Nichrome (alloy of Ni, Fe, Cr) | 100·10 -8 | 0,0004 |
| Semiconductors 1) | ||
| Carbon (graphite) | (3-60)·10 -5 | -0,0005 |
| Germanium | (1-500)·10 -5 | -0,05 |
| Silicon | 0,1 - 60 | -0,07 |
| Dielectrics | ||
| Glass | 10 9 - 10 12 | |
| Hard rubber | 10 13 - 10 15 | |
| 1) Real values strongly depend on the presence of even small amounts of impurities. | ||
Silver has the lowest resistivity, which thus turns out to be the best conductor; however it is expensive. Copper is slightly inferior to silver; It is clear why wires are most often made of copper.
Aluminum has a higher resistivity than copper, but it has a much lower density and is preferred in some applications (for example, in power lines) because the resistance of aluminum wires of the same mass is less than that of copper. The reciprocal of resistivity is often used:
σ = 1/ρ (26.5)
σ called specific conductivity. Specific conductivity is measured in units (Ohm m) -1.
The resistivity of a substance depends on temperature. As a rule, the resistance of metals increases with temperature. This should not be surprising: as temperature increases, atoms move faster, their arrangement becomes less ordered, and we can expect them to interfere more with the flow of electrons. In narrow temperature ranges, the resistivity of the metal increases almost linearly with temperature:
Where ρ T- resistivity at temperature T, ρ 0 - resistivity at standard temperature T 0 , a α - temperature coefficient of resistance (TCR). The values of a are given in table. 26.2. Note that for semiconductors the TCR can be negative. This is obvious, since with increasing temperature the number of free electrons increases and they improve the conductive properties of the substance. Thus, the resistance of a semiconductor may decrease with increasing temperature (although not always).
The values of a depend on temperature, so you should pay attention to the temperature range within which this value is valid (for example, according to a reference book of physical quantities). If the range of temperature changes turns out to be wide, then linearity will be violated, and instead of (26.6) it is necessary to use an expression containing terms that depend on the second and third powers of temperature:
ρ T = ρ 0 (1+αT+ + βT 2 + γT 3),
where are the coefficients β And γ usually very small (we put T 0 = 0°С), but at large T the contributions of these members become significant.
At very low temperatures, the resistivity of some metals, as well as alloys and compounds, drops to zero within the accuracy of modern measurements. This property is called superconductivity; it was first observed by the Dutch physicist Geike Kamerling-Onnes (1853-1926) in 1911 when mercury was cooled below 4.2 K. At this temperature, the electrical resistance of mercury suddenly dropped to zero.
Superconductors enter a superconducting state below the transition temperature, which is typically a few degrees Kelvin (just above absolute zero). An electric current was observed in a superconducting ring, which practically did not weaken in the absence of voltage for several years.
In recent years, superconductivity has been intensively studied to understand its mechanism and to find materials that superconduct at higher temperatures to reduce the cost and inconvenience of having to cool to very low temperatures. The first successful theory of superconductivity was created by Bardeen, Cooper and Schrieffer in 1957. Superconductors are already used in large magnets, where the magnetic field is created by an electric current (see Chapter 28), which significantly reduces energy consumption. Of course, maintaining a superconductor at a low temperature also requires energy.
Comments and suggestions are accepted and welcome!
Despite the fact that this topic may seem completely banal, in it I will answer one very important question about calculating voltage loss and calculating short-circuit currents. I think this will be the same discovery for many of you as it was for me.
I recently studied one very interesting GOST:
GOST R 50571.5.52-2011 Low-voltage electrical installations. Part 5-52. Selection and installation of electrical equipment. Electrical wiring.
This document provides a formula for calculating voltage loss and states:
p is the resistivity of conductors under normal conditions, taken equal to the resistivity at temperature under normal conditions, that is, 1.25 resistivity at 20 °C, or 0.0225 Ohm mm 2 /m for copper and 0.036 Ohm mm 2 / m for aluminum;
I didn’t understand anything =) Apparently, when calculating voltage loss and when calculating short-circuit currents, we must take into account the resistance of the conductors, as under normal conditions.
It is worth noting that all table values are given at a temperature of 20 degrees.
What are normal conditions? I thought 30 degrees Celsius.
Let's remember physics and calculate at what temperature the resistance of copper (aluminum) will increase by 1.25 times.
R1=R0
R0 – resistance at 20 degrees Celsius;
R1 - resistance at T1 degrees Celsius;
T0 - 20 degrees Celsius;
α=0.004 per degree Celsius (copper and aluminum are almost the same);
1.25=1+α (T1-T0)
Т1=(1.25-1)/ α+Т0=(1.25-1)/0.004+20=82.5 degrees Celsius.
As you can see, this is not 30 degrees at all. Apparently, all calculations must be performed at the maximum permissible cable temperatures. The maximum operating temperature of the cable is 70-90 degrees depending on the type of insulation.
To be honest, I don’t agree with this, because... this temperature corresponds to a practically emergency mode of the electrical installation.
In my programs, I set the resistivity of copper as 0.0175 Ohm mm 2 /m, and for aluminum as 0.028 Ohm mm 2 /m.
If you remember, I wrote that in my program for calculating short-circuit currents, the result is approximately 30% less than the table values. There, the phase-zero loop resistance is calculated automatically. I tried to find the error, but I couldn't. Apparently, the inaccuracy of the calculation lies in the resistivity used in the program. And everyone can ask about resistivity, so there should be no questions about the program if you indicate the resistivity from the above document.
But I will most likely have to make changes to the programs for calculating voltage losses. This will result in a 25% increase in the calculation results. Although in the ELECTRIC program, the voltage losses are almost the same as mine.
If this is your first time on this blog, then you can see all my programs on the page
In your opinion, at what temperature should voltage losses be calculated: at 30 or 70-90 degrees? Are there regulations that will answer this question?