It is a queue to find out what resistance is. Imagine now an ordinary crystal lattice. So ... The more dense the crystals are located to each other, the more charges will be lured. So, in simple language, the more metal resistance. By the way, the resistance of any conventional metal can be increased for a while, heating it. "Why?", - Ask. Yes, because when heated, the metal atoms begin to fluctuately fluctuate near their configurations of the position. Therefore, moving charges will often encounter atoms, which means more often and linger more in the nodes crystal lattice. Figure 1 shows a visual assembly scheme, so to speak for "uninitiated", where it is immediately visible how to measure the resistance voltage. In the same way, the voltage and light bulb can be measured. By the way, if, as can be seen from the figure, our battery has a voltage, allow, 15B (Volt), and the resistance is such that it "settles" 10V, then the remaining 5B will come to the light bulb.

So the law of Oma looks like a closed chain.

If you do not go into details, this law suggests that the power supply voltage is equal to the amount of stress drops in all its sections. Those. In our case, 15B \u003d 10V + 5V. But ... if you still feel a little bit into details, then you need to know what we called the battery voltage, there is nothing more than its value when the consumer connected E (in our case is a light bulb + resistance). If the bulb with resistance is disconnected and measure the voltage value on the battery, it will be somewhat more than 15V. It will be the idle stroke and "call" it is EDC battery - electromotive force. In fact, the scheme will work as shown in Fig.2. In reality, the battery can be represented as a different voltage battery, allow, 16B, which has its own internal resistance of the RVN. The value of this resistance is very little and is due to technological features of manufacture. It can be seen from the figure that when the load is connected, part of the voltage of the battery will "fall" on its internal resistance and at its output will not be 16V, and 15V, i.e. 1B "will absorb" its internal resistance. And here will also work the law of Oma for a closed chain. The amount of stresses at all parts of the chain will be equal to the emf of the battery. 16B \u003d 1B + 10V + 5V. The unit of measuring resistance is the value called OM. It is named so in honor of the German physicagueorga Simona Om, who was engaged in these works. 1 is equal to the electrical resistance of the conductor (it can, for example, be a light bulb) between the ends of which the voltage of 1 volt occurs at a direct current of 1 ampere. To determine the resistance of the lamp, it is necessary to measure the voltage on it and measure the current in the chain (see Fig. 5). And then the resulting voltage value is divided into the current value (r \u003d u / i). Resistance in electrical circuits can be connected sequentially (the end of the first one with the beginning of the second - in this case they can be designated arbitrarily) and in parallel (beginning with the beginning, the end with the end - and in this case they can be denoted arbitrarily). Consider both cases on the example of the light bulbs - after all, their filaments consist of their tungsten, i.e. represent resistance. The sequential compound case is shown in Fig.3.

It turned out to be known to everyone (and, it means, we will consider and understandable). With this connection, the current I will be the same independent of what is the same lamps on the same voltage or different. We must immediately make a reservation that the lamps are the same, in which:

1. the same voltage and current are indicated (like light bulbs from a pocket lamp);
2. the same voltage and power are indicated (like lighting lamps).

The voltage of the power of the power supply in this case is "scattered" on all lamps, i.e. U \u003d U1 + U2 + U3. At the same time, if the lamps are the same - on all of them, the voltage will be the same. If the lamps are not identical, then depending on the resistance of each particular lamp. In the first case, the voltage on each lamp can be easily calculated by dividing the source voltage to the total number of lamps. In the second case, you need to dig in the calculations. All this we will look at the tasks of this section. So, we found out that with a sequential connection of the conductors (in this case - lamps), the voltage U at the ends of the entire circuit is equal to the sum of the voltages of the connected conductors (lamps) - U \u003d u1 + U2 + U3. Under the law of Ovyadl, the chain section: U1 \u003d I * R1, U2 \u003d I * R2, U3 \u003d I * R3, U \u003d I * R where R1 is the resistance of the thread of the first lamp (conductor), R2 - the second and R3 - third, R - Full resistance of all lamps. Replacing in the expression "U \u003d U1 + U2 + U" the value of U to I * R, U1 on I * R1, U2 on I * R2, U3 on I * R3, we obtain I * R \u003d I * (R1 + R2 + R3 ). Hence the R \u003d R1 + R2 + R3. Living: With a sequential connection of the conductors, their overall resistance is equal to the sum of the resistance of all conductors. We conclude: Sequential inclusion is used for several consumers (for example, New Year's Garlands lamps) with a low voltage voltage of the source.

The case of parallel connection of the conductors is shown in Fig.4.

With parallel connection of the conductors of their start and ends, have common connection points to the source. In this case, the voltage on all lamps (conductor) is equally no matter which one of them is designed for which voltage is directly connected to the source. Naturally, if the lamp is less voltage than the voltage source - it will be overgrown. But the current I will be equal to the sum of currents in all lamps, i.e. I \u003d i1 + i2 + i3. And the lamps can be different power - each will take the current to which it is designed. This can be understood if instead of a source to present a power outlet with a voltage of 220V, and instead of lamps are connected to it, for example, iron, a table lamp and a charging device from the phone. The resistance of each device in such a circuit is determined by the division of its voltage on the current, which it consumes ... Again, according to the Ohm's law for the circuit section, i.e.

Immediately state the fact that there is a magnitude, reverse resistance and is called - conductivity. It is denoted by y. In the system, the system is denoted as cm (Siemens). Reverse resistance means that

Without going into mathematical conclusions, I immediately say that with a parallel connection of the conductors (be it lamps, irons, microwaves or TVs) the value, inverse the total resistance, is equal to the amount of quantities, inverse resistances of all parallel conductor turned on, i.e.

Considering that

Sometimes in the tasks they write y \u003d y1 + y2 + y3. This is the same. There is also a more convenient formula for finding the overall resistance of two parallel resisters. She looks like this:

We conclude: a parallel inclusion method is used to connect lighting lamps and household appliances to an electrical network.

As we found out, the collisions of free electrons in conductors with the atoms of the crystal lattice inhibit their translational movement ... This is counteraction to the directional movement of free electrons, i.e. dCIt is the physical essence of the resistance of the conductor. Simulated continuous current resistance mechanism in electrolytes and gases. Conductive material properties determine its volumetric resistivity ρv equal to the resistance between the opposite sides of the cube with a rebier 1m made from this material. The value of the inverse voltage resistivity is called volumetric specific conductivity and is equal to γ \u200b\u200b\u003d 1 / ρv. The unit of volumetric resistance serves as the 1st * m, the volumetric conductivity is 1cm / m. Resistance conductor DC depends on temperature. In general, there is a rather complicated dependence. But with changes in temperature in relatively narrow limits (approximately 200 ° C), it can be expressed by the formula:

where R2 and R1 resistance, respectively, at temperatures T1 and T2; α is the temperature coefficient of resistance equal to the relative resistance change when the temperature changes by 1 ° C.

Important concepts

Electrical device with resistance and used to limit the current is called a resistor. Adjustable resistor (i.e. it is possible to change its resistance) is called a row.

The resistive elements are idealized models of resistors and any other electrical devices or their parts that have a constant current resistance regardless of the physical nature of this phenomenon. They are used in the preparation of circuits of chains and calculations of their modes. Under idealization, neglect the currents of the insulating coatings of the resistors, the framework of wire rosostates, etc.

The linear resistive element is a diagram of substitution of any part of the electrical device, in which the current is proportional to the voltage. Its parameter is the resistance R \u003d const. R \u003d const means that the resistance value is invariably (const means constant).
If the dependence of the current from the voltage is nonlinear, then the substitution scheme contains a nonlinear resistive element, which is set to nonlinear VAC (volt-ampere characteristic) I (U) - read as "and from y". Fig. 5 shows the volt-ampere characteristics of the linear (line A) and nonlinear (line b) resistive elements, as well as their designation on substitution schsam.

Among other indicators characterizing the electrical circuit, the conductor, it is worth highlighting electrical resistance. It determines the ability of the material atoms to prevent the directional passage of electrons. Assistance in determining this value can provide both a specialized device - an ohmmeter and mathematical calculations on the basis of knowledge of the relationship between values \u200b\u200band physical properties material. The measurement of the indicator is made in Omah (OM), the symbol R.

OMA's law is a mathematical approach when determining resistance

The ratio set by the George Omom determines the relationship between the voltage, current force, resistance based on the mathematical relationship of concepts. The validity of a linear relationship is R \u003d U / I (voltage ratio to current) - noted in all cases.
Unit of measurement [R] \u003d b / a \u003d Ohm. 1 Ohm - the resistance of the material by which current is 1 amp at a voltage of 1 volt.

Empirical resistance calculation formula

The objective data on the conductivity of the material follows from its physical characteristicsdefining both its own properties and reactions to external influences. Based on this, conductivity depends on:

• Size.
• Geometry.
• Temperatures.

The atoms of the conductive material are faced with directional electrons, preventing further promotion. At high concentration of the latter, atoms are not able to resist them and conductivity is high. Large resistance values \u200b\u200bare characteristic of dielectrics that differ almost zero conductivity.

One of the defining characteristics of each conductor is its specific resistance - ρ. It determines the dependence of resistance from the material of the conductor and exposure from the outside. This is fixed (within the same material) the value that represents the data of the conductor of the following dimensions - length 1 m (ℓ), the cross-sectional area of \u200b\u200b1 sq.m. Therefore, the relationship between these values \u200b\u200bis expressed by the relation: R \u003d ρ * ℓ / S:

• The conductivity of the material falls as its length increases.
• An increase in the cross-sectional area of \u200b\u200bthe conductor entails a decrease in its resistance. Such a pattern is due to a decrease in the density of electrons, and, consequently, the contact of the particles of the material with them becomes more rare.
• The growth of the material temperature stimulates the growth of resistance, while the temperature drop entails its decline.

The calculation of the cross-sectional area is advisable to produce according to the formula S \u003d πd 2/4 in determining the length of the roulette will help.

Power relationship (P)

Based on the formula of the Ohm, U \u003d I * R and P \u003d I * U. Consequently, p \u003d i 2 * R and p \u003d u 2 / r.
Knowing the amount of current and power, resistance can be defined as: R \u003d P / I 2.
Knowing the amount of voltage and power, resistance is easy to calculate according to the formula: R \u003d U 2 / p.

The resistance of the material and the magnitude of other concomitant characteristics can be obtained using special measuring instruments or on the basis of established mathematical patterns.

As already noted, the current of the current in the chain depends not only on the voltage at the ends of the site, but also on the properties of the conductor included in the chain. The dependence of the current from the properties of the conductors is explained by the fact that different conductors have different electrical resistance.

Electrical resistance R - physical scalar value, characterizing the property of the conductor to reduce the rate of ordered movement of free charge carriers in the conductor. The resistance of the letter R. is indicated in the system of resistance of the conductor is OM (OM).

1 Ohm - the resistance of such a conductor, the current of the current in which is 1 and at a voltage of 1 V.

Other units are used: kilome (com), mega (IOM), Millis (MOM): 1 com \u003d 10 3 ohms; 1 Mom \u003d 10 6 ohms; 1 Mom \u003d 10 -3 Ohm.

The physical value of G, inverse resistance, is called electrical conductivity

The unit of electrical conductivity in C is Siemens: 1 cm is the conductivity of the conductor resistance to 1 ohm.

The conductor contains not only free charged particles - electrons, but also neutral particles and related charges. All of them are involved in a chaotic thermal motion equal to any directions. When turned on electric field Under the influence electric forces A directed ordered movement of free charges will prevail, which should move with acceleration and their speed should have increased over time. But in conductors, free charges are moving at a certain permanent average. Consequently, the conductor has resistance to an ordered movement of free charges, part of the energy of this movement is transmitted by the conductor, as a result of which its internal energy increases. Because of the movement of free charges, even the perfect crystal conductor grille is distorted, the energy of the ordered movement of free charges is dissipated on distortions of the crystal structure. The conductor has resistance to the passage of electric current.

The conductor resistance depends on the material from which it is made, the length of the conductor and the cross-sectional area. To verify this dependence, you can use the same electrical scheme as to verify the Ohm law (Fig. 2), including in the MN circuit section of various cylindrical conductors made from the same material, as well as from different materials.

The results of the experiment showed that the resistance of the conductor is directly proportional to the length L of the conductor, inversely proportional to the area S of its cross section and depends on the genus of the substance from which the conductor is made:

where is the specific resistance of the conductor.

Scalar physical value, numerically equal to the resistance of a homogeneous cylindrical conductor made of this substance and having a length of 1 m and a cross-sectional area of \u200b\u200b1 m 2, or a cube resistance with an edge of 1 m. The unit of resistivity in C is an OM-meter (Ohm · m) .

The resistivity of the metal conductor depends on

1. concentration of free electrons in the conductor;
2. the intensity of dispersion of free electrons on the ions of the crystal lattice performing thermal fluctuations;
3. the intensity of dispersion of free electrons on defects and impurities of the crystal structure.

Silver and copper has the smallest resistance. Very large resistivity at alloy nickel, iron, chromium and manganese - "Nichrome". The resistivity of metal crystals is largely depends on the presence of impurities in them. For example, the introduction of 1% of manganese impurities increases the resistivity of copper three times.

To begin with, consider the question, how at your time the researchers came to an understanding of the magnitude, called " tok resistance" When considering the foundations of electrostatics, the issues of electrical conductivity have already affected, including the fact that different substances have different conductivity (the ability to skip free charged particles). For example, metals are characterized by good conductivity (because of which they are called conductor), and plastics and wood - bad (dielectric or non-conductive). Such differences are associated with the peculiarities of the molecular structure of different substances.

The most effective work on the study of conductivity of different substances was the experiments, which carried out Georg Ohm (1789-1854) (Fig. 1).

The essence of Omar's work was as follows. Scientist used electrical circuitconsisting of current source, conductor, as well as a special tracking device tok forces . Changing the conductors in the scheme, Ohm tracks the following pattern: the current of the current in the chain increased by increasing the voltage. The next opening of Ohm was that when replacing the conductors, the degree of increasing current of the current was changed by increasing the voltage. An example of such a dependence is shown in Figure 2.

X axis demonstrates voltage, and the Y axis - tok strength. The graph shows two straight lines, showing different speeds of increasing current of current with an increase in voltage depending on the conductor included in the chain.

The result of Omar's research was the following conclusion: "Different conductors have different conductivity properties," resulting in a concept tok resistance.

Electrical current resistance.

Electrical resistance is a physical value that characterizes the ability of the conductor to influence electricityflowing in the conductor.

• Number designation: R
• Unit of measurement: Ohm

The result of experiments with conductors was determined that the relationship between current power and voltage B. electrical chain Depends also on the size of the conductor used, and not only from the substance. More detailed influence of the size of the conductor will be considered in a separate lesson.

Due to what appears tok resistance? During the movement of free electrons, there is constant interaction between ions belonging to the structure of the crystal lattice, and electrons. As a result of this interaction, the electron movement is slowed down (in fact, due to the collision of electrons with atoms - nodes of the crystal lattice), so that the current resistance is created.

The other physical value is also associated with electrical resistance - conductivity, Inverse value relative to the resistance.

Current resistance formulas.

Consider the relationship between the values \u200b\u200bstudied at the last lessons. As it was said, with an increase in voltage increases in the chain and tok PowerThese values \u200b\u200bare proportional to: I ~ U.

An increase in the resistance of the conductor leads to a decrease in the strength of the current in the chain, thus, the data of the values \u200b\u200bare inversely proportional to each other: I ~ 1 / R

As a result of the research, the following pattern was revealed: R \u003d U / I

We paint receive a unit tok resistance: 1st \u003d 1B / 1A

Thus, 1 Ω is such a current resistance in which the current in the conductor is 1 A, and the voltage at the ends of the conductor 1 V.

Actually, tok resistance In 1, there are too small and in practice conductors are used, which are characterized by higher resistance (1 com, 1 MΩ, etc.).

The strength of the current and the voltage are interrelated values \u200b\u200bthat influence each other. It will be considered more detailed in the next lesson.

Immediately disclaim that it will be about measuring resistance electric Toku.. What does it represent, and what is the measured resistance?

Three whales

Where does such resistance come from? All materials in nature, from the point of view of electrical conductivity, are divided into 3 categories - insulators, semiconductors, and conductors. The first does not conduct an electric current in general (for example, glass, plastic, air), the second - passes the current only under certain conditions (silicon, germanium), and on their basis all the modern electronics are built. But you are interested in our last - all familiar guides. Ordinary copper wire, wire that is connected to your computer into the outlet - all this is conductors.

How can conductors can have electrical stream resistance? The fact is that there is no ideal conductor in nature. In any, even the "pure" conductor, there is always some of the impurities that have resistance to electrons moving in the body of the conductor. The collision of electrons with these impurities causes heating, and sometimes (if the flux density is too large, i.e. too high) and the destruction of the conductor (the action of heating elements and fuses is based on this).

A little mathematics

What is measured by the resistance of the conductor, or rather to say the electrical circuit? The unit of measurement of this magnitude is named after Physics Georg Simon Ohm. Yes, that Ohm himself, whose law we all leined at school. In technical literature is indicated by the letter "Omega". The resistance itself in the calculations is recorded as "R" (U - voltage, I - current, P - power, etc.). What does this value mean? Consider an example. According to the law, the same Ohm, if our conductor has 1 ohm resistance, applying a 220 volt voltage to its ends, we get a current (current \u003d voltage divided by resistance) 220 amps. Multiplying current to tension, we learn power: 220 volts * 220 amps \u003d 48400 watts, or 48 kilowatt. This is a very big power that no household wiring will withstand. In fact, this current will be current short circuit. This shows how important it is to know the resistance of the chain, before serving the voltage! Fortunately, it is not so difficult to know it, and not even necessarily carry out some calculations. There are special measuring instruments - ohmmeters that show the amount of resistance to DC. Their type of megommeters are designed to measure large resistance values, and are used mainly to check insulation. Now to meet Ommers as separate devices are difficult. For the most part, they are part of the combined devices - autometers, or multimeters that are sold in each stall Chinese goods.

So, successful to you measurements!