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:
Silver - 0.016 , Lead - 0.21, Copper - 0.017, Nickelin - 0.42, Aluminum - 0.026, Manganin - 0.42, Tungsten - 0.055, Constantan - 0.5, Zinc - 0.06, Mercury - 0.96, Brass - 0.07, Nichrome - 1.05, Steel - 0.1, Fechral - 1.2, Phosphor bronze - 0.11, Chromal - 1.45.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.
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 is expensive, 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, it will be difficult to get the correct result. 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, the material will play the main 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. A very clear example of this would 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 cross-sectional shape of the conductor is neglected. 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. With alternating current, the skin effect also appears, increasing as the frequency of the current 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 the display of dimensions, resistivity is expressed in different systems of 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 a current density and electric field strength. 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.
The resistivity of metals is their ability to resist electric current passing through them. The unit of measurement for this quantity is Ohm*m (Ohm-meter). The symbol used is the Greek letter ρ (rho). High resistivity values mean poor conductivity of electrical charge by a particular material.
Steel Specifications
Before considering the resistivity of steel in detail, you should familiarize yourself with its basic physical and mechanical properties. Due to its qualities, this material is widely used in the manufacturing sector and other areas of people’s lives and activities.
Steel is an alloy of iron and carbon, contained in an amount not exceeding 1.7%. In addition to carbon, steel contains a certain amount of impurities - silicon, manganese, sulfur and phosphorus. In terms of its qualities, it is much better than cast iron; it can easily be hardened, forged, rolled and other types of processing. All types of steels are characterized by high strength and ductility.
According to its purpose, steel is divided into structural, instrumental, and also with special physical properties. Each of them contains a different amount of carbon, thanks to which the material acquires certain specific qualities, for example, heat resistance, heat resistance, resistance to rust and corrosion.
A special place is occupied by electrical steels, produced in sheet format and used in the production of electrical products. To obtain this material, silicon is doped, which can improve its magnetic and electrical properties.
In order for electrical steel to acquire the necessary characteristics, certain requirements and conditions must be met. The material must be easily magnetized and remagnetized, that is, have high magnetic permeability. Such steels have good , and their magnetization reversal is carried out with minimal losses.
The dimensions and weight of magnetic cores and windings, as well as the efficiency of transformers and their operating temperature depend on compliance with these requirements. The fulfillment of the conditions is influenced by many factors, including the resistivity of steel.
Resistivity and other indicators
The value of electrical resistivity is the ratio of the electric field strength in the metal and the current density flowing in it. For practical calculations, the formula is used: in which ρ is the resistivity of the metal (Ohm*m), E- electric field strength (V/m), and J- electric current density in the metal (A/m2). At very high electric field strength and low current density, the resistivity of the metal will be high.
There is another quantity called electrical conductivity, the inverse of resistivity, indicating the degree to which a material conducts electric current. It is determined by the formula and expressed in units of S/m - siemens per meter.
Resistivity is closely related to electrical resistance. However, they have differences among themselves. In the first case, this is a property of the material, including steel, and in the second case, the property of the entire object is determined. The quality of a resistor is influenced by a combination of several factors, primarily the shape and resistivity of the material from which it is made. For example, if a thin and long wire was used to make a wirewound resistor, then its resistance will be greater than that of a resistor made from a thick and short wire of the same metal.
Another example is resistors made of wires of the same diameter and length. However, if in one of them the material has a high resistivity, and in the other it is low, then, accordingly, the electrical resistance in the first resistor will be higher than in the second.
Knowing the basic properties of the material, you can use the resistivity of steel to determine the resistance value of a steel conductor. For calculations, in addition to the electrical resistivity, you will need the diameter and length of the wire itself. Calculations are performed using the following formula: , in which R is (Ohm), ρ - resistivity of steel (Ohm*m), L- corresponds to the length of the wire, A- its cross-sectional area.
There is a dependence of the resistivity of steel and other metals on temperature. In most calculations, room temperature is used - 20 0 C. All changes under the influence of this factor are taken into account using the temperature coefficient.
Specific electrical resistance, or simply the resistivity of a substance, is a physical quantity that characterizes the ability of a substance to prevent the passage of electric current.
Resistivity is denoted by the Greek letter ρ. The reciprocal of resistivity is called specific conductivity (electrical conductivity). Unlike electrical resistance, which is a property of a conductor and depends on its material, shape and size, electrical resistivity is a property of a substance only.
The electrical resistance of a homogeneous conductor with resistivity ρ, length l and cross-sectional area S can be calculated using the formula (assuming that neither the area nor the cross-sectional shape changes along the conductor). Accordingly, for ρ we have
From the last formula it follows: the physical meaning of the resistivity of a substance is that it represents the resistance of a homogeneous conductor of unit length and with unit cross-sectional area made from this substance.
The unit of resistivity in the International System of Units (SI) is Ohm m.
From the relationship it follows that the unit of measurement of resistivity in the SI system is equal to the resistivity of a substance at which a homogeneous conductor 1 m long with a cross-sectional area of 1 m², made from this substance, has a resistance equal to 1 Ohm. Accordingly, the resistivity of an arbitrary substance, expressed in SI units, is numerically equal to the resistance of a section of an electrical circuit made of a given substance with a length of 1 m and a cross-sectional area of 1 m².
In technology, the outdated non-systemic unit Ohm mm²/m is also used, equal to 10 −6 of 1 Ohm m. This unit is equal to the resistivity of a substance at which a homogeneous conductor 1 m long with a cross-sectional area of 1 mm², made from this substance, has a resistance equal to 1 Ohm. Accordingly, the resistivity of a substance, expressed in these units, is numerically equal to the resistance of a section of an electrical circuit made of this substance, 1 m long and a cross-sectional area of 1 mm².
Electromotive force (EMF) is a scalar physical quantity that characterizes the work of external forces, that is, any forces of non-electric origin acting in quasi-stationary DC or AC circuits. In a closed conducting circuit, the EMF is equal to the work of these forces to move a single positive charge along the entire circuit.
By analogy with the electric field strength, the concept of external force strength is introduced, which is understood as a vector physical quantity equal to the ratio of the external force acting on a test electric charge to the magnitude of this charge. Then in a closed loop the EMF will be equal to:
where is the contour element.
EMF, like voltage, is measured in volts in the International System of Units (SI). We can talk about electromotive force at any part of the circuit. This is the specific work of external forces not throughout the entire circuit, but only in a given area. The EMF of a galvanic cell is the work of external forces when moving a single positive charge inside the element from one pole to another. The work of external forces cannot be expressed through a potential difference, since external forces are non-potential and their work depends on the shape of the trajectory. So, for example, the work of external forces when moving a charge between the terminals of the current outside itself? source is zero.
Therefore, it is important to know the parameters of all elements and materials used. And not only electrical, but also mechanical. And have at your disposal some convenient reference materials that allow you to compare the characteristics of different materials and choose for design and work exactly what will be optimal in a particular situation.
In energy transmission lines, where the goal is to deliver energy to the consumer in the most productive way, that is, with high efficiency, both the economics of losses and the mechanics of the lines themselves are taken into account. The final economic efficiency of the line depends on the mechanics - that is, the device and arrangement of conductors, insulators, supports, step-up/step-down transformers, the weight and strength of all structures, including wires stretched over long distances, as well as the materials selected for each structural element. , its work and operating costs. In addition, in lines transmitting electricity, there are higher requirements for ensuring the safety of both the lines themselves and everything around them where they pass. And this adds costs both for providing electricity wiring and for an additional margin of safety of all structures.
For comparison, data are usually reduced to a single, comparable form. Often the epithet “specific” is added to such characteristics, and the values themselves are considered based on certain standards unified by physical parameters. For example, electrical resistivity is the resistance (ohms) of a conductor made of some metal (copper, aluminum, steel, tungsten, gold) having a unit length and a unit cross-section in the system of units of measurement used (usually SI). In addition, the temperature is specified, since when heated, the resistance of the conductors can behave differently. Normal average operating conditions are taken as a basis - at 20 degrees Celsius. And where properties are important when changing environmental parameters (temperature, pressure), coefficients are introduced and additional tables and dependency graphs are compiled.
Types of resistivity
Since resistance happens:
- active - or ohmic, resistive - resulting from the expenditure of electricity on heating the conductor (metal) when an electric current passes through it, and
- reactive - capacitive or inductive - which occurs from the inevitable losses due to the creation of any changes in the current passing through the conductor of electric fields, then the resistivity of the conductor comes in two varieties:
- Specific electrical resistance to direct current (having a resistive nature) and
- Specific electrical resistance to alternating current (having a reactive nature).
Here, type 2 resistivity is a complex value; it consists of two TC components - active and reactive, since resistive resistance always exists when current passes, regardless of its nature, and reactive resistance occurs only with any change in current in the circuits. In DC circuits, reactance occurs only during transient processes that are associated with turning on the current (change in current from 0 to nominal) or turning off (difference from nominal to 0). And they are usually taken into account only when designing overload protection.
In alternating current circuits, the phenomena associated with reactance are much more diverse. They depend not only on the actual passage of current through a certain cross section, but also on the shape of the conductor, and the dependence is not linear.
The fact is that alternating current induces an electric field both around the conductor through which it flows and in the conductor itself. And from this field, eddy currents arise, which give the effect of “pushing” the actual main movement of charges, from the depths of the entire cross-section of the conductor to its surface, the so-called “skin effect” (from skin - skin). It turns out that eddy currents seem to “steal” its cross-section from the conductor. The current flows in a certain layer close to the surface, the remaining thickness of the conductor remains unused, it does not reduce its resistance, and there is simply no point in increasing the thickness of the conductors. Especially at high frequencies. Therefore, for alternating current, resistance is measured in such sections of conductors where its entire section can be considered near-surface. Such a wire is called thin; its thickness is equal to twice the depth of this surface layer, where eddy currents displace the useful main current flowing in the conductor.
Of course, reducing the thickness of round wires does not exhaust the effective conduction of alternating current. The conductor can be thinned, but at the same time made flat in the form of a tape, then the cross-section will be higher than that of a round wire, and accordingly, the resistance will be lower. In addition, simply increasing the surface area will have the effect of increasing the effective cross-section. The same can be achieved by using stranded wire instead of single-core; moreover, stranded wire is more flexible than single-core wire, which is often valuable. On the other hand, taking into account the skin effect in wires, it is possible to make the wires composite by making the core from a metal that has good strength characteristics, for example, steel, but low electrical characteristics. In this case, an aluminum braid is made over the steel, which has a lower resistivity.
In addition to the skin effect, the flow of alternating current in conductors is affected by the excitation of eddy currents in surrounding conductors. Such currents are called induction currents, and they are induced both in metals that do not play the role of wiring (load-bearing structural elements), and in the wires of the entire conductive complex - playing the role of wires of other phases, neutral, grounding.
All of these phenomena occur in all electrical structures, making it even more important to have a comprehensive reference for a wide variety of materials.
The resistivity for conductors is measured with very sensitive and precise instruments, since metals with the lowest resistance are selected for wiring - on the order of ohms * 10 -6 per meter of length and sq. m. mm. sections. To measure insulation resistivity, you need instruments, on the contrary, that have ranges of very large resistance values - usually megohms. It is clear that conductors must conduct well, and insulators must insulate well.
Table
| Table of resistivity of conductors (metals and alloys) |
||||
| Conductor material | Composition (for alloys) | Resistivity ρ mΩ × mm 2/m |
||
| copper, zinc, tin, nickel, lead, manganese, iron, etc. | ||||
| Aluminum | ||||
| Tungsten | ||||
| Molybdenum | ||||
| copper, tin, aluminum, silicon, beryllium, lead, etc. (except zinc) | ||||
| iron, carbon | ||||
| copper, nickel, zinc | ||||
| Manganin | copper, nickel, manganese | |||
| Constantan | copper, nickel, aluminum | |||
| nickel, chromium, iron, manganese | ||||
| iron, chromium, aluminum, silicon, manganese | ||||
Iron as a conductor in electrical engineering
Iron is the most common metal in nature and technology (after hydrogen, which is also a metal). It is the cheapest and has excellent strength characteristics, therefore it is used everywhere as the basis for the strength of various structures.
In electrical engineering, iron is used as a conductor in the form of flexible steel wires where physical strength and flexibility are needed, and the required resistance can be achieved through the appropriate cross-section.
Having a table of resistivities of various metals and alloys, you can calculate the cross-sections of wires made from different conductors.
As an example, let's try to find the electrically equivalent cross-section of conductors made of different materials: copper, tungsten, nickel and iron wire. Let's take aluminum wire with a cross-section of 2.5 mm as the initial one.
We need that over a length of 1 m the resistance of the wire made of all these metals is equal to the resistance of the original one. The resistance of aluminum per 1 m length and 2.5 mm section will be equal to
Where R- resistance, ρ – resistivity of the metal from the table, S- cross-sectional area, L- length.
Substituting the original values, we get the resistance of a meter-long piece of aluminum wire in ohms.
After this, let us solve the formula for S
We will substitute the values from the table and obtain the cross-sectional areas for different metals.
Since the resistivity in the table is measured on a wire 1 m long, in microohms per 1 mm 2 section, then we got it in microohms. To get it in ohms, you need to multiply the value by 10 -6. But we don’t necessarily need to get the number ohm with 6 zeros after the decimal point, since we still find the final result in mm2.
As you can see, the resistance of the iron is quite high, the wire is thick.
But there are materials for which it is even greater, for example, nickel or constantan.