This site could not do without an article about resistance. Well, no way! There is the most fundamental concept in electronics, which is also a physical property. You probably already know these friends:

Resistance is the property of a material to interfere with the flow of electrons. The material, as it were, resists, impedes this flow, like the sails of a frigate against a strong wind!

Almost everything in the world has the ability to resist: air resists the flow of electrons, water also resists the flow of electrons, but they still slip through. Copper wires also resist the flow of electrons, but lazily. So they pass such a stream very well.

Only superconductors have no resistance, but this is another story, since since they have no resistance, today they are not of interest to us.

By the way, the flow of electrons is the electric current. The formal definition is more pedantic, so look for it yourself in the same dry book.

And yes, electrons interact with each other. The strength of this interaction is measured in Volts and is called voltage. You say that sounds strange? Yes, nothing strange. The electrons tense up and move other electrons with force. Somewhat rustic, but the basic principle is clear.

It remains to mention the power. Power is when current, voltage and resistance gather at the same table and start working. Then the power appears - the energy that the electrons lose when passing through the resistance. By the way:

I = U/R P = U * I

Do you have, for example, a 60W light bulb with a wire. You plug it into a 220V outlet. What's next? The light bulb provides some resistance to the flow of electrons with a potential of 220V. If the resistance is too low - boom, burned out. If too large, the filament will glow very little, if at all. But if it is "just right", then the light bulb eats 60W and turns this energy into light and heat.

Heat in this case is a side effect and is called "loss" of energy, since instead of shining brighter, the light bulb spends energy on heating. enjoy energy-saving lamps! By the way, the wire also has resistance, and if the electron flow is too large, it will also heat up to a noticeable temperature. Here you can suggest reading a note about why high-voltage lines are used.

I'm sure you understand more about resistance now. At the same time, we did not fall into details like the resistivity of the material and formulas like

where ρ is resistivity conductor substances, Ohm m, l— conductor length, m, a S— cross-sectional area, m².

A few animations to complete the picture

And clearly about how the electron flow changes from depending on the temperature of the conductor and its thickness

- an electrical quantity that characterizes the property of a material to prevent the flow of electric current. Depending on the type of material, resistance can tend to zero - be minimal (mi/micro ohms - conductors, metals), or be very large (giga ohms - insulation, dielectrics). The reciprocal of electrical resistance is .

unit of measurement electrical resistance - Ohm. It is denoted by the letter R. The dependence of resistance on current and in a closed circuit is determined.

Ohmmeter- a device for direct measurement of circuit resistance. Depending on the range of the measured value, they are divided into gigaohmmeters (for large resistance - when measuring insulation), and into micro / milliohmmeters (for small resistances - when measuring transient resistance of contacts, motor windings, etc.).

There is a wide variety of ohmmeters by design. different manufacturers, from electromechanical to microelectronic. It is worth noting that a classic ohmmeter measures the active part of the resistance (the so-called ohms).

Any resistance (metal or semiconductor) in the circuit alternating current has an active and a reactive component. The sum of active and reactance is AC circuit impedance and is calculated by the formula:

where, Z is the total resistance of the AC circuit;

R is the active resistance of the AC circuit;

Xc is the capacitive reactance of the AC circuit;

(C is the capacitance, w is the angular velocity of the alternating current)

Xl is the inductive reactance of the AC circuit;

(L is the inductance, w is the angular velocity of the alternating current).

Active resistance is part of the total resistance electrical circuit, the energy of which is completely converted into other types of energy (mechanical, chemical, thermal). A distinctive feature of the active component is the complete consumption of all electricity (energy is not returned to the network back to the network), and reactance returns part of the energy back to the network (a negative property of the reactive component).

The physical meaning of active resistance

Every environment where electric charges, creates obstacles on their way (it is believed that these are the nodes of the crystal lattice), into which they seem to hit and lose their energy, which is released in the form of heat.

Thus, there is a drop (loss of electrical energy), part of which is lost due to internal resistance conducting medium.

The numerical value characterizing the ability of a material to prevent the passage of charges is called resistance. It is measured in Ohms (Ohm) and is inversely proportional to the electrical conductivity.

Miscellaneous elements periodic system Mendeleev have different electrical resistivity (p), for example, the smallest sp. silver (0.016 Ohm * mm2 / m), copper (0.0175 Ohm * mm2 / m), gold (0.023) and aluminum (0.029) have resistance. They are used in industry as the main materials on which all electrical engineering and energy are built. Dielectrics, on the other hand, have a high sp. resistance and used for insulation.

The resistance of a conducting medium can vary significantly depending on the cross section, temperature, magnitude and frequency of the current. In addition, different media have different charge carriers (free electrons in metals, ions in electrolytes, "holes" in semiconductors), which are the determining factors of resistance.

The physical meaning of reactance

In coils and capacitors, when applied, energy is accumulated in the form of magnetic and electric fields, which requires some time.

Magnetic fields in alternating current networks change following the changing direction of movement of charges, while providing additional resistance.

In addition, there is a stable phase shift and current strength, and this leads to additional losses of electricity.

Resistivity

How to find out the resistance of a material if it does not flow through it and we do not have an ohmmeter? There is a special value for this - electrical resistivity of the material in

(these are tabular values ​​that are determined empirically for most metals). With this value and the physical quantities of the material, we can calculate the resistance using the formula:

where, p- resistivity (units of measurement ohm * m / mm 2);

l is the length of the conductor (m);

S - cross section (mm 2).

Let's do a simple experiment. Using two short wires, we connect a light bulb from the headlight of the car to the car battery. The light is on and quite bright. And now we will connect the same lamp with much longer connectors. The light has clearly become weaker. What's the matter? in wire resistance.

What is electrical resistance

There are different formulations of the description of this phenomenon. Let's use one of them:

"Electrical resistance is a physical quantity that characterizes the property of a conductor to resist the flow of electric current."

In our experiment, the wires supplying voltage from the battery to the light bulb provide electrical resistance to the current flowing through the closed circuit. From the voltage source - the battery, through the wires - conductors, to the load - the lamp.

The physical essence of the phenomenon

When the load is connected to a voltage source by connectors, a closed circuit arises in which an electric field appears, causing a directed movement of wire metal electrons from the negative pole of the battery to the positive one. The electrons carry electricity from the source to the load, and cause the lamp coil to glow. On the way of their movement, the electrons hit the ions of the crystal lattice of the conductor, lose part of the energy that goes to heat the material of the connectors.

Another definition: "The cause of the appearance of electrical resistance is the result of the interaction of the electron flow with the molecules (ions) that make up the conductor."

Important note! Although electrons move from the minus of the voltage source to the plus, the direction of the electric current is historically considered the opposite - from plus to minus.

Current can flow not only in solid materials, metals, but also in liquid substances, solutions of salts, acids, alkalis. There, the main energy carriers are ions of positive and negative charge. For example, in car batteries, current flows through water solution sulfuric acid.

Conductor resistance measurement

The unit of electrical resistance in the SI system is 1 ohm. If you use Ohm's law for a section of an electrical circuit:

I=U/R,

• I is the current flowing in the circuit;
• U - voltage;
• R is the electrical resistance.

transforming the formula R = U / I, we can say that 1 ohm is equal to the ratio of a voltage of 1 volt to a current of 1 ampere.

R in this formula is a constant value and does not depend on the voltage and current values.

For larger values, units are applied:

• 1 kOhm = 1000 Ohm;
• 1 MΩ = 1,000,000 ohms;
• 1 GΩ = 1,000,000,000 ohms.

What determines the electrical resistance of a conductor

First of all, it depends on the material from which the connector is made. Different metals prevent the passage of electric current in different ways. It is known that silver, copper, aluminum conduct electric current well, and steel is much worse.

There is a concept of electrical resistivity of a material, which was designated by the Greek letter p (rho). This characteristic depends only on the internal properties of the substance from which the conductor is made. But its total resistance will also depend on the length and cross-sectional area. Here is the formula that relates all these quantities:

R = p * L / S,

• p is the resistivity of the material;
• L is the length;
• S is the cross-sectional area.

The cross-sectional area S in practical electrical engineering is usually considered in sq. mm., Then the dimension p is expressed as Ohm * sq. mm / meter.

Conclusion: to reduce the electrical resistance, and hence the losses in the electrical circuit, the material must have a minimum resistivity, and the conductor itself must be as short as possible and have a sufficiently large cross section.

Indicators for solid materials

The table shows that for the manufacture of connectors, on which the minimum amount of electricity will be lost, silver, copper and aluminum are best suited, but thermoelectric heaters (heaters) will be made from fechral and nichrome.

It should be noted that all these values ​​are valid for a temperature of 20 0 C. When the temperature rises, the electrical resistivity of metals increases, when it decreases, it falls, the exception is Constantan, its specific characteristic changes slightly.

With a strong decrease in temperature, close to absolute zero, the resistance of metals can become zero, the phenomenon of superconductivity sets in. This is explained by the fact that the ions of the crystal lattice "freeze", stop vibrating, and do not interfere with the electrons in their movement.

Indicators for liquid conductors

The specific electrical resistance of solutions of salts, acids and alkalis depends not only on their chemical composition, but also on the concentration of the solution. The temperature dependence is inverse to that of metals. When heated, the resistivity decreases, when cooled, it increases. Fluid can freeze at low temperatures and stop conducting.

A good example is the behavior car batteries in severe frost. The electrolyte - a solution of sulfuric acid, at significant sub-zero temperatures (-20, -30С 0) increases the internal electrical resistance of the battery, and the full return of current to the starter becomes impossible.

electrical conductivity

In some cases, it is more convenient to use the concept of electric current conductivity. This characteristic is measured in Siemens (cm):

• G - conductivity;
• R - resistance,
• and 1 cm \u003d 1 / ohm.

Case Study

Having received some information about electrical resistance, it is worth making a simple calculation and finding out how the characteristics of connectors affect the parameters of electrical circuits.

Back to the simplest wiring diagram, consisting of a battery, a light bulb and wires:

• Battery voltage 12.5 V.
• The lamp has a power of 21 watts.
• Copper connectors, length 1 meter x 2 pcs., section 1.5 sq. mm.

Let's find the electrical resistance of the wires: R \u003d p * L / S. We substitute our data: R \u003d 0.017 * 2 / 1.5 \u003d 0.023 Ohm.

Find the resistance of the lamp. Her electric power 21 W, when connected to a 12.5 V power source, the current in the circuit will be:

I=P/U

• I is the desired current;
• P is the lamp power;
• U is the source voltage.

We substitute the numbers: I \u003d 21 / 12.5 \u003d 1.68 A.

The resistance of the lamp is found according to Ohm's law for the circuit section. If I = U/R, then R = U/I. Or: R = 12.5 / 1.68 = 7.44 ohms.

In the calculation, we neglected the resistance of the wires, it is more than 300 times less than the electrical resistance of the load.

Find the power loss on the wires and compare it with useful power loads. We know the current in the circuit, we know the parameters of the connectors, we find the power lost on the wires:

P \u003d U * I,

we replace the voltage in the formula according to Ohm's law: U \u003d I * R, we substitute in the power formula:

P \u003d I * R * I \u003d I 2 * R.

After substituting the numbers: P \u003d 1.68 2 * 0.023 \u003d 0.065 W.

The result is excellent, the connectors take only 0.3% of the power from the load.

But if you connect the lamp through long wires (20 meters), and even thin ones, with a cross section of 0.75 sq. mm, then the picture will change. Without repeating the whole calculation here, it can be noted that with such connectors, the effective power of the lamp will decrease by almost 11%, and the energy loss on the conductors will be already 6%.

Remember the rule - to reduce losses in electrical networks it is necessary to reduce the electrical resistance of the wires, use copper or aluminum, if possible, reduce the length and increase the cross section of the conductors.

What is resistance: video

Or electric circuit electric current.

Electrical resistance is defined as a proportionality factor R between voltage U and direct current I in Ohm's law for a chain section.

The unit of resistance is called ohm(Ohm) in honor of the German scientist G. Ohm, who introduced this concept into physics. One ohm (1 ohm) is the resistance of such a conductor in which, at a voltage 1 AT current strength is 1 BUT.

Resistivity.

The resistance of a homogeneous conductor of constant cross section depends on the material of the conductor, its length l and cross section S and can be determined by the formula:

where ρ is the resistivity of the material from which the conductor is made.

Resistivity of matter- this is a physical quantity showing the resistance of a conductor made of this substance of unit length and unit cross-sectional area.

It follows from the formula that

Value, reciprocal ρ , is called conductivity σ :

Since in SI the unit of resistance is 1 ohm. unit of area is 1 m 2, and the unit of length is 1 m, then the unit of resistivity in SI will be 1 Ohm · m 2 /m, or 1 ohm m. The unit of conductivity in SI is Ohm -1 m -1.

In practice, the cross-sectional area of ​​thin wires is often expressed in square millimeters (mm2). In this case, a more convenient unit of resistivity is Ohm mm 2 /m. Since 1 mm 2 \u003d 0.000001 m 2, then 1 Ohm mm 2 / m \u003d 10 -6 Ohm m. Metals have very low resistivity - of the order of (1 10 -2) Ohm mm 2 /m, dielectrics - 10 15 -10 20 large.

Dependence of resistance on temperature.

As the temperature rises, the resistance of metals increases. However, there are alloys whose resistance almost does not change with increasing temperature (for example, constantan, manganin, etc.). The resistance of electrolytes decreases with increasing temperature.

temperature coefficient of resistance conductor is the ratio of the change in the resistance of the conductor when heated by 1 ° C to the value of its resistance at 0 º C:

.

The dependence of the resistivity of conductors on temperature is expressed by the formula:

.

In general α depends on temperature, but if the temperature interval is small, then temperature coefficient can be considered permanent. For pure metals α \u003d (1/273) K -1. For electrolyte solutions α < 0 . For example, for 10% saline solution α \u003d -0.02 K -1. For constantan (copper-nickel alloy) α \u003d 10 -5 K -1.

The dependence of conductor resistance on temperature is used in resistance thermometers.

Introduction………………………………………………………………………………2

DC resistance measurement…………………..…….3

Ammeter-voltmeter method……………………………………………….……3

Direct assessment method………………………………………………..4

Bridges for measuring DC resistance………………...6

Measurement of very high resistances………………………………………9

AC resistance measurement………………….…...10

Immitance meter…………………………………………..……………...10

Measuring line…………………………………………………..……….11

Measurement of ultra-low resistance…………………………..…………13

findings………………………………………………………………….………..…14

Introduction

Electrical resistance - the main electrical characteristic of a conductor, a value that characterizes the resistance of an electrical circuit or its section electric current. Also, resistance can be called a part (it is often called a resistor) that provides electrical resistance to current. Electrical resistance is due to the conversion of electrical energy into other forms of energy and is measured in ohms.

Resistance (often denoted by the letter R) is considered, within certain limits, a constant value for a given conductor and can be defined as

R - resistance;

U is the difference in electrical potentials at the ends of the conductor, measured in volts;

I - current flowing between the ends of the conductor under the action of a potential difference, measured in amperes.

For the practical measurement of resistance, many different methods are used, depending on the measurement conditions and the nature of the objects, on the required accuracy and speed of measurements. For example, there are methods for measuring resistance at direct current and at alternating current, measuring high resistances, small and ultra-small resistances, direct and indirect, etc.

The purpose of the work is to identify the main, most common in practice, methods of measuring resistance.

DC resistance measurement

The main methods for measuring DC resistance are the indirect method, the direct evaluation method, and the bridge method. The choice of measurement method depends on the expected value of the measured resistance and the required measurement accuracy. Of the indirect methods, the most universal is the ammeter-voltmeter method.

Ammeter-voltmeter method

This method is based on measuring the current flowing through the measured resistance and the voltage drop across it. Two measurement schemes are used: measurement of high resistances (a) and measurement of low resistances (b). According to the results of measuring current and voltage, the desired resistance is determined.

For circuit (a), the desired resistance and the relative methodological error can be determined by the formulas:

where Rx is the measured resistance, and Ra is the resistance of the ammeter.

For circuit (b), the required resistance and the relative methodological measurement error are determined by the formulas:

It can be seen from the formula that when calculating the desired resistance according to the approximate formula, an error occurs, because when measuring currents and voltages in the second circuit, the ammeter also takes into account the current that passes through the voltmeter, and in the first circuit, the voltmeter measures voltage in addition to the resistor also on the ammeter .

From the definition of relative methodological errors, it follows that measurement according to scheme (a) provides a smaller error when measuring large resistances, and measurement according to scheme (b) - when measuring low resistances. Measurement error according to this method is calculated by the expression:

“The instruments used in the measurement must have an accuracy class of no more than 0.2. The voltmeter is connected directly to the measured resistance. The current during measurement should be such that the readings are read on the second half of the scale. In accordance with this, the shunt is also selected, which is used to be able to measure the current with a class 0.2 device. In order to avoid heating the resistance and, accordingly, reducing the accuracy of measurements, the current in the measurement circuit should not exceed 20% of the nominal value.

The advantage of the schemes of the method of measuring with an ammeter and a voltmeter is that the same current can be passed through the resistor with the measured resistance as in the condition of its operation, which is important when measuring resistances, the values ​​of which depend on the current.

Method of direct assessment.

The direct evaluation method involves measuring the DC resistance with an ohmmeter. An ohmmeter is a direct-reading measuring device for determining electrical active (active resistances are also called ohmic resistances) resistances. Typically, the measurement is made using direct current, however, some electronic ohmmeters can use alternating current. Varieties of ohmmeters: megaohmmeters, teraohmmeters, gigaohmmeters, milliohmmeters, microohmmeters, differing in the ranges of measured resistances.

According to the principle of operation, ohmmeters can be divided into magnetoelectric - with a magnetoelectric meter or magnetoelectric logometer (megaohmmeters) and electronic, which are analog or digital.

“The action of a magnetoelectric ohmmeter is based on measuring the strength of the current flowing through the measured resistance at a constant voltage of the power source. To measure resistances from hundreds of ohms to several megaohms, the meter and the measured resistance rx are connected in series. In this case, the current strength I in the meter and the deviation of the moving part of the device a are proportional: I = U/(r0 + rx), where U is the power supply voltage; r0 - meter resistance. For small values ​​of rx (up to several ohms), the meter and rx are connected in parallel.

The ratiometric megaohmmeters are based on a ratiometer, to the shoulders of which are connected in different combinations (depending on the measurement limit) exemplary internal resistors and the measured resistance, the reading of the ratiometer depends on the ratio of these resistances. As a source of high voltage necessary for such measurements, such devices usually use a mechanical inductor - a manually operated electric generator; in some megohmmeters, a semiconductor voltage converter is used instead of an inductor.

The principle of operation of electronic ohmmeters is based on the conversion of the measured resistance into a voltage proportional to it using an operational amplifier. The measured resistor is included in the circuit feedback(linear scale) or to the amplifier input. The digital ohmmeter is a measuring bridge with automatic balancing. Balancing is performed by a digital control device by selecting precision resistors in the bridge arms, after which the measuring information from the control device is fed to the display unit.

“When measuring low resistances, an additional error may occur due to the influence of transient resistance at the connection points. To avoid this, the so-called four-wire connection method is used. The essence of the method is that two pairs of wires are used - one pair of wires is applied to the measured object with a current of a certain strength, with the help of another pair, a voltage drop proportional to the current strength and object resistance is applied to the device from the object. The wires are connected to the terminals of the measured two-terminal network in such a way that each of the current wires does not directly touch the voltage wire corresponding to it, while it turns out that the transient resistances at the contacts are not included in the measuring circuit.