Copper resistivity: how the value is measured, calculation formulas, indicators for iron and aluminum

Each substance is capable of conducting current to a different degree, this value is influenced by the resistance of the material. The resistivity of copper, aluminum, steel and any other element is denoted by the letter of the Greek alphabet ρ. This value does not depend on such characteristics of the conductor as size, shape and physical state, while ordinary electrical resistance takes these parameters into account. Resistivity is measured in Ohms multiplied by mm² and divided by meter.

Categories and their description

Any material is capable of exhibiting two types of resistance, depending on the electricity supplied to it. The current can be alternating or constant, which significantly affects the technical parameters of the substance. So, there are such resistances:

1. Omicheskoe. It manifests itself under the influence of direct current. It characterizes the friction created by the movement of electrically charged particles in a conductor.
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2. Active. It is determined according to the same principle, but it is already created under the influence of alternating current.

In this regard, there are also two definitions of the specific value. For direct current, it is equal to the resistance, which is exerted by a unit of length of a conductive material with a unit fixed cross-sectional area. The potential electric field affects all conductors, as well as semiconductors and solutions capable of conducting ions. This value determines the conductive properties of the material itself. The shape of the conductor and its dimensions are not taken into account, therefore it can be called basic in electrical engineering and materials science.

Under the condition of the passage of alternating current, the specific value is calculated taking into account the thickness of the conductive material. Here, not only the potential, but also the eddy current is influenced, in addition, the frequency of the electric fields is taken into account. The resistivity of this type is greater than at constant current, since here the positive value of the resistance to the vortex field is taken into account. Also, this value depends on the shape and size of the conductor itself. It is these parameters that determine the nature of the vortex motion of charged particles.

Alternating current causes certain electromagnetic phenomena in conductors. They are very important for the electrical performance of a conductive material:

1. The skin effect is characterized by the weakening of the electromagnetic field, the more the further it penetrates into the conductor's medium. This phenomenon is also called surface effect.
2. The proximity effect reduces the current density due to the proximity and influence of adjacent wires.

These effects are very important when calculating the optimal conductor thickness, since when using a wire with a radius more depth of current penetration into the material, the rest of its mass will remain unused, and therefore, such an approach will be ineffective. In accordance with the calculations performed, the effective diameter of the conductive material in some situations will be as follows:

• for a current of 50 Hz - 2.8 mm;
• 400 Hz - 1 mm;
• 40 kHz - 0.1 mm.

In view of this, for high-frequency currents, the use of flat multicore cables, consisting of many thin wires, is actively used.

Characteristics of metals

Specific indicators of metal conductors are contained in special tables. Based on these data, the necessary further calculations can be made. An example of such a resistivity table can be seen in the image.

The table shows that silver has the highest conductivity - it is an ideal conductor among all existing metals and alloys. If you calculate how many wires from this material are required to obtain a resistance of 1 Ohm, then 62.5 m will come out.Wire made of iron for the same value will need as much as 7.7 m.

The virtues of copper

No matter how wonderful properties silver may have, it is too expensive material for mass use in power grids, so it is widely used in everyday life and industry copper. In terms of the specific indicator, it is in second place after silver, and in terms of prevalence and ease of production, it is much better than it. Copper has other advantages that have made it the most widely used conductor. These include:

• high resistance to corrosion;
• mechanical strength;
• resistance to deformation;
• ease of fixing by soldering and welding;
• high machinability (due to its softness, copper is rolled into sheets of any thickness, and stretched from it, the wire can be so thin that its cross section will have the value of thousandths millimeter).

For use in electrical engineering, refined copper is used, which, after smelting from sulfide ore, undergoes roasting and blowing processes, and then necessarily undergoes electrolytic purification. After such processing, you can get a material of very high quality (grades M1 and M0), which will contain from 0.1 to 0.05% impurities. An important nuance is the presence of oxygen in extremely small quantities, since it negatively affects the mechanical characteristics of copper.

This metal is often replaced with cheaper materials - aluminum and iron, as well as various bronzes (alloys with silicon, beryllium, magnesium, tin, cadmium, chromium and phosphorus). Such compositions have a higher strength than pure copper, albeit with lower conductivity.

Benefits of aluminum

Although aluminum has greater resistance and is more fragile, its widespread use is due to the fact that it is not as scarce as copper, and therefore is cheaper. Aluminum has a resistivity of 0.028, and its low density makes it 3.5 times lighter than copper.

For electrical work, purified aluminum grade A1 is used, containing no more than 0.5% impurities. The higher grade AB00 is used for the manufacture of electrolytic capacitors, electrodes and aluminum foil. The content of impurities in this aluminum is not more than 0.03%. There is also a pure metal AB0000, including no more than 0.004% additives. The impurities themselves are also important: nickel, silicon and zinc insignificantly affect the conductivity of aluminum, and the content of copper, silver and magnesium in this metal gives a tangible effect. Thallium and manganese decrease the conductivity the most.

Aluminum has good anti-corrosion properties. Upon contact with air, it becomes covered with a thin oxide film, which protects it from further destruction. To improve the mechanical characteristics, the metal is alloyed with other elements.

Indicators of steel and iron

The specific resistance of iron is very high in comparison with copper and aluminum, however, due to availability, strength and resistance to deformation, the material is widely used in electrical production.

Although iron and steel, whose resistivity is even higher, have significant drawbacks, manufacturers of conductive material have found methods to compensate for them. In particular, the low corrosion resistance is overcome by coating the steel wire with zinc or copper.

Sodium properties

Metallic sodium is also very promising in conductor production. In terms of resistance, it significantly exceeds copper, but has a density 9 times less than that of it. This allows the material to be used in the manufacture of ultra-light wires.

Metallic sodium is very soft and completely unstable to any kind of deformation effects, which makes it use is problematic - a wire made of this metal must be covered with a very strong sheath with an extremely small flexibility. The casing must be airtight, since sodium is highly reactive in the most neutral conditions. It instantly oxidizes in air and shows a violent reaction with water, including air contained.

Another benefit of using sodium is its availability. It can be obtained in the process of electrolysis of molten sodium chloride, of which there is an unlimited amount in the world. Other metals are clearly losing in this regard.

To calculate the performance of a specific conductor, it is necessary to divide the product of the specific number and length of the wire by its cross-sectional area. The result is the resistance value in Ohms. For example, to determine what the resistance of 200 m of iron wire with a nominal cross-section of 5 mm² is equal to, you need to multiply 0.13 by 200 and divide the result by 5. The answer is 5.2 ohms.

Calculation rules and features

Microohmmeters are used to measure the resistance of metallic media. Today they are produced in digital form, so the measurements carried out with their help are accurate. It can be explained by the fact that metals have a high level of conductivity and have extremely low resistance. For example, the lower threshold of the gauges is 10 ^-7 Ohm.

With the help of microohmmeters, you can quickly determine how good the contact is and what resistance the windings of generators, electric motors and transformers, as well as electric buses show. The presence of inclusions of other metal in the ingot can be calculated. For example, a gold-plated tungsten piece exhibits half the conductivity of an all-gold piece. In the same way, you can identify internal defects and cavities in the conductor.

To calculate the parameters of a wire - its length, diameter and resistance - you just need to know the value of its specific value ρ.

The resistivity formula is as follows: ρ = Ohmmm²/ m. In words, it can be described as the resistance of 1 meter of a conductorwith a cross-sectional area of ​​1 mm². The temperature is assumed to be standard - 20 ° C.

Influence of temperature on measurement

Heating or cooling some conductors has a significant effect on the performance of measuring instruments. As an example, the following experiment can be cited: it is necessary to connect a spirally wound wire to the battery and connect an ammeter to the circuit.

The more the conductor heats up, the less the instrument readings become. The strength of the current is inversely proportional to the resistance. Therefore, it can be concluded that as a result of heating, the conductivity of the metal decreases. To a greater or lesser extent, all metals behave in this way, however, practically no changes in conductivity are observed in some alloys.

It is noteworthy that liquid conductors and some solid non-metals tend to decrease their resistance with increasing temperature. But scientists turned to this ability of metals to their advantage. Knowing the temperature coefficient of resistance (α) when heating some materials, it is possible to determine the external temperature. For example, a platinum wire placed on a mica frame is placed in an oven and the resistance is measured. Depending on how much it has changed, a conclusion is made about the temperature in the oven. This design is called a resistance thermometer.

If at temperature t0 conductor resistance is r0, and at a temperature t equals rt, then the temperature coefficient of resistance is

This formula can only be calculated within a certain temperature range (up to about 200 ° C).