Specific electrical resistance of conductors

Electrical resistance

Electrical resistance, one of the components of Ohm's law, is expressed in ohms (Ohms). It should be noted that electrical resistance and resistivity are not the same thing. Resistivity is a property of a material, while electrical resistance is a property of an object.

The electrical resistance of a resistor is determined by a combination of its shape and the resistivity of the material from which it is made.

For example, a wirewound resistor made from a long, thin wire has a higher resistance than a resistor made from a short, thick wire of the same metal.

At the same time, a wirewound resistor made of a high resistivity material has greater electrical resistance than a resistor made of a low resistivity material. And all this despite the fact that both resistors are made of wire of the same length and diameter.

To illustrate this, we can draw an analogy with a hydraulic system, where water is pumped through pipes.

• The longer and thinner the pipe, the greater the resistance to water.
• A pipe filled with sand will resist water more than a pipe without sand.

High alloy steels

High-alloy steels have electrical resistivity several times higher than carbon and low-alloy steels. According to the table, it can be seen that at a temperature of 20°C its value is (30...86)·10-8 Ohm·m.

At a temperature of 1300°C, the resistance of high- and low-alloy steels becomes almost the same and does not exceed 131·10-8 Ohm·m.
Electrical resistivity of high-alloy steels ρе·108, Ohm·m

Wire resistance

The amount of wire resistance depends on three parameters: the resistivity of the metal, the length and diameter of the wire itself. Formula for calculating wire resistance:

where: R - wire resistance (Ohm) ρ - metal resistivity (Ohm.m) L - wire length (m) A - cross-sectional area of ​​the wire (m2)

As an example, consider a nichrome wirewound resistor with a resistivity of 1.10×10-6 Ohm.m. The wire has a length of 1500 mm and a diameter of 0.5 mm. Based on these three parameters, we calculate the resistance of the nichrome wire:

R=1.1*10-6*(1.5/0.000000196) = 8.4 Ohm

Nichrome and constantan are often used as resistance materials. Below in the table you can see the resistivity of some of the most commonly used metals.

Chromium stainless steels

Chromium stainless steels have a high concentration of chromium atoms, which increases their resistivity - the electrical conductivity of such stainless steel is not high.
At normal temperatures, its resistance is (50...60)·10-8 Ohm·m. Electrical resistivity of chromium stainless steels ρе·108, Ohm·m

Properties of resistive materials

The resistivity of a metal depends on temperature. Their values ​​are usually given for room temperature (20°C). The change in resistivity as a result of a change in temperature is characterized by a temperature coefficient.

For example, thermistors (thermistors) use this property to measure temperature. On the other hand, in precision electronics, this is a rather undesirable effect. Metal film resistors have excellent temperature stability properties. This is achieved not only due to the low resistivity of the material, but also due to the mechanical design of the resistor itself.

Many different materials and alloys are used in the manufacture of resistors. Nichrome (an alloy of nickel and chromium), due to its high resistivity and resistance to oxidation at high temperatures, is often used as a material for making wirewound resistors. Its disadvantage is that it cannot be soldered. Constantan, another popular material, is easy to solder and has a lower temperature coefficient.

Sources: joyta.ru, dpva.ru

Resistivity of metals, electrolytes and substances (Table)

Resistivity of metals and insulators

The reference table gives the values ​​of resistivity p of some metals and insulators at a temperature of 18-20 ° C, expressed in ohm cm. The value of p for metals strongly depends on impurities; the table shows the values ​​of p for chemically pure metals, and for insulators they are given approximately. Metals and insulators are arranged in the table in order of increasing p .

Metal resistivity table

Table of resistivity of insulators

Resistivity of pure metals at low temperatures

The table gives the resistivity values ​​(in ohm cm) of some pure metals at low temperatures (0°C).

Resistance ratio Rt/Rq of pure metals at temperatures T ° K and 273 ° K.

The reference table gives the ratio Rt/Rq of the resistances of pure metals at temperatures T ° K and 273 ° K.

Specific resistance of electrolytes

The table gives the values ​​of the resistivity of electrolytes in ohm cm at a temperature of 18 ° C. The concentration of solutions is given in percentages, which determine the number of grams of anhydrous salt or acid in 100 g of solution.

_______________

Source of information: BRIEF PHYSICAL AND TECHNICAL GUIDE / Volume 1, - M.: 1960.

AISI 304

International standard American ASTM A240 European EN 10088-2 Russian GOST 5632-72

AMS 5513 ASTM A 240

ASTM A 666

Classification

corrosion-resistant, heat-resistant steel

Application

• Household items
• Sinks
• Frames for metal structures in the construction industry
• Kitchen utensils and catering equipment
• Dairy equipment, brewing
• Welded structures
• Tanks on ships and land tankers for food, beverages and some chemicals

Typically, steel manufacturers divide the grade into three main classes (grades) according to their drawing ability:

• AISI 304 - Main grade
• AISI 304 DDQ (Normal and deep drawing) - Deep drawing grade
• AISI 304 DDS (Extra deep drawing) - Extra deep drawing grade

Main characteristics

• good overall corrosion resistance
• good ductility
• excellent weldability

Chemical composition (% by weight)

standard grade C Si Mn PS Cr Ni

Mechanical properties

AISI 304 Tensile strength (σв), N/mm² Yield strength (σ0.2), N/mm² Yield strength (σ1.0), N/mm² Elongation (σ), % Brinell hardness (HB) Rockwell hardness (HRB)

Mechanical properties at high temperatures

All these values ​​refer only to AISI 304

.

Physical properties

Physical properties Symbols Unit of measurement Temperature Value

Corrosion resistance

304 steels have good resistance to general corrosive environments, but are not recommended where there is a risk of intergranular corrosion. They are well suited for use in fresh water and urban and rural environments. In all cases, regular cleaning of external surfaces is necessary to maintain their original condition.

304 steels have good resistance to various acids:

• phosphoric acid in all concentrations at ambient temperature,
• nitric acid up to 65% at temperatures 20°C - 50°C,
• formic and lactic acid at room temperature,
• acetic acid at a temperature of 20°C - 50°C.

They are recommended for the production of equipment in contact with cold or hot food products: wine, beer, milk (fermented milk products), alcohol, natural fruit juices, syrups, molasses, etc.

Acidic environments

Temperature, °C 20 80

Code: 0 = high degree of protection - Corrosion rate less than 100 µm/year 1 = partial protection - Corrosion rate from 100 to 1000 µm/year

2 = no protection - Corrosion rate more than 1000 µm/year

Atmospheric influences

Comparison of 304

grades with other metals in various environments (Corrosion rate calculated for 10-year exposure).
Environment Corrosion rate (µm/year)AISI 304 Aluminum-3S Carbon steel

Resistant to corrosion in boiling chemicals

Boiling environment Metal condition Corrosion rate (mm/year)

High conductivity materials

The most widespread materials of high conductivity include copper and aluminum (Superconducting materials, which have a typical resistance 10-20 times lower than ordinary conductive materials (metals), are discussed in the section Superconductivity).

Copper

The advantages of copper, which ensure its widespread use as a conductor material, are as follows:

1. low resistivity;
2. sufficiently high mechanical strength;
3. corrosion resistance is satisfactory in most applications;
4. good workability: copper is rolled into sheets, strips and drawn into wire, the thickness of which can be increased to thousandths of a millimeter;
5. relative ease of soldering and welding.

Copper is most often obtained by processing sulfide ores. After a series of ore smelting and roasting with intense blasting, copper intended for electrical purposes must undergo a process of electrolytic purification.

Copper grades M1 and M0 are most often used as conductor material. M1 grade copper contains 99.9% Cu, and in the total amount of impurities (0.1%) oxygen should be no more than 0.08%. The presence of oxygen in copper worsens its mechanical properties. The best mechanical properties are found in M0 grade copper, which contains no more than 0.05% impurities, including no more than 0.02% oxygen.

Copper is a relatively expensive and scarce material, so it is increasingly being replaced by other metals, especially aluminum.

In some cases, alloys of copper with tin, silicon, phosphorus, beryllium, chromium, magnesium, and cadmium are used. Such alloys, called bronzes, with the correct composition, have significantly higher mechanical properties than pure copper.

Aluminum

Aluminum is the second most important conductor material after copper. This is the most important representative of the so-called light metals: the density of cast aluminum is about 2.6, and rolled aluminum is 2.7 Mg/m3. Thus, aluminum is approximately 3.5 times lighter than copper. The temperature coefficient of expansion, specific heat capacity and heat of fusion of aluminum are greater than those of copper. Due to the high values ​​of specific heat capacity and heat of fusion, heating aluminum to the melting point and transferring it to a molten state requires more heat than heating and melting the same amount of copper, although the melting point of aluminum is lower than that of copper.

Aluminum has lower properties compared to copper - both mechanical and electrical. With the same cross-section and length, the electrical resistance of an aluminum wire is 1.63 times greater than that of a copper wire. It is very important that aluminum is less scarce than copper.

For electrical purposes, aluminum containing no more than 0.5% impurities, grade A1, is used. Even purer AB00 grade aluminum (no more than 0.03% impurities) is used for the manufacture of aluminum foil, electrodes and housings of electrolytic capacitors. Aluminum of the highest purity AB0000 has an impurity content of no more than 0.004%. Additives of Ni, Si, Zn or Fe at a content of 0.5% reduce the γ of annealed aluminum by no more than 2-3%. A more noticeable effect is exerted by Cu, Ag and Mg impurities, which, at the same mass content, reduce γ aluminum by 5-10%. Ti and Mn greatly reduce the electrical conductivity of aluminum.

Aluminum oxidizes very actively and becomes covered with a thin oxide film with high electrical resistance. This film protects the metal from further corrosion.

It will be interesting➡ Capacitor energy

Aluminum alloys have increased mechanical strength. An example of such an alloy is Aldrey, containing 0.3-0.5% Mg, 0.4-0.7% Si and 0.2-0.3% Fe. In aldrey, the Mg2Si compound is formed, which imparts high mechanical properties to the alloy.

Iron and steel

Iron (steel), as the cheapest and most accessible metal, which also has high mechanical strength, is of great interest for use as a conductor material. However, even pure iron has a significantly higher resistivity compared to copper and aluminum; ρ steel, i.e. iron mixed with carbon and other elements is even higher. Ordinary steel has low corrosion resistance: even at normal temperatures, especially in conditions of high humidity, it quickly rusts; As the temperature rises, the corrosion rate increases sharply. Therefore, the surface of steel wires must be protected by a layer of more resistant material. Zinc coating is usually used for this purpose.

In some cases, to reduce the consumption of non-ferrous metals, the so-called bimetal is used. It is steel coated on the outside with a layer of copper, with both metals connected to each other firmly and continuously.

Sodium

Sodium metal is a very promising conductor material. Sodium can be obtained by electrolysis of molten sodium chloride NaCl in virtually unlimited quantities. From a comparison of the properties of sodium with the properties of other conductor metals, it is clear that the resistivity of sodium is approximately 2.8 times greater than ρ of copper and 1.7 times greater than ρ of aluminum, but due to the extremely low density of sodium (its density is almost 9 times less than the density of copper), a wire made of sodium for a given conductivity per unit length should be significantly lighter than a wire made of any other metal. However, sodium is extremely active chemically (it oxidizes intensely in air and reacts violently with water), which is why the sodium wire must be protected with a sealing sheath. The sheath must give the wire the necessary mechanical strength, since sodium is very soft and has a low tensile strength during deformation.

What do resistivity numbers mean?

In order to be able to compare the resistivity of different materials, from products such as copper and aluminum to other metals and substances including bismuth, brass and even semiconductors, it is necessary to use a standard measurement.

The unit of resistivity in the International System of Units (SI) is Ohm m.

The SI unit of resistivity is equal to the resistivity of a substance such that a homogeneous conductor 1 m long with a cross-sectional area of ​​1 m2, made from this substance, has a resistance of 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

Chromium-nickel austenitic steels

Chromium-nickel austenitic steels are also stainless, but due to the addition of nickel they have a resistivity almost one and a half times higher than that of chromium steels - it reaches a value of (70...90)·10 -8 Ohm·m.

Electrical resistivity of chromium-nickel stainless steels ρe·10 8 , Ohm m

Capacitance

It has a different nature than inductive. It is convenient to illustrate this concept using the example of an electrical circuit consisting of a power source, the terminals of which are connected to the plates of a capacitor. Immediately after connection, a charge will gradually accumulate on them, creating a current in the circuit.

After reaching the limit value, which is determined by the capacitance of the part, the current will not flow through the circuit. If you then disconnect the wires from the terminals and then connect the latter, then charges will begin to move between them until the potential difference becomes zero.

If you connect an AC source to the capacitor, the following will happen. As the potential difference increases, the charge on the capacitor plates will increase. When the voltage enters the decreasing phase, the accumulated charge will begin to drain from them, forming a current in the opposite direction. Then the potential difference will become negative, but in absolute value it will increase to its maximum value. In this case, the capacitor will begin to charge again, but the sign of the incoming charges will not be the same as it was before.

When the voltage begins to increase (decreasing in absolute value), the charge will drain from the capacitor plates. When the potential difference at the source reaches zero and continues to increase, a new cycle of changes will begin.

At each stage of the described situation, the current from the capacitor plates will have the opposite direction to that generated by the variable potential difference of the power source.

The decrease in current that occurs in this way represents the physical meaning of capacitance. It is denoted by the letters XC and is calculated using the formula:

XС = 1/(w×C) = 1/(2π×f×C), where

• C is the capacitance of the capacitor used;
• w is the circular frequency of alternating current;
• π—pi number;
• f is the frequency of alternating current.

In the case under consideration, changes in current lag behind voltage.

What does it depend on

Resistance depends on temperature. It increases when the thermometer rises. This is explained by physicists in such a way that as the temperature increases, atomic vibrations in the crystalline conductor lattice increase. This prevents free electrons from moving around.

Note! As for semiconductors and dielectrics, the value decreases due to the fact that the structure of the concentration of charging carriers increases.

Temperature dependence as the main property of conductive resistance

Impedance

When using several varieties, it is important to know how they fit together. Active resistance is present in any circuit. It helps convert part of the electrical energy into heat. Reactance occurs only in an alternating current circuit. To determine its value, it is necessary to subtract capacitive from inductive. This characteristic shows the energy that pulsates in a circuit, moving from one form to another.

Impedance is the sum of active and reactance in an AC circuit, but this addition must be done in a special way. To do this, you need to draw a right triangle, the legs of which should have a length equal to the value of active and reactive resistance, respectively.

The length of the hypotenuse will numerically express the total resistance of the electrical circuit. To determine it, a rule is used that says that the sum of the squares of the legs is equal to the square of the hypotenuse. This rule is called the Pythagorean theorem. Therefore, the formula that can be used to find the total resistance is:

Z = √(R^2+〖(XL-XC)〗^2 ), where

• Z—impedance;
• R is the value of the active component;
• XL and XC are the values ​​of the inductive and capacitive parameters, respectively.

Therefore, when calculating impedance or impedance, you need to consider what capacitance and inductance are and how they may appear in electrical circuits. These quantities are also called parasitic, since they can negatively affect the operation of the electrical appliance. Their occurrence is attributed to unpredictable factors. In this case, capacitive or inductive reactance, which has a small value, can be neglected when performing calculations.

What is it measured in?

According to the international system of units, the value is measured in ohms multiplied by a meter. In some cases, the unit used is ohm multiplied by millimeter squared divided by meter. This is a designation for a conductor having a meter length and a square millimeter cross-sectional area.

Unit

Why resistance occurs

Electrons, colliding with charged atoms (ions) that make up the crystal lattice of the conductor, lose speed. The mass of an atom significantly exceeds the mass of an electron, so their collision leads to a loss of speed (“braking”) and a change in the direction of motion of the electron. This creates resistance to the flow (increase) of current. This means that resistance is a physical quantity.

Collisions of electrons with atoms.

Surface resistance

The surface resistance value is calculated in the same way as the wire resistance. In this case, the cross-sectional area can be represented as the product of w and t:

For some materials, such as thin films, the relationship between resistivity and film thickness is called sheet sheet resistance RS: where RS is measured in ohms. For this calculation, the film thickness must be constant.

Often, resistor manufacturers cut tracks into the film to increase resistance to increase the path for electrical current.

What is the resistance of copper wire

In metals, a current is formed when an electric field appears. It “forces” electrons to move in an orderly manner, in one direction. Electrons from the distant orbits of an atom, weakly held by the nucleus, form a current.

Copper wires

As negative particles pass through the crystal lattice of copper molecules, they collide with atoms and other electrons. There is an obstacle or resistance to the directional movement of particles.

To evaluate the resistance to current, the value of “electrical resistance” or “electrical impedance” was introduced. It is designated by the letter “R” or “r”. Resistance is calculated using Georg Ohm's formula: R=, where U is the potential difference or voltage acting on a section of the circuit, I is the current strength.

Concept of resistance

Important! The higher the impedance value of a metal, the less current passes through it, and it is copper conductors that are so widespread in electrical engineering due to this property.

Based on Ohm's formula, the magnitude of the current is affected by the applied voltage at a constant R. But the resistance of copper wires varies depending on their physical characteristics and operating conditions.

Carbon steels

Carbon steels at room temperature, as already mentioned, have low electrical resistivity due to their high iron content. At 20°C, the value of their resistivity is in the range from 13·10 -8 (for steel 08KP) to 20·10 -8 Ohm m (for U12).

When heated to temperatures above 1000°C, the ability of carbon steels to conduct electric current is greatly reduced. The resistance value increases by an order of magnitude and can reach a value of 130·10 -8 Ohm·m.

Electrical resistivity of carbon steels ρe·10 8 , Ohm m

What affects the resistance of a copper wire

The electrical impedance of a copper cable depends on several factors:

• Specific resistance;
• Wire cross-sectional area;
• Wire lengths;
• External temperature.

The last point can be neglected in conditions of domestic use of the cable. A noticeable change in impedance occurs at temperatures above 100°C.

Resistance dependence

Resistivity in the SI system is denoted by the letter ρ. It is defined as the resistance value of a conductor having a cross-section of 1 m2 and a length of 1 m, measured in Ohm ∙ m2. This dimension is inconvenient in electrical calculations, so the unit of measurement Ohm ∙ mm2 is often used.

Important! This parameter is a characteristic of the substance - copper. It does not depend on the shape or cross-sectional area. The purity of the copper, the presence of impurities, the method of making the wire, and the temperature of the conductor are factors that affect the resistivity.

The dependence of the parameter on temperature is described by the following formula: ρt= ρ20[1+ α(t−20°C)]. Here ρ20 is the resistivity of copper at 20°C, α is an empirically found coefficient, from 0°C to 100°C for copper it has a value equal to 0.004 °C-1, t is the temperature of the conductor.

Below is a table of ρ values ​​for different metals at a temperature of 20°C.

Resistivity table

According to the table, copper has a low resistivity, lower only for silver. This ensures good conductivity of the metal.

The thicker the wire, the lower its resistance. The dependence of R of the conductor on the cross-section is called “inversely proportional”.

Important! As the cross-sectional area of ​​the cable increases, it is easier for electrons to pass through the crystal lattice. Therefore, with increasing load and increasing current density, the cross-sectional area should be increased.

An increase in the length of a copper cable entails an increase in its resistance. Impedance is directly proportional to the length of the wire. The longer the conductor, the more atoms there are in the path of free electrons.

conclusions

The last element that affects the resistance of copper is the temperature of the environment. The higher it is, the greater the amplitude of movement of the atoms of the crystal lattice. Thus, they create an additional obstacle for electrons participating in directed movement.

Important! If you lower the temperature to absolute zero, which has a value of 0° K or -273°C, then the opposite effect will be observed - the phenomenon of superconductivity. In this state, the substance has zero resistance.

Temperature correlation