Specific resistance. What is conductor resistivity

The term “resistivity” refers to a parameter possessed by copper or any other metal, and is quite often found in the specialized literature. It is worth understanding what is meant by this.

One of the types of copper cable

General information about electrical resistance

First, we should consider the concept of electrical resistance. As is known, under the influence of electric current on a conductor (and copper is one of the best conductor metals), some of the electrons in it leave their place in the crystal lattice and rush towards the positive pole of the conductor. However, not all electrons leave the crystal lattice; some of them remain in it and continue to rotate around the atomic nucleus. It is these electrons, as well as atoms located at the nodes of the crystal lattice, that create electrical resistance, preventing the movement of released particles.

This process, which we briefly outlined, is typical for any metal, including copper. Naturally, different metals, each of which has a special shape and size of the crystal lattice, resist the passage of electric current through them in different ways. It is precisely these differences that characterize resistivity - an indicator individual for each metal.

Applications of copper in electrical and electronic systems

In order to understand the reason for the popularity of copper as a material for the manufacture of electrical and electronic systems, just look at the value of its resistivity in the table. For copper, this parameter is 0.0175 Ohm*mm2/meter. In this regard, copper is second only to silver.

It is the low resistivity, measured at a temperature of 20 degrees Celsius, that is the main reason that almost no electronic and electrical device can do without copper today. Copper is the main material for the production of wires and cables, printed circuit boards, electric motors and power transformer parts.

The low resistivity that copper is characterized by allows it to be used for the manufacture of electrical devices characterized by high energy-saving properties. In addition, the temperature of copper conductors increases very little when electric current passes through them.

What affects the resistivity value?

It is important to know that there is a dependence of the resistivity value on the chemical purity of the metal. When copper contains even a small amount of aluminum (0.02%), the value of this parameter can increase significantly (up to 10%).

This coefficient is also affected by the temperature of the conductor. This is explained by the fact that as the temperature increases, the vibrations of metal atoms in the nodes of its crystal lattice intensify, which leads to the fact that the resistivity coefficient increases.

That is why in all reference tables the value of this parameter is given taking into account a temperature of 20 degrees.

How to calculate the total resistance of a conductor?

Knowing what the resistivity is is important in order to carry out preliminary calculations of the parameters of electrical equipment when designing it. In such cases, the total resistance of the conductors of the designed device, having a certain size and shape, is determined. Having looked at the resistivity value of the conductor using a reference table, determining its dimensions and cross-sectional area, you can calculate the value of its total resistance using the formula:

This formula uses the following notation:

• R is the total resistance of the conductor, which must be determined;
• p is the resistivity of the metal from which the conductor is made (determined from the table);
• l is the length of the conductor;
• S is its cross-sectional area.

Electrical resistance is the main characteristic of conductor materials. Depending on the area of ​​application of the conductor, the value of its resistance can play both a positive and negative role in the functioning of the electrical system. Also, the peculiarities of using a conductor may require taking into account additional characteristics, the influence of which in a particular case cannot be neglected.

Conductors are pure metals and their alloys. In a metal, atoms fixed in a single “strong” structure have free electrons (the so-called “electron gas”). It is these particles that in this case are charge carriers. Electrons are in constant, random motion from one atom to another. When electric field(connecting a voltage source to the ends of the metal), the movement of electrons in the conductor becomes ordered. Moving electrons encounter obstacles on their path caused by the peculiarities of the molecular structure of the conductor. When they collide with a structure, charge carriers lose their energy, giving it to the conductor (heating it). The more obstacles a conductive structure creates to charge carriers, the higher the resistance.

As the cross section of the conducting structure increases for one number of electrons, the “transmission channel” will become wider and the resistance will decrease. Accordingly, as the length of the wire increases, there will be more such obstacles and the resistance will increase.

Thus, the basic formula for calculating resistance includes the length of the wire, the cross-sectional area and a certain coefficient that relates these dimensional characteristics to the electrical quantities of voltage and current (1). This coefficient is called resistivity.
R= r*L/S (1)

Resistivity

Resistivity is unchanged and is a property of the substance from which the conductor is made. Units of measurement r - ohm*m. Often the resistivity value is given in ohm*mm sq./m. This is due to the fact that the cross-sectional area of ​​the most commonly used cables is relatively small and is measured in mm2. Let's give a simple example.

Task No. 1. Copper wire length L = 20 m, cross-section S = 1.5 mm. sq. Calculate the wire resistance.
Solution: resistivity of copper wire r = 0.018 ohm*mm. sq./m. Substituting the values ​​into formula (1) we get R=0.24 ohms.
When calculating the resistance of the power system, the resistance of one wire must be multiplied by the number of wires.
If instead of copper you use aluminum with a higher resistivity (r = 0.028 ohm * mm sq. / m), then the resistance of the wires will increase accordingly. For the example above, the resistance will be R = 0.373 ohms (55% more). Copper and aluminum are the main materials for wires. There are metals with lower resistivity than copper, such as silver. However, its use is limited due to its obvious high cost. The table below shows the resistance and other basic characteristics of conductor materials.
Table - main characteristics of conductors

Heat losses of wires

If using the cable from the above example to single-phase network 220 V connect a load of 2.2 kW, then current I = P / U or I = 2200/220 = 10 A will flow through the wire. Formula for calculating power losses in the conductor:
Ppr=(I^2)*R (2)
Example No. 2. Calculate active losses when transmitting power of 2.2 kW in a network with a voltage of 220 V for the mentioned wire.
Solution: substituting the values ​​of current and wire resistance into formula (2), we obtain Ppr=(10^2)*(2*0.24)=48 W.
Thus, when transmitting energy from the network to the load, losses in the wires will be slightly more than 2%. This energy is converted into heat generated by the conductor in environment. According to the heating condition of the conductor (according to the current value), its cross-section is selected, guided by special tables.
For example, for the above conductor, the maximum current is 19 A or 4.1 kW in a 220 V network.

To reduce active losses in power lines, increased voltage is used. At the same time, the current in the wires decreases, losses fall.

Effect of temperature

An increase in temperature leads to an increase in vibrations of the metal crystal lattice. Accordingly, electrons meet large quantity obstacles, which leads to increased resistance. The magnitude of the “sensitivity” of the metal resistance to an increase in temperature is called the temperature coefficient α. The formula for calculating temperature is as follows
R=Rн*, (3)
where Rн – wire resistance at normal conditions(at temperature t°n); t° is the temperature of the conductor.
Usually t°n = 20° C. The value of α is also indicated for temperature t°n.
Task 4. Calculate the resistance of a copper wire at a temperature t° = 90° C. α copper = 0.0043, Rн = 0.24 Ohm (task 1).
Solution: substituting the values ​​into formula (3) we get R = 0.312 Ohm. The resistance of the heated wire being analyzed is 30% greater than its resistance at room temperature.

Effect of frequency

As the frequency of the current in the conductor increases, the process of displacing charges closer to its surface occurs. As a result of an increase in the concentration of charges in the surface layer, the resistance of the wire also increases. This process is called the “skin effect” or surface effect. Skin coefficient– the effect also depends on the size and shape of the wire. For the above example, at an AC frequency of 20 kHz, the wire resistance will increase by approximately 10%. Note that high-frequency components may have a current signal from many modern industrial and household consumers ( energy-saving lamps, switching power supplies, frequency converters and so on).

Influence of neighboring conductors

There is a magnetic field around any conductor through which current flows. The interaction of the fields of neighboring conductors also causes energy loss and is called the “proximity effect”. Also note that any metal conductor has inductance created by the conductive core and capacitance created by the insulation. These parameters are also characterized by the proximity effect.

Technologies

High voltage wires with zero resistance

This type of wire is widely used in car ignition systems. Resistance high voltage wires quite small and amounts to a few fractions of an ohm per meter of length. Let us remind you that resistance of this magnitude cannot be measured with an ohmmeter. general use. Often, measuring bridges are used for the task of measuring low resistances.
Structurally, such wires have a large number of copper conductors with insulation based on silicone, plastics or other dielectrics. The peculiarity of the use of such wires is not only the operation at high voltage, but also the transfer of energy in a short period of time (pulse mode).

Bimetallic cable

The main area of ​​application of the mentioned cables is the transmission of high-frequency signals. The core of the wire is made of one type of metal, the surface of which is coated with another type of metal. Since at high frequencies only the surface layer of the conductor is conductive, it is possible to replace the inside of the wire. This saves expensive material and improves the mechanical characteristics of the wire. Examples of such wires: silver-plated copper, copper-plated steel.

Conclusion

Wire resistance is a value that depends on a group of factors: conductor type, temperature, current frequency, geometric parameters. The significance of the influence of these parameters depends on the operating conditions of the wire. Optimization criteria, depending on the tasks for wires, can be: reducing active losses, improving mechanical characteristics, reducing prices.

Specific electrical resistance, or simply resistivity of a substance - physical quantity characterizing 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 conductivity(specific 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.

Concept of electrical resistance and conductivity

Any body through which electric current flows exhibits a certain resistance to it. The property of a conductor material to prevent electric current from passing through it is called electrical resistance.

Electronic theory This explains the essence of the electrical resistance of metal conductors. Free electrons, when moving along a conductor, encounter atoms and other electrons on their way countless times and, interacting with them, inevitably lose part of their energy. Electrons experience a kind of resistance to their movement. Different metal conductors, having different atomic structures, offer different resistance to electric current.

The same thing explains the resistance of liquid conductors and gases to the passage of electric current. However, we should not forget that in these substances it is not electrons, but charged particles of molecules that encounter resistance during their movement.

Resistance is denoted by the Latin letters R or r.

The unit of electrical resistance is the ohm.

Ohm is the resistance of a column of mercury 106.3 cm high with a cross section of 1 mm2 at a temperature of 0° C.

If, for example, the electrical resistance of a conductor is 4 ohms, then it is written like this: R = 4 ohms or r = 4 ohms.

To measure large resistances, a unit called megohm is used.

One megohm is equal to one million ohms.

The greater the resistance of a conductor, the worse it conducts electric current, and, conversely, the lower the resistance of the conductor, the easier it is for electric current to pass through this conductor.

Consequently, to characterize a conductor (from the point of view of the passage of electric current through it), one can consider not only its resistance, but also the reciprocal of the resistance and called conductivity.

Electrical conductivity is the ability of a material to pass electric current through itself.

Since conductivity is the reciprocal of resistance, it is expressed as 1/R, and conductivity is denoted by the Latin letter g.

The influence of conductor material, its dimensions and ambient temperature on the value of electrical resistance

The resistance of various conductors depends on the material from which they are made. To characterize electrical resistance various materials the concept of so-called resistivity was introduced.

Resistivity is the resistance of a conductor with a length of 1 m and a cross-sectional area of ​​1 mm2. Resistivity is denoted by the letter p of the Greek alphabet. Each material from which a conductor is made has its own resistivity.

For example, the resistivity of copper is 0.017, i.e. a copper conductor 1 m long and 1 mm2 cross-section has a resistance of 0.017 ohms. The resistivity of aluminum is 0.03, the resistivity of iron is 0.12, the resistivity of constantan is 0.48, the resistivity of nichrome is 1-1.1.

The resistance of a conductor is directly proportional to its length, i.e. the longer the conductor, the greater its electrical resistance.

The resistance of a conductor is inversely proportional to its cross-sectional area, i.e. the thicker the conductor, the lower its resistance, and, conversely, the thinner the conductor, the greater its resistance.

To better understand this relationship, imagine two pairs of communicating vessels, with one pair of vessels having a thin connecting tube, and the other having a thick one. It is clear that when one of the vessels (each pair) is filled with water, its transfer to the other vessel through a thick tube will occur much faster than through a thin tube, i.e., a thick tube will have less resistance to the flow of water. In the same way, it is easier for electric current to pass through a thick conductor than through a thin one, i.e., the first offers it less resistance than the second.

The electrical resistance of a conductor is equal to the resistivity of the material from which the conductor is made, multiplied by the length of the conductor and divided by the cross-sectional area of ​​the conductor:

R = р l/S,

Where - R is the resistance of the conductor, ohm, l is the length of the conductor in m, S is the cross-sectional area of ​​the conductor, mm 2.

Cross-sectional area of ​​a round conductor calculated by the formula:

S = π d 2 / 4

Where π - constant value equal to 3.14; d is the diameter of the conductor.

And this is how the length of the conductor is determined:

l = S R / p,

This formula makes it possible to determine the length of the conductor, its cross-section and resistivity, if the other quantities included in the formula are known.

If it is necessary to determine the cross-sectional area of ​​the conductor, then the formula takes the following form:

S = р l / R

Transforming the same formula and solving the equality with respect to p, we find the resistivity of the conductor:

R = R S / l

The last formula must be used in cases where the resistance and dimensions of the conductor are known, but its material is unknown and, moreover, difficult to determine by appearance. To do this, you need to determine the resistivity of the conductor and, using the table, find a material that has such a resistivity.

Another reason that affects the resistance of conductors is temperature.

It has been established that with increasing temperature the resistance of metal conductors increases, and with decreasing temperature it decreases. This increase or decrease in resistance for pure metal conductors is almost the same and averages 0.4% per 1°C. The resistance of liquid conductors and carbon decreases with increasing temperature.

The electronic theory of the structure of matter provides the following explanation for the increase in resistance of metal conductors with increasing temperature. When heated, the conductor receives thermal energy, which is inevitably transmitted to all atoms of the substance, as a result of which the intensity of their movement increases. The increased movement of atoms creates greater resistance to the directional movement of free electrons, which is why the resistance of the conductor increases. With a decrease in temperature, Better conditions for the directional movement of electrons, and the resistance of the conductor decreases. This explains interesting phenomenon - superconductivity of metals.

Superconductivity, i.e., a decrease in the resistance of metals to zero, occurs at a huge negative temperature - 273 ° C, called absolute zero. At a temperature of absolute zero, metal atoms seem to freeze in place, without at all interfering with the movement of electrons.

We know that the cause of the electrical resistance of a conductor is the interaction of electrons with ions of the metal crystal lattice (§ 43). Therefore, it can be assumed that the resistance of a conductor depends on its length and cross-sectional area, as well as on the substance from which it is made.

Figure 74 shows the setup for conducting such an experiment. Various conductors are included in the current source circuit in turn, for example:

1. nickel wires same thickness, but of different lengths;
2. nickel wires of the same length, but different thicknesses ( different sizes cross section);
3. nickel and nichrome wires of the same length and thickness.

The current in the circuit is measured with an ammeter, and the voltage with a voltmeter.

Knowing the voltage at the ends of the conductor and the current in it, using Ohm's law, you can determine the resistance of each of the conductors.

Rice. 74. Dependence of conductor resistance on its size and type of substance

After performing these experiments, we will establish that:

1. of two nickel wires of the same thickness, the longer wire has greater resistance;
2. of two nickelin wires of the same length, the wire with a smaller cross-section has the greater resistance;
3. Nickel and nichrome wires of the same size have different resistances.

Ohm was the first to study experimentally the dependence of the resistance of a conductor on its size and the substance from which the conductor is made. He found that resistance is directly proportional to the length of the conductor, inversely proportional to its cross-sectional area and depends on the substance of the conductor.

How to take into account the dependence of resistance on the material from which the conductor is made? To do this, calculate the so-called resistivity of a substance.

Specific resistance is a physical quantity that determines the resistance of a conductor made of a given substance with a length of 1 m and a cross-sectional area of ​​1 m 2.

Let us introduce the letter designations: ρ is the resistivity of the conductor, I is the length of the conductor, S is its cross-sectional area. Then the conductor resistance R will be expressed by the formula

From it we get that:

From the last formula you can determine the unit of resistivity. Since the unit of resistance is 1 ohm, the unit of cross-sectional area is 1 m2, and the unit of length is 1 m, then the unit of resistivity is:

It is more convenient to express the cross-sectional area of ​​the conductor in square millimeters, since it is most often small. Then the unit of resistivity will be:

Table 8 shows the resistivity values ​​of some substances at 20 °C. Specific resistance changes with temperature. It has been experimentally established that for metals, for example, the resistivity increases with increasing temperature.

Table 8. Electrical resistivity of some substances (at t = 20 °C)

Of all the metals, silver and copper have the lowest resistivity. Therefore, silver and copper are the best conductors of electricity.

When wiring electrical circuits, aluminum, copper and iron wires are used.

In many cases, devices with high resistance are needed. They are made from specially created alloys - substances with high resistivity. For example, as can be seen from Table 8, the nichrome alloy has a resistivity almost 40 times greater than aluminum.

Porcelain and ebonite have such a high resistivity that they almost do not conduct electric current at all; they are used as insulators.

Questions

1. How does the resistance of a conductor depend on its length and cross-sectional area?
2. How to experimentally show the dependence of the resistance of a conductor on its length, cross-sectional area and the substance from which it is made?
3. What is the resistivity of a conductor?
4. What formula can be used to calculate the resistance of conductors?
5. What units is the resistivity of a conductor expressed in?
6. What substances are conductors used in practice made from?