Electrical resistivity of steel at 20 degrees. The physical meaning of active resistance

Despite the fact that this topic may seem completely banal, in it I will answer one very important question by calculating voltage loss and calculating currents short circuit. 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? Whether there is a regulations who will answer this question?

Content:

In electrical engineering, one of the main elements of electrical circuits are wires. Their task is to pass electric current with minimal losses. It has long been determined experimentally that to minimize electricity losses, wires are best made of silver. It is this metal that provides the properties of a conductor with minimal resistance in ohms. But since this noble metal roads, its use in industry is very limited.

Aluminum and copper became the main metals for wires. Unfortunately, the resistance of iron as a conductor of electricity is too high to make a good wire. Despite its lower cost, it is used only as a supporting base for power line wires.

Such different resistances

Resistance is measured in ohms. But for wires this value turns out to be very small. If you try to take measurements with a tester in resistance measurement mode, you will get correct result it will be hard. Moreover, no matter what wire we take, the result on the device display will differ little. But this does not mean that in fact the electrical resistance of these wires will have the same effect on electricity losses. To verify this, you need to analyze the formula used to calculate the resistance:

This formula uses quantities such as:

It turns out that resistance determines resistance. There is a resistance calculated by a formula using another resistance. This electrical resistivity ρ (Greek letter rho) is what determines the advantage of a particular metal as an electrical conductor:

Therefore, if you use copper, iron, silver or any other material to make identical wires or conductors of a special design, main role It is the material that will play a role in its electrical properties.

But in fact, the situation with resistance is more complex than simply calculating using the formulas given above. These formulas do not take into account the temperature and shape of the conductor diameter. And with increasing temperature, the resistivity of copper, like any other metal, becomes greater. Very a clear example it could be an incandescent light bulb. You can measure the resistance of its spiral with a tester. Then, having measured the current in the circuit with this lamp, use Ohm’s law to calculate its resistance in the glow state. The result will be much greater than when measuring resistance with a tester.

Likewise, copper will not give the expected efficiency at high currents if the shape is neglected cross section conductor. The skin effect, which occurs in direct proportion to the increase in current, makes conductors with a circular cross-section ineffective, even if silver or copper is used. For this reason, the resistance of a round copper wire at high current may be higher than that of a flat aluminum wire.

Moreover, even if their diameter areas are the same. At alternating current The skin effect also appears, increasing as the current frequency increases. Skin effect means the tendency of current to flow closer to the surface of a conductor. For this reason, in some cases it is more profitable to use silver coating of wires. Even a slight reduction in the surface resistivity of a silver-plated copper conductor significantly reduces signal loss.

Generalization of the concept of resistivity

As in any other case that is associated with displaying dimensions, resistivity is expressed in different systems units. The SI (International System of Units) uses ohm m, but it is also acceptable to use Ohm*kV mm/m (this is a non-systemic unit of resistivity). But in a real conductor, the resistivity value is not constant. Since all materials have a certain purity, which can vary from point to point, it was necessary to create a corresponding representation of the resistance in the actual material. This manifestation was Ohm’s law in differential form:

This law most likely will not apply to household payments. But during the design of various electronic components, for example, resistors, crystal elements, it is certainly used. Since it allows you to perform calculations based on a given point for which there is current density and voltage electric field. And the corresponding resistivity. The formula is used for inhomogeneous isotropic as well as anisotropic substances (crystals, gas discharge, etc.).

How to obtain pure copper

In order to minimize losses in copper wires and cable cores, it must be especially pure. This is achieved by special technological processes:

• based on electron beam and zone melting;
• repeated electrolysis cleaning.

In practice, it is often necessary to calculate the resistance of various wires. This can be done using formulas or using the data given in table. 1.

The effect of the conductor material is taken into account using the resistivity, denoted by the Greek letter? and having a length of 1 m and a cross-sectional area of ​​1 mm2. Lowest resistivity? = 0.016 Ohm mm2/m has silver. Let us give the average value of the resistivity of some conductors:

With different amounts of impurities and with different ratios of components included in the composition of rheostatic alloys, the resistivity may change slightly.

Resistance is calculated using the formula:

where R is resistance, Ohm; resistivity, (Ohm mm2)/m; l - wire length, m; s - cross-sectional area of ​​the wire, mm2.

If the wire diameter d is known, then its cross-sectional area is equal to:

It is best to measure the diameter of the wire using a micrometer, but if you don’t have one, you should wind 10 or 20 turns of wire tightly onto a pencil and measure the length of the winding with a ruler. Dividing the length of the winding by the number of turns, we find the diameter of the wire.

To determine the length of a wire of a known diameter made of a given material necessary to obtain the required resistance, use the formula

Table 1.

Note. 1. Data for wires not listed in the table should be taken as some average values. For example, for a nickel wire with a diameter of 0.18 mm, we can approximately assume that the cross-sectional area is 0.025 mm2, the resistance of one meter is 18 Ohms, and the permissible current is 0.075 A.

2. For a different value of current density, the data in the last column must be changed accordingly; for example, at a current density of 6 A/mm2, they should be doubled.

Example 1. Find the resistance of 30 m of copper wire with a diameter of 0.1 mm.

Solution. We determine according to the table. 1 resistance of 1 m of copper wire, it is equal to 2.2 Ohms. Therefore, the resistance of 30 m of wire will be R = 30 2.2 = 66 Ohms.

Calculation using the formulas gives the following results: cross-sectional area of ​​the wire: s = 0.78 0.12 = 0.0078 mm2. Since the resistivity of copper is 0.017 (Ohm mm2)/m, we get R = 0.017 30/0.0078 = 65.50 m.

Example 2. How much nickel wire with a diameter of 0.5 mm is needed to make a rheostat with a resistance of 40 Ohms?

Solution. According to the table 1, we determine the resistance of 1 m of this wire: R = 2.12 Ohm: Therefore, to make a rheostat with a resistance of 40 Ohms, you need a wire whose length is l = 40/2.12 = 18.9 m.

Let's do the same calculation using the formulas. We find the cross-sectional area of ​​the wire s = 0.78 0.52 = 0.195 mm2. And the length of the wire will be l = 0.195 40/0.42 = 18.6 m.

When an electrical circuit is closed, at the terminals of which there is a potential difference, an electric current occurs. Free electrons, under the influence of electric field forces, 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 electron movement continuously changes: when electrons collide with atoms, molecules and other electrons, it decreases, then under the influence of an electric field it increases and decreases again during 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 passing electric current through the conductor the latter is heated.

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 convert electrical energy into thermal energy 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.

A long conductor with a small cross-section creates a large resistance to current. Short conductors with a large cross-section offer little resistance to current.

If you 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 copper wire with a cross section of 1 mm² it 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 – specific resistance of the 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 slightly change their resistance with heating. Some special alloys show virtually no change in resistance when temperature changes. The resistance of metal conductors increases with increasing temperature, while 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 greater the resistance of a conductor, the less conductivity it has, the worse it conducts electric current, and, conversely, the lower the resistance of a conductor, the greater 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 denoted 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)

The appearance of electric current occurs when the circuit is closed, when a potential difference occurs at the terminals. The movement of free electrons in a conductor is carried out under the influence of an electric field. As they move, electrons collide with atoms and partially transfer their accumulated energy to them. This leads to a decrease in their speed of movement. Subsequently, under the influence of the electric field, the speed of electron movement increases again. The result of this resistance is heating of the conductor through which the current flows. Exist various ways calculations of this value, including the resistivity formula used for materials with individual physical properties.

Electrical resistivity

The essence of electrical resistance lies in the ability of a substance to convert electrical energy into thermal energy during the action of current. This quantity is denoted by the symbol R, and the unit of measurement is Ohm. The value of resistance in each case is associated with the ability of one or another.

During the research, a dependence on resistance was established. One of the main qualities of the material is its resistivity, which varies depending on the length of the conductor. That is, as the length of the wire increases, the resistance value also increases. This dependence is defined as directly proportional.

Another property of a material is its cross-sectional area. It represents the dimensions of the cross section of the conductor, regardless of its configuration. In this case, an inversely proportional relationship is obtained when with increasing cross-sectional area it decreases.

Another factor influencing resistance is the material itself. During research, different resistance was found in different materials. Thus, the electrical resistivity values ​​for each substance were obtained.

It turned out that metals are the best conductors. Among them, silver also has the lowest resistance and high conductivity. They are used in the most critical places in electronic circuits; moreover, copper has a relatively low cost.

Substances whose resistivity is very high are considered poor conductors of electric current. Therefore they are used as insulating materials. Dielectric properties are most characteristic of porcelain and ebonite.

Thus, the resistivity of the conductor has great importance, since it can be used to determine the material from which the conductor was made. To do this, the cross-sectional area is measured, the current and voltage are determined. This allows you to set the value of the electrical resistivity, after which, using a special table, you can easily determine the substance. Therefore, resistivity is one of the most characteristic features one material or another. This indicator allows you to determine the most optimal length of the electrical circuit so that balance is maintained.

Formula

Based on the data obtained, we can conclude that resistivity will be considered the resistance of any material with unit area and unit length. That is, a resistance equal to 1 ohm occurs at a voltage of 1 volt and a current of 1 ampere. This indicator is influenced by the degree of purity of the material. For example, if you add just 1% manganese to copper, its resistance will increase 3 times.

Resistivity and conductivity of materials

Conductivity and resistivity are generally considered at a temperature of 20 0 C. These properties will differ for different metals:

• Copper. Most often used for the manufacture of wires and cables. It has high strength, corrosion resistance, easy and simple processing. In good copper, the proportion of impurities is no more than 0.1%. If necessary, copper can be used in alloys with other metals.
• Aluminum. His specific gravity less than copper, but it has a higher heat capacity and melting point. Melting aluminum requires significantly more energy than copper. Impurities in high-quality aluminum do not exceed 0.5%.
• Iron. Along with its availability and low cost, this material has high resistivity. In addition, it has low corrosion resistance. Therefore, it is practiced to coat steel conductors with copper or zinc.

The formula for resistivity under conditions of low temperatures. In these cases, the properties of the same materials will be completely different. For some of them, resistance may drop to zero. This phenomenon is called superconductivity, in which the optical and structural characteristics of the material remain unchanged.