How does the resistance of a conductor vary with increasing temperature? Dependence of metal resistance on temperature

Each substance has its own resistivity. Moreover, the resistance will depend on the temperature of the conductor. Let us verify this by conducting the following experiment.

Let's pass current through a steel spiral. In a circuit with a spiral, we connect an ammeter in series. It will show some value. Now we will heat the spiral in the flame of a gas burner. The current value shown by the ammeter will decrease. That is, the current strength will depend on the temperature of the conductor.

Change in resistance depending on temperature

Let at a temperature of 0 degrees, the resistance of the conductor is equal to R0, and at a temperature t the resistance is equal to R, then the relative change in resistance will be directly proportional to the change in temperature t:

• (R-R0)/R=a*t.

In this formula, a is the proportionality coefficient, which is also called the temperature coefficient. It characterizes the dependence of the resistance possessed by a substance on temperature.

Temperature coefficient of resistance numerically equal to the relative change in the resistance of the conductor when it is heated by 1 Kelvin.

For all metals temperature coefficient more than zero. It will change slightly with temperature changes. Therefore, if the temperature change is small, then the temperature coefficient can be considered constant and equal to the average value from this temperature range.

Electrolyte solutions' resistance decreases with increasing temperature. That is, for them the temperature coefficient will be less than zero.

The conductor resistance depends on resistivity conductor and the size of the conductor. Since the dimensions of the conductor change slightly when heated, the main component of the change in the resistance of the conductor is the resistivity.

Dependence of conductor resistivity on temperature

Let's try to find the dependence of the resistivity of the conductor on temperature.

Let us substitute the resistance values ​​R=p*l/S R0=p0*l/S into the formula obtained above.

We get the following formula:

• p=p0(1+a*t).

This dependence is presented in the following figure.

Let's try to figure out why the resistance increases

When we increase the temperature, the amplitude of vibrations of ions at the nodes of the crystal lattice increases. Therefore, free electrons will collide with them more often. In a collision, they will lose the direction of their movement. Consequently, the current will decrease.

2. How does the resistivity of a conductor depend on its temperature? In what units is the temperature coefficient of resistance measured?

3. How can we explain the linear dependence of the resistivity of a conductor on temperature?

4. Why does the resistivity of semiconductors decrease with increasing temperature?

5. Describe the process of intrinsic conduction in semiconductors.

One of the characteristics of any conductive electric current material is the dependence of resistance on temperature. If it is depicted as a graph on where horizontal axis time intervals (t) are marked, and along the vertical - the value of ohmic resistance (R), then it turns out broken line. The dependence of resistance on temperature schematically consists of three sections. The first corresponds to slight heating - at this time the resistance changes very slightly. This happens until a certain point, after which the line on the graph sharply goes up - this is the second section. The third and final component is a straight line extending upward from the point at which the growth of R stopped, at a relatively small angle to the horizontal axis.

Physical meaning of this schedule the following: the dependence of the resistance on the temperature of the conductor is described as simple until the amount of heating exceeds some value characteristic of a given material. Let's give abstract example: if at a temperature of +10°C the resistance of the substance is 10 Ohms, then up to 40°C the value of R will practically not change, remaining within the measurement error. But already at 41°C there will be a jump in resistance to 70 Ohms. If further growth temperature does not stop, then for each subsequent degree there will be an additional 5 Ohms.

This property is widely used in various electrical devices, so it is natural to provide data on copper as one of the most common materials in So, for a copper conductor, heating for every additional degree leads to an increase in resistance by half a percent of specific value(can be found in reference tables, given for 20°C, 1 m length with a cross-section of 1 sq. mm).

When an electric current appears in a metal conductor - directional movement elementary particles, having a charge. Ions located in metal nodes are not able to hold electrons in their outer orbits for a long time, so they move freely throughout the entire volume of the material from one node to another. This chaotic movement is due to external energy- warmth.

Although the fact of movement is obvious, it is not directional, and therefore is not considered as a current. When electric field the electrons are oriented according to its configuration, forming a directed movement. But since the thermal effect has not disappeared anywhere, chaotically moving particles collide with directed fields. The dependence of metal resistance on temperature shows the amount of interference with the passage of current. How higher temperature, the higher the R of the conductor.

The obvious conclusion: by reducing the degree of heating, you can reduce the resistance. (about 20°K) is precisely characterized by a significant decrease in the thermal chaotic movement of particles in the structure of the substance.

This property of conductive materials has found wide application in electrical engineering. For example, the dependence of conductor resistance on temperature is used in electronic sensors. Knowing its value for any material, you can make a thermistor, connect it to a digital or analog reading device, perform the appropriate scale calibration and use it as an alternative. Most modern temperature sensors are based on exactly this principle, because the reliability is higher and the design is simpler.

In addition, the dependence of resistance on temperature makes it possible to calculate the heating of electric motor windings.

Conductor particles (molecules, atoms, ions) that do not participate in the formation of current are in thermal motion, and particles that form the current are simultaneously in thermal and directional motion under the influence of an electric field. Due to this, numerous collisions occur between particles that form the current and particles that do not participate in its formation, in which the former give up part of the energy they carry from the current source to the latter. The more collisions, the lower the speed of the ordered movement of particles that form the current. As can be seen from the formula I = enνS, a decrease in speed leads to a decrease in current. Scalar quantity, which characterizes the property of a conductor to reduce current, is called conductor resistance. From the formula of Ohm's law, resistance Ohm - the resistance of the conductor in which a current of strength is obtained 1 a with a voltage at the ends of the conductor of 1 V.

The resistance of a conductor depends on its length l, cross-section S and the material, which is characterized by resistivity The longer the conductor, the more collisions per unit time of particles that form the current with particles that do not participate in its formation, and therefore the greater the resistance of the conductor. The less cross section conductor, the denser the flow of particles that form the current, and the more often they collide with particles that do not participate in its formation, and therefore the greater the resistance of the conductor.

Under the influence of an electric field, the particles that form the current move at an accelerated pace between collisions, increasing their kinetic energy due to the energy of the field. When colliding with particles that do not produce current, they transfer to them part of their kinetic energy. As a result internal energy conductor increases, which is externally manifested in its heating. Let's consider whether the resistance of a conductor changes when it is heated.

The electrical circuit contains a coil of steel wire (string, Fig. 81, a). Having closed the circuit, we begin to heat the wire. The more we heat it, the less current the ammeter shows. Its decrease occurs because when metals are heated, their resistance increases. Thus, the resistance of a hair of an electric light bulb when it is not lit is approximately 20 ohm, and when it burns (2900° C) - 260 ohm. When the metal is heated, the thermal movement of electrons and the rate of vibration of ions increases. crystal lattice, as a result of this, the number of collisions of current-forming electrons with ions increases. This causes an increase in conductor resistance *. In metals, unfree electrons are very tightly bound to ions, so when metals are heated, the number of free electrons practically does not change.

* (Based on electron theory, it is impossible to derive an exact law for the dependence of resistance on temperature. Such a law is established quantum theory, in which the electron is considered as a particle with wave properties, and the movement of a conduction electron through a metal is a process of propagation electron waves, the length of which is determined by the de Broglie relation.)

Experiments show that when the temperature of conductors from various substances For the same number of degrees, their resistance changes differently. For example, if a copper conductor had a resistance 1 ohm, then after heating to 1°C he will have resistance 1.004 ohm, and tungsten - 1.005 ohm. To characterize the dependence of the resistance of a conductor on its temperature, a quantity called the temperature coefficient of resistance was introduced. A scalar quantity measured by the change in resistance of a conductor in 1 ohm, taken at 0° C, from a change in its temperature by 1° C, is called the temperature coefficient of resistance α. So, for tungsten this coefficient is equal to 0.005 deg -1, for copper - 0.004 deg -1. The temperature coefficient of resistance depends on temperature. For metals, it changes little with temperature. For a small temperature range, it is considered constant for a given material.

Let us derive a formula that calculates the resistance of a conductor taking into account its temperature. Let's assume that R0- conductor resistance at 0°С, when heated to 1°C it will increase by αR 0, and when heated to t°- on αRt° and it becomes R = R 0 + αR 0 t°, or

The dependence of the resistance of metals on temperature is taken into account, for example, in the manufacture of spirals for electric heating devices and lamps: the length of the spiral wire and the permissible current are calculated from their resistance in the heated state. The dependence of the resistance of metals on temperature is used in resistance thermometers, which are used to measure the temperature of heat engines, gas turbines, metal in blast furnaces, etc. This thermometer consists of a thin platinum (nickel, iron) spiral wound on a porcelain frame and placed in a protective case. Its ends are included in electrical circuit with an ammeter, the scale of which is graduated in degrees of temperature. When the coil heats up, the current in the circuit decreases, this causes the ammeter needle to move, which shows the temperature.

The reciprocal of the resistance of a given section or circuit is called electrical conductivity conductor(electrical conductivity). Electrical conductivity of a conductor The greater the conductivity of a conductor, the lower its resistance and the better it conducts current. Name of electrical conductivity unit Conductor conductivity resistance 1 ohm called Siemens.

As the temperature decreases, the resistance of metals decreases. But there are metals and alloys, the resistance of which, at a low temperature specific for each metal and alloy, sharply decreases and becomes vanishingly small - almost equal to zero(Fig. 81, b). Coming superconductivity- the conductor has practically no resistance, and since the current excited in it exists for a long time, while the conductor is at the superconducting temperature (in one of the experiments, the current was observed for more than a year). When passing a current density through a superconductor 1200 a/mm 2 no release of heat was observed. Monovalent metals, which are the best conductors of current, do not transform into a superconducting state down to the extremely low temperatures at which the experiments were carried out. For example, in these experiments copper was cooled to 0.0156°K, gold - up to 0.0204° K. If it were possible to obtain alloys with superconductivity at ordinary temperatures, then this would have great importance for electrical engineering.

According to modern ideas, the main reason for superconductivity is the formation of bound electron pairs. At superconducting temperatures between free electrons Exchange forces begin to act, causing electrons to form bound electron pairs. Such an electron gas of bound electron pairs has different properties than ordinary electron gas - it moves in a superconductor without friction against the nodes of the crystal lattice.

For metals that do not have superconductivity, when low temperatures due to the presence of impurities, an area is observed 1 – region of residual resistance, almost independent of temperature (Fig. 10.5). Residual resistance- r ost the less, the purer the metal.

Rice. 10.5. Dependence of metal resistivity on temperature

Rapid increase in resistivity at low temperatures up to the Debye temperature Q dcan be explained by the excitation of new frequencies of thermal vibrations of the lattice, at which scattering of charge carriers occurs - the region 2 .

At T> Q d, when the oscillation spectrum is fully excited, an increase in the oscillation amplitude with increasing temperature leads to a linear increase in resistance to approximately T pl - region 3 . When the periodicity of the structure is violated, the electron experiences scattering, leading to a change in the direction of motion, finite mean free paths and conductivity of the metal. The energy of conduction electrons in metals is 3–15 eV, which corresponds to wavelengths of 3–7 Å. Therefore, any violations of periodicity caused by impurities, defects, the crystal surface or thermal vibrations of atoms (phonons) cause an increase in the resistivity of the metal.

Let's carry out qualitative analysis of the temperature dependence of the resistivity of metals. Electron gas in metals is degenerate and the main mechanism of electron scattering in the region high temperatures is scattering by phonons.

Attemperature drop to absolute zero the resistance of normal metals tends to a constant value- residual resistance. An exception to this rule are superconducting metals and alloys, in which the resistance disappears below a certain critical temperature T sv (temperature of transition to the superconducting state).

With increasing temperature, the deviation of resistivity from a linear dependence for most metals occurs near the melting point T pl. Some deviation from the linear dependence can be observed in ferromagnetic metals, in which additional electron scattering occurs on violations of the spin order.

Upon reaching the melting temperature and transition to liquid state Most metals show a sharp increase in resistivity and some have a decrease. If the melting of a metal or alloy is accompanied by an increase in volume, then the resistivity increases by two to four times (for example, for mercury by 4 times).

In metals whose volume decreases during melting, on the contrary, there is a decrease in resistivity (for gallium by 53%, for antimony -29% and for bismuth -54%). Such an anomaly can be explained by an increase in density and compressibility modulus during the transition of these metals from solid to liquid state. For some molten (liquid) metals, the resistivity stops increasing with increasing temperature at a constant volume, in others it grows more slowly than in the solid state. Such anomalies, apparently, can be associated with the phenomena of lattice disorder, which occur differently in different metals during their transition from one state of aggregation to another.

An important characteristic of metals is temperature coefficient electrical resistivity showing the relative change in resistivity with a change in temperature of one Kelvin (degree)

a r - positive when the resistivity increases with increasing temperature. It is obvious that the value a r is also a function of temperature. In region 3 of linear dependence r( T) (see Figure 10.3) the following relation holds:

where r 0 and a r - resistivity and temperature coefficient of resistivity at temperatureT 0 , and r - resistivity at temperatureT. Experimental data show that for most metals a r at room temperature approximately 0.004 TO-1 .For ferromagnetic metals the value a r is slightly higher.

Residual resistivity of metals . As mentioned above, the resistance of normal metals tends to a constant value - residual resistance, as the temperature decreases to absolute zero. In normal metals (not superconductors), residual resistance arises due to scattering of conduction electrons by static defects

The general purity and perfection of a metal conductor can be determined by the ratio of resistances r = R 273 /R 4,2 K. For standard 99.999 purity copper, this ratio is 1000. More values r can be achieved by additional zone remelting and preparation of samples in the form of single crystals.

Extensive experimental material contains numerous data on measuring the resistance in metals caused by the presence of impurities in them. The following most characteristic changes in metals caused by alloying can be noted. Firstly, apart from phonon perturbations, an impurity is local violation The ideality of the lattice is perfect in all other respects. Secondly, doping affects the band structure by shifting the Fermi energy and changing the state density and effective mass, i.e. parameters that partially determine the ideal resistance of a metal. Thirdly, doping can change the elastic constants and, accordingly, the vibrational spectrum of the lattice, affecting the ideal resistance.

Total conductor resistivity at temperatures above 0K it consists of residual resistance r ost and resistivity due to scattering by thermal vibrations of the lattice - r T

This relationship is known as Matthiessen's rule of resistivity additivity. Often, however, significant deviations from Matthiessen's rule are observed, and some of these deviations may not be in favor of the applicability of the main factors affecting the resistance of metals when impurities are introduced into them. However, the second and third factors noted at the beginning of this section also make a significant contribution. But still a stronger effect on the resistance of diluted solid solutions has the first factor.

Change in residual resistance by 1 at. % impurity for monovalent metals can be found using Linde’s rule, according to which

Where a And b- constants depending on the nature of the metal and the period that occupies in Periodic table elements impurity atom;Δ Ζ - the difference between the valences of the solvent metal and the impurity atom. Calculations of resistance due to vacancies and interstitial atoms are of significant practical interest. Such defects easily arise when a sample is irradiated with particles. high energies, for example, neutrons from a reactor or ions from an accelerator.