How does electrical resistance vary with temperature? How does the resistance of a conductor depend on temperature?

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 one explain the linear dependence of the conductor resistivity on temperature?

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

5. Describe the process of intrinsic conduction in semiconductors.

There are various conditions under which charge carriers pass through certain materials. And the charge of electric current is directly affected by resistance, which has a dependence on the environment. The factors that change the flow of electric current include temperature. In this article, we will consider the dependence of conductor resistance on temperature.

Metals

How does temperature affect metals? To find out this dependence, such an experiment was carried out: a battery, an ammeter, a wire and a burner are connected to each other using wires. Then you need to measure the current in the circuit. After the readings have been taken, you need to bring the burner to the wire and heat it. When the wire is heated, it can be seen that the resistance increases, and the conductivity of the metal decreases.

1. metal wire
2. Battery
3. Ammeter

The dependence is indicated and justified by the formulas:

From these formulas it follows that R conductor is determined by the formula:

An example of the dependence of the resistance of metals on temperature is provided in the video:

You also need to pay attention to such a property as superconductivity. If the environmental conditions are normal, then cooling down, the conductors reduce their resistance. The graph below shows how temperature and resistivity in mercury depend.

Superconductivity is a phenomenon that occurs when a material reaches a critical temperature (closer to zero Kelvin), at which the resistance drops sharply to zero.

gases

Gases act as a dielectric and cannot conduct electricity. And in order for it to form, charge carriers are needed. Ions play their role, and they arise due to the influence of external factors.

The dependency can be seen with an example. For the experiment, the same design is used as in the previous experiment, only the conductors are replaced by metal plates. There should be a small space between them. The ammeter should indicate no current. When the burner is placed between the plates, the device will indicate the current that passes through the gaseous medium.

Below is a graph of the current-voltage characteristic of a gas discharge, which shows that the growth of ionization at the initial stage increases, then the dependence of current on voltage remains unchanged (that is, with increasing voltage, the current remains the same) and a sharp increase in current strength, which leads to breakdown of the dielectric layer .

Consider the conductivity of gases in practice. The passage of electric current in gases is used in fluorescent lamps and lamps. In this case, the cathode and anode, two electrodes are placed in a flask, inside which there is an inert gas. How does this phenomenon depend on the gas? When the lamp is turned on, the two filaments heat up and thermionic emission is created. The inside of the bulb is coated with a phosphor that emits the light we see. How does mercury depend on the phosphor? Mercury vapor, when bombarded with electrons, produces infrared radiation, which in turn emits light.

If a voltage is applied between the cathode and the anode, then gas conduction occurs.

Liquids

Current conductors in a liquid are anions and cations that move due to an electric external field. The electrons provide little conduction. Consider the dependence of resistance on temperature in liquids.

1. Electrolyte
2. Battery
3. Ammeter

The dependence of the effect of electrolytes on heating is prescribed by the formula:

Where a is the negative temperature coefficient.

How R depends on heating (t) is shown in the graph below:

This dependence must be taken into account when charging accumulators and batteries.

Semiconductors

And how does resistance depend on heating in semiconductors? First, let's talk about thermistors. These are devices that change their electrical resistance when exposed to heat. This semiconductor has a temperature coefficient of resistance (TCR) an order of magnitude higher than metals. Both positive and negative conductors, they have certain characteristics.

Where: 1 is TKS less than zero; 2 - TKS is greater than zero.

In order for conductors such as thermistors to start working, any point on the I–V characteristic is taken as a basis:

• if the temperature of the element is less than zero, then such conductors are used as a relay;
• to control the changing current as well as what temperature and voltage, use a linear plot.

Thermistors are used when checking and measuring electromagnetic radiation, which are carried out at microwave frequencies. Due to this, these conductors are used in systems such as fire alarms, heat testing and control of the use of bulk media and liquids. Those thermistors with TCR less than zero are used in cooling systems.

Now about thermoelements. How does the Seebeck phenomenon affect thermoelements? The dependence lies in the fact that such conductors function on the basis of this phenomenon. When the temperature of the junction rises when heated, an emf appears at the junction of a closed circuit. Thus, their dependence is manifested and thermal energy is converted into electricity. To fully understand the process, I recommend that you study our instructions on how to

The resistance of metals is due to the fact that the electrons moving in the conductor interact with the ions of the crystal lattice and lose part of the energy that they acquire in the electric field.

Experience shows that the resistance of metals depends on temperature. Each substance can be characterized by a constant value for it, called temperature coefficient of resistance α. This coefficient is equal to the relative change in the resistivity of the conductor when it is heated by 1 K: α =

where ρ 0 is the resistivity at a temperature T 0 = 273 K (0 ° C), ρ is the resistivity at a given temperature T. Hence, the dependence of the resistivity of a metal conductor on temperature is expressed as a linear function: ρ = ρ 0 (1+ αT).

The dependence of resistance on temperature is expressed by the same function:

R = R0 (1+αT).

The temperature coefficients of resistance of pure metals differ relatively little from each other and are approximately equal to 0.004 K -1 . A change in the resistance of conductors with a change in temperature leads to the fact that their current-voltage characteristic is not linear. This is especially noticeable in cases where the temperature of the conductors changes significantly, for example, when an incandescent lamp is operating. The figure shows its volt - ampere characteristic. As can be seen from the figure, the current strength in this case is not directly proportional to the voltage. However, one should not think that this conclusion contradicts Ohm's law. The dependence formulated in Ohm's law is valid only with constant resistance. The dependence of the resistance of metal conductors on temperature is used in various measuring and automatic devices. The most important of these is resistance thermometer. The main part of the resistance thermometer is a platinum wire wound on a ceramic frame. The wire is placed in an environment whose temperature is to be determined. By measuring the resistance of this wire and knowing its resistance at t 0 \u003d 0 ° С (i.e. R0), calculate the temperature of the medium using the last formula.

Superconductivity. However, until the end of the XIX century. it was impossible to check how the resistance of conductors depends on temperature in the region of very low temperatures. Only at the beginning of the XX century. The Dutch scientist G. Kamerling-Onnes managed to turn the most difficultly condensed gas, helium, into a liquid state. The boiling point of liquid helium is 4.2 K. This made it possible to measure the resistance of some pure metals when they are cooled to a very low temperature.

In 1911, the work of Kamerling-Onnes ended with a major discovery. Investigating the resistance of mercury during its constant cooling, he found that at a temperature of 4.12 K, the resistance of mercury abruptly dropped to zero. Subsequently, he managed to observe the same phenomenon in a number of other metals when they were cooled to temperatures close to absolute zero. The phenomenon of complete loss of electrical resistance by a metal at a certain temperature is called superconductivity.

Not all materials can become superconductors, but their number is quite large. However, many of them were found to have a property that greatly hindered their use. It turned out that for most pure metals, superconductivity disappears when they are in a strong magnetic field. Therefore, when a significant current flows through a superconductor, it creates a magnetic field around itself and superconductivity in it disappears. Nevertheless, this obstacle turned out to be surmountable: it was found that some alloys, such as niobium and zirconium, niobium and titanium, etc., have the property of retaining their superconductivity at high current strengths. This allowed more widespread use of superconductivity.

The electrical resistance of almost all materials depends on temperature. The nature of this dependence is different for different materials.

In metals having a crystalline structure, the free path of electrons as charge carriers is limited by their collisions with ions located at the nodes of the crystal lattice. In collisions, the kinetic energy of the electrons is transferred to the lattice. After each collision, the electrons, under the influence of the electric field forces, pick up speed again and, during the next collisions, give the acquired energy to the ions of the crystal lattice, increasing their oscillations, which leads to an increase in the temperature of the substance. Thus, electrons can be considered intermediaries in the conversion of electrical energy into thermal energy. An increase in temperature is accompanied by an increase in the chaotic thermal motion of particles of matter, which leads to an increase in the number of collisions of electrons with them and makes it difficult for the orderly movement of electrons.

For most metals, within operating temperatures, the resistivity increases linearly

where and - resistivity at initial and final temperatures;

- a coefficient constant for a given metal, called the temperature coefficient of resistance (TCS);

T1 and T2 - initial and final temperatures.

For conductors of the second kind, an increase in temperature leads to an increase in their ionization, so the TCR of this type of conductor is negative.

The values ​​of the resistivity of substances and their TCS are given in reference books. It is customary to give resistivity values ​​at a temperature of +20 °C.

The resistance of the conductor is determined by the expression

R2 = R1
(2.1.2)

Task 3 Example

Determine the resistance of the copper wire of a two-wire transmission line at + 20 ° C and + 40 ° C, if the wire cross section S =

120 mm , and the length of the line is l = 10 km.

Decision

According to the reference tables, we find the resistivity copper at + 20 °C and temperature coefficient of resistance :

= 0.0175 ohm mm /m; = 0.004 deg .

Let's determine the resistance of the wire at T1 = +20 ° С according to the formula R = , considering the length of the forward and reverse wires of the line:

R1=0.0175
2 = 2.917 ohms.

The resistance of the wires at a temperature of + 40 ° C is found by the formula (2.1.2)

R2 \u003d 2.917 \u003d 3.15 ohms.

Exercise

An overhead three-wire line with a length L is made with a wire, the brand of which is given in table 2.1. It is necessary to find the value indicated by the sign "?", using the example given and choosing the option with the data indicated in it in Table 2.1.

It should be noted that the task, unlike the example, provides for calculations related to one wire of the line. In the brands of bare wires, the letter indicates the material of the wire (A - aluminum; M - copper), and the number - the cross section of the wire in mm .

Table 2.1

The study of the material of the topic ends with work with tests No. 2 (TOE-

ETM/PM” and No. 3 (TOE – ETM/IM)

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

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

Change in resistance with 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 Above zero. With temperature changes, it will change slightly. 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.

Solutions of electrolytes with increasing temperature, the resistance decreases. That is, for them the temperature coefficient will be less than zero.

The resistance of a conductor depends on the resistivity of the conductor and on the dimensions 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.

Substitute in the formula obtained above the resistance values ​​R=p*l/S R0=p0*l/S.

We get the following formula:

• p=p0(1+a*t).

This dependence is shown in the following figure.

Let's try to figure out why the resistance increases

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