Ignorance of the law is not an excuse.
Aphorism

I wonder what laws will be discussed in lesson number three. Is there really a whole mountain or even a bunch of these laws in electrical engineering, and they all need to be remembered? Now we'll find out. Hello dear! Probably, many of you are already looking at the next lesson with annoyance in your eyes and thinking to yourself: “What a boring thing!”, Or maybe even going to leave our orderly ranks? Don't rush, everything is just beginning! First stage always boring ... From this lesson, all the most interesting things will go. Today I will tell you who is a friend in electrical engineering and who is an enemy, what will happen if you wake up an electronics student in the middle of the night, and how to understand half of all electrical engineering with one finger. Interesting? Then let's go!

We met our first friend in the last lesson - this is the strength of the current. It characterizes electricity in terms of the rate of charge transfer from one point in space to another under the action of a field. But, as it was noted, the current strength also depends on the properties of the conductor through which this current "runs". The magnitude of the electrical conductivity of the material directly affects the current strength. Now let's imagine a certain conductor (suitable as in Figure 3) with electrons moving in it. The main drawback of the electron, I would call the lack of a steering wheel. Due to this shortcoming, the movement of electrons is determined only by the field acting on them and the structure of the material in which they move.

Since the electrons "can't" turn, some of them can collide with nodes that vibrate under the influence of temperature. crystal lattice, lose its speed from the collision, and thereby reduce the charge transfer rate, that is, reduce the current strength. Some electrons can lose so much energy that they "stick" to an ion and turn it into a neutral atom. Now, if we increase the length of the conductor, it is obvious that the number of such collisions will also increase, and the electrons will give off even more energy, that is, the current strength will decrease. But with an increase in the cross-sectional area of ​​\u200b\u200bthe conductor, only the number of free electrons increases, and the number of collisions per unit area remains practically unchanged, therefore, with an increase in the area, the current also increases. So, we found out that electrical conductivity (it has already become not specific, since it takes into account the geometric dimensions of a particular conductor) depends immediately on three characteristics of the conductor: length, cross-sectional area and material.

However, than better material conducts an electric current, the less it "resists" its passage. These statements are equivalent. It's time to meet our second friend - electrical resistance. This is the reciprocal of the conductivity and depends on the same characteristics of the conductor.

Figure 3.1 - What determines the resistance of the conductor

In order to take into account the influence of the type of substance on its electrical resistance in numerical calculations, the value of specific electrical resistance is introduced, which characterizes the ability of a substance to conduct electric current. Note that the definitions of electrical conductivity and electrical resistance are identical, as well as the statements above. Resistivity is defined as the resistance of a conductor with a length of 1m and a cross-sectional area of ​​1m 2. It is denoted by the Latin letter ρ (“ro”) and has the dimension of Ohm m. Ohm is a unit of resistance, which is the reciprocal of Siemens. Also, to determine the resistivity, the dimension of Ohm mm 2 / m can be used, which is a million times smaller than the main dimension.
Thus, the electrical resistance of a conductor can be described in terms of its geometric and physical properties in the following way:

where ρ is the specific electrical resistance of the conductor material;
l is the length of the conductor;
S is the cross-sectional area of ​​the conductor.

It can be seen from the dependence that the resistance of the conductor increases with an increase in the length of the conductor and decreases with an increase in the cross-sectional area, and also directly depends on the value of the resistivity of the material.

And now remember that the magnitude of the current in the conductor is influenced by the intensity electric field, which generates an electric current. Oh, how many millions of thousands of times it has already been mentioned that an electric current arises under the influence of an electric field! This fact must always be kept in mind. There are, of course, other ways to create a current, but for now we will consider only this one. As mentioned above, an increase in the field strength leads to an increase in current, and more recently we found that the more energy an electron retains when moving along a conductor, the higher the value of the electric current. From the course of mechanics it is known that the energy of a body is determined by its kinetic and potential energy. So, a point charge placed in an electric field has at the initial moment of time only potential energy (since its speed is zero). To characterize this potential energy of the field, which the charge has, the value of the electrostatic potential was introduced, equal to the ratio of the potential energy to the value of the point charge:

where W p is the potential energy,
q is the value of the point charge.

After the charge falls under the action of an electric field, it will begin to move at a certain speed and part of its potential energy will turn into kinetic energy. Thus, at two points of the field, the charge will have a different value of potential energy, that is, two points of the field can be characterized by different values ​​of the potential. The potential difference is defined as the ratio of the change in potential energy (perfect work of the field) to the value of the point charge:

Moreover, the work of the field does not depend on the path of charge movement and characterizes only the magnitude of the change in potential energy. Potential difference is also called electrical voltage. Voltage is usually denoted English letter U ("y"), the unit of voltage is the value volt (V), named after the Italian physicist and physiologist Alessandro Volta, who invented the first electric battery.

Well, we met three inseparable friends in electrical engineering: ampere, volt and ohm or current, voltage and resistance. Any component of an electrical circuit can be unambiguously characterized by these three electrical characteristics. The first who met and became friends with all three at once was Georg Ohm, who discovered that voltage, current and resistance are related to each other by a certain ratio:

which was later called Ohm's law.

The strength of the electric current in a conductor is directly proportional to the voltage at the ends of the conductor and inversely proportional to the resistance of the conductor.

This wording must be known from the capital letter C to the dot at the end. Rumor has it that the first phrase of any electronics student woken up in the middle of the night will be exactly the formulation of Ohm's law. This is one of the basic laws of electrical engineering. This formulation is called integral. In addition to it, there is also a differential formulation that reflects the dependence of the current density on the characteristics of the field and the material of the conductor:

where σ is the conductivity of the conductor,
E is the electric field strength.

This formulation follows from the formula given in the second lesson, and differs from the integral one in that it does not take into account the geometric characteristics of the conductor, taking into account only its physical characteristics. This formulation is interesting only from the point of view of theory and is not applied in practice.
For quick memorization and using Ohm's law, you can apply the diagram shown in the figure below.

Figure 3.2 - Ohm's "triangular" law

The rule for using the diagram is simple: it is enough to close the desired value and two other symbols will give a formula for calculating it. For example.

Figure 3.3 - How to remember Ohm's law

We are done with the triangle. It is worth adding that only one of the above formulas is called Ohm's law - the one that reflects the dependence of current on voltage and resistance. The other two formulas, although they are a consequence of it, physical sense Dont Have. So don't get confused!
A good interpretation of Ohm's law is a drawing that most clearly reflects the essence of this law:

Figure 3.4 - Ohm's Law clearly

As we can see, this figure shows just three of our new friends: Ohm, Ampere and Volt. Volt tries to push Ampere through the conductor section (current strength is directly proportional to voltage), and Ohm, on the contrary, interferes with this (and is inversely proportional to resistance). And the more Om "pulls" the conductor, the harder it will be for Ampere to climb. But if Volt kicks harder...

It remains to figure out why the term "many laws" appears in the title of the lesson, because we have one law - Ohm's law. Well, firstly, there are two formulations for it, secondly, we only learned the so-called Ohm's law for a chain section, and there is also Ohm's law for a complete chain, which we will consider in the next lesson, thirdly, we have , at least two consequences from Ohm's law, allowing you to find the resistance value of a circuit section and the voltage in this section. So there is only one law, but it can be used in different ways.

Finally, I'll tell you one more interesting fact. 10 years after the appearance of Ohm's law, a French physicist (and Ohm's work was not yet known in France) came to the same conclusions based on experiments. But he was pointed out that the law established by him back in 1827. was discovered by Ohm. It turns out that French schoolchildren are still studying Ohm's law under a different name - for them it is Poulier's law. That's it. This concludes another lesson. See you soon!

• Any section or element of an electrical circuit can be unambiguously characterized using three characteristics: current, voltage and resistance.
• Resistance (R)- a characteristic of a conductor, reflecting the degree of its electrical conductivity and depending on the geometric dimensions of the conductor and the type of material from which it is made.
• Voltage (U)- the same as the potential difference; a value equal to the ratio of the work of the electric field to move a point charge from one point in space to another.
• Current, voltage and resistance are interconnected by the ratio I = U / R, called Ohm's law (the strength of the electric current in the conductor is directly proportional to the voltage at the ends of the conductor and inversely proportional to the resistance of the conductor).

And also puzzles:

• If the length of the wire is doubled by stretching, how will its resistance change?
• Which conductor presents more resistance: a solid copper rod or a copper tube having an outer diameter equal to the diameter of the rod?
• The potential difference at the ends of the aluminum conductor is 10V. Determine the density of the current flowing through the conductor if its length is 3 m.

The magnitude of the effect that the current can have on the conductor depends, whether it is thermal, chemical or magnetic effect of the current. That is, by adjusting the strength of the current, you can control its effect. Electric current, in turn, is the ordered movement of particles under the influence of an electric field.

Dependence of current and voltage

Obviously, the stronger the field acts on the particles, the greater the current in the circuit. The electric field is characterized by a quantity called voltage. Therefore, we conclude that the current strength depends on the voltage.

Indeed, it was possible to establish empirically that the current strength is directly proportional to the voltage. In cases where the voltage in the circuit was changed without changing all other parameters, the current increased or decreased by the same amount as the voltage was changed.

Relationship with resistance

However, any circuit or section of a circuit is characterized by another important value called resistance to electric current. Resistance is inversely related to current. If the resistance value is changed at any section of the circuit without changing the voltage at the ends of this section, the current strength will also change. Moreover, if we reduce the resistance value, then the current strength will increase by the same amount. Conversely, as the resistance increases, the current decreases proportionally.

Ohm's law formula for a chain section

Comparing these two dependencies, one can come to the same conclusion reached by the German scientist Georg Ohm in 1827. He linked together the three above physical quantities and brought forth a law which is named after him. Ohm's law for a section of a circuit reads:

The current strength in a circuit section is directly proportional to the voltage at the ends of this section and inversely proportional to its resistance.

where I is the current strength,
U - voltage,
R is resistance.

Application of Ohm's law

Ohm's law is one of fundamental laws of physics. Its discovery at one time made it possible to make a huge leap in science. At present, it is impossible to imagine any most elementary calculation of the basic electrical quantities for any circuit without using Ohm's law. The idea of ​​​​this law is not the lot of exclusively electronic engineers, but a necessary part of the basic knowledge of any more or less educated person. No wonder there is a saying: "If you don't know Ohm's law, stay at home."

U=IR and R=U/I

True, it should be understood that in the assembled circuit, the resistance value of a certain section of the circuit is a constant value, therefore, when the current strength changes, only the voltage will change and vice versa. To change the resistance of a section of the circuit, the circuit must be reassembled. The calculation of the required resistance value during the design and assembly of the circuit can be made according to Ohm's law, based on the estimated values ​​of the current and voltage that will be passed through this section of the circuit.

The basic law of electrical engineering, with which you can study and calculate electrical circuits, is Ohm's law, which establishes the relationship between current, voltage and resistance. It is necessary to clearly understand its essence and be able to use it correctly in solving practical problems. Often mistakes are made in electrical engineering due to the inability to correctly apply Ohm's law.

Ohm's law for a section of a circuit states that current is directly proportional to voltage and inversely proportional to resistance.

If the voltage acting in an electrical circuit is increased several times, then the current in this circuit will increase by the same amount. And if you increase the resistance of the circuit several times, then the current will decrease by the same amount. Likewise, the flow of water in a pipe is greater, the greater the pressure and the less resistance the pipe exerts to the movement of water.

In popular form, this law can be formulated as follows: the higher the voltage for the same resistance, the higher the current, and at the same time, the higher the resistance for the same voltage, the lower the current.

To express Ohm's law mathematically most simply, consider that the resistance of a conductor in which a current of 1 A flows at a voltage of 1 V is 1 ohm.

The current in amps can always be determined by dividing the voltage in volts by the resistance in ohms. That's why Ohm's law for a circuit section is written by the following formula:

I = U/R.

magic triangle

Any section or element of an electrical circuit can be characterized using three characteristics: current, voltage and resistance.

How to use Ohm's Triangle: close the desired value - the other two characters will give a formula for its calculation. By the way, only one formula from a triangle is called Ohm's law - the one that reflects the dependence of current on voltage and resistance. The other two formulas, although they are its consequence, have no physical meaning.

Ohm's law calculations for a circuit section will be correct when voltage is expressed in volts, resistance in ohms, and current in amperes. If multiple units of these quantities are used (for example, milliamps, millivolts, megaohms, etc.), then they should be converted to amperes, volts and ohms, respectively. To emphasize this, sometimes the formula for Ohm's law for a chain section is written like this:

ampere = volt/ohm

You can also calculate the current in milliamps and microamps, while the voltage should be expressed in volts, and the resistance in kiloohms and megaohms, respectively.

Other articles about electricity in a simple and accessible presentation:

Ohm's law is valid for any section of the circuit. If it is required to determine the current in a given section of the circuit, then it is necessary to divide the voltage acting on this section (Fig. 1) by the resistance of this particular section.

Fig 1. Application of Ohm's law for a circuit section

Let's give an example of calculating the current according to Ohm's law. Let it be required to determine the current in a lamp having a resistance of 2.5 ohms, if the voltage applied to the lamp is 5 V. Dividing 5 V by 2.5 ohms, we get the current value equal to 2 A. In the second example, we determine the current, which will be flow under the action of a voltage of 500 V in a circuit whose resistance is 0.5 MΩ. To do this, we express the resistance in ohms. Dividing 500 V by 500,000 ohms, we find the value of the current in the circuit, which is equal to 0.001 A or 1 mA.

Often, knowing the current and resistance, the voltage is determined using Ohm's law. Let's write the formula for determining the voltage

U=IR

From this formula it can be seen that the voltage at the ends of a given section of the circuit is directly proportional to the current and resistance. The meaning of this dependence is not difficult to understand. If you do not change the resistance of the circuit section, then you can increase the current only by increasing the voltage. This means that with constant resistance, more current corresponds to more voltage. If it is necessary to obtain the same current at different resistances, then with a greater resistance there must be a correspondingly greater voltage.

The voltage across a section of a circuit is often referred to as voltage drop. This often leads to misunderstanding. Many people think that a voltage drop is some kind of wasted unnecessary voltage. In fact, the concepts of voltage and voltage drop are equivalent.

The calculation of voltage using Ohm's law can be shown in the following example. Let a current of 5 mA pass through a section of a circuit with a resistance of 10 kΩ, and it is required to determine the voltage in this section.

Multiplying I \u003d 0.005 A at R -10000 ohms, we get a voltage equal to 5 0 V. We could get the same result by multiplying 5 mA by 10 kOhm: U \u003d 50 V

In electronic devices, current is usually expressed in milliamps and resistance in kiloohms. Therefore, it is convenient to use these units of measurements in calculations according to Ohm's law.

According to Ohm's law, resistance is also calculated if the voltage and current are known. The formula for this case is written as follows: R = U/I.

Resistance is always the ratio of voltage to current. If the voltage is increased or decreased several times, then the current will increase or decrease by the same number of times. The ratio of voltage to current, equal to the resistance, remains unchanged.

The formula for determining resistance should not be understood in the sense that the resistance of a given conductor depends on outflow and voltage. It is known that it depends on the length, cross-sectional area and material of the conductor. In appearance, the formula for determining resistance resembles the formula for calculating current, but there is a fundamental difference between them.

The current in a given section of the circuit really depends on the voltage and resistance and changes when they change. And the resistance of a given section of the circuit is a constant value, independent of changes in voltage and current, but equal to the ratio of these quantities.

When the same current flows in two sections of the circuit, and the voltages applied to them are different, it is clear that the section to which the greater voltage is applied has a correspondingly greater resistance.

And if, under the influence of the same voltage, a different current passes in two different sections of the circuit, then a smaller current will always be in that section that has a greater resistance. All this follows from the basic formulation of Ohm's law for a section of the circuit, i.e., from the fact that the current is greater, the greater the voltage and the lower the resistance.

We will show the calculation of resistance using Ohm's law for a section of the circuit in the following example. Let it be required to find the resistance of the section through which, at a voltage of 40 V, a current of 50 mA passes. Expressing the current in amperes, we get I \u003d 0.05 A. Divide 40 by 0.05 and find that the resistance is 800 ohms.

Ohm's law can be visualized in the form of the so-called volt-ampere characteristic. As you know, a direct proportional relationship between two quantities is a straight line passing through the origin. Such a dependence is called linear.

On fig. 2 shows, as an example, a graph of Ohm's law for a circuit section with a resistance of 100 ohms. The horizontal axis is voltage in volts and the vertical axis is current in amps. The scale of current and voltage can be chosen as you like. A straight line is drawn so that for any point on it, the ratio of voltage to current is 100 ohms. For example, if U \u003d 50 V, then I \u003d 0.5 A and R \u003d 50: 0.5 \u003d 100 Ohms.

Rice. 2. Ohm's law (voltage characteristic)

The plot of Ohm's law for negative values ​​of current and voltage has the same form. This means that the current in the circuit flows equally in both directions. The greater the resistance, the less current is obtained at a given voltage and the more flat the straight line goes.

Devices in which the current-voltage characteristic is a straight line passing through the origin, i.e., the resistance remains constant when the voltage or current changes, are called linear devices. The terms linear circuits, linear resistances are also used.

There are also devices in which the resistance changes with a change in voltage or current. Then the relationship between current and voltage is expressed not according to Ohm's law, but more complicated. For such devices, the current-voltage characteristic will not be a straight line passing through the origin, but is either a curve or a broken line. These devices are called non-linear.

Mnemonic diagram for Ohm's law

Ohm's law for a circuit section is a law obtained experimentally (empirically) that establishes a connection between the current strength in a circuit section and the voltage at the ends of this section and its resistance. The strict formulation of Ohm's law for a circuit section is written as follows: the current strength in the circuit is directly proportional to the voltage in its section and inversely proportional to the resistance of this section.

Ohm's law formula for a chain section is written as follows:

I - current strength in the conductor [A];

U- electrical voltage(potential difference) [V];

R is the electrical resistance (or simply resistance) of the conductor [Ohm].

Historically, the resistance R in Ohm's law for a circuit section is considered the main characteristic of a conductor, since it depends solely on the parameters of this conductor. It should be noted that Ohm's law in the mentioned form is valid for metals and solutions (melts) of electrolytes and only for those circuits where there is no real current source or the current source is ideal. An ideal current source is one that does not have its own (internal) resistance. More information about Ohm's law as applied to a circuit with a current source can be found in our article. We agree to consider the positive direction from left to right (see the figure below). Then the voltage across the section is equal to the potential difference.

φ 1 - potential at point 1 (at the beginning of the section);

φ 2 - potential at point 2 (and the end of the section).

If the condition φ 1 > φ 2 is satisfied, then the voltage U > 0. Therefore, the lines of tension in the conductor are directed from point 1 to point 2, and hence the current flows in this direction. It is this direction of the current that we will consider positive I > O.

Consider the simplest example determination of resistance in a circuit section using Ohm's law. As a result of an experiment with an electrical circuit, an ammeter (a device that shows current strength) shows, and a voltmeter. It is necessary to determine the resistance of the circuit section.

By definition of Ohm's law for a chain section

When studying Ohm's law for a section of a circuit in the 8th grade of a school, teachers often ask students the following questions to reinforce the material covered:

Between what quantities does Ohm's Law for a chain section establish a relationship?

Correct answer: between current [I], voltage [U] and resistance [R].

Why does current depend on voltage?

Correct Answer: resistance

How does the current strength depend on the voltage of the conductor?

Correct Answer: Directly proportional

How does current depend on resistance?

Correct answer: inversely proportional.

These questions are asked so that in grade 8 students can remember Ohm's law for circuit sections, the definition of which says that the current strength is directly proportional to the voltage at the ends of the conductor, if the resistance of the conductor does not change.