Ohm's Four Laws. Ohm's law for a complete electrical circuit

For an electrician and electronics engineer, one of the basic laws is Ohm's Law. Every day, work poses new challenges for a specialist, and often it is necessary to select a replacement for a burnt out resistor or group of elements. An electrician often has to change cables; to choose the right one, you need to “estimate” the current in the load, so you have to use the simplest physical laws and relationships in everyday life. The importance of Ohm's Law in electrical engineering is colossal; by the way, most diploma works in electrical engineering specialties are calculated by 70-90% according to one formula.

Historical background

The year Ohm's Law was discovered was 1826 by the German scientist Georg Ohm. He empirically determined and described the law on the relationship between current, voltage and type of conductor. Later it turned out that the third component is nothing more than resistance. Subsequently, this law was named after the discoverer, but the matter was not limited to the law; a physical quantity was named after his name, as a tribute to his work.

The quantity in which resistance is measured is named after Georg Ohm. For example, resistors have two main characteristics: power in watts and resistance - unit of measurement in Ohms, kilo-ohms, mega-ohms, etc.

Ohm's law for a circuit section

For description electrical circuit not containing EMF, you can use Ohm's law for a section of the circuit. This is the most simple form records. It looks like this:

Where I is the current, measured in Amperes, U is the voltage in volts, R is the resistance in Ohms.

This formula tells us that current is directly proportional to voltage and inversely proportional to resistance - this is the exact formulation of Ohm's Law. The physical meaning of this formula is to describe the dependence of the current through a section of the circuit with a known resistance and voltage.

Attention! This formula is valid for DC, For AC it has slight differences, we will return to this later.

In addition to the ratio of electrical quantities this form tells us that the graph of the current versus voltage in the resistance is linear and the function equation is satisfied:

f(x) = ky or f(u) = IR or f(u)=(1/R)*I

Ohm's law for a section of a circuit is used to calculate the resistance of a resistor in a section of a circuit or to determine the current through it at a known voltage and resistance. For example, we have a resistor R with a resistance of 6 ohms, a voltage of 12 V is applied to its terminals. We need to find out how much current will flow through it. Let's calculate:

I=12 V/6 Ohm=2 A

An ideal conductor has no resistance, but due to the structure of the molecules of the substance of which it is composed, any conducting body has resistance. For example, this was the reason for the transition from aluminum to copper wires in home electrical networks. The resistivity of copper (Ohm per 1 meter length) is less than that of aluminum. Accordingly, copper wires heat up less and withstand high currents, which means you can use a wire of a smaller cross-section.

Another example is that the spirals of heating devices and resistors have a high resistivity, because are made from various high-resistivity metals, such as nichrome, kanthal, etc. When charge carriers move through a conductor, they collide with particles in the crystal lattice, as a result of which energy is released in the form of heat and the conductor heats up. The greater the current, the more collisions, the greater the heating.

To reduce heating, the conductor must either be shortened or its thickness (cross-sectional area) increased. This information can be written as a formula:

R wire =ρ(L/S)

Where ρ – resistivity in Ohm*mm 2 /m, L – length in m, S – cross-sectional area.

Ohm's law for parallel and series circuits

Depending on the type of connection, different patterns of current flow and voltage distribution are observed. For a section of a circuit connecting elements in series, voltage, current and resistance are found according to the formula:

This means that the same current flows in a circuit of an arbitrary number of elements connected in series. In this case, the voltage applied to all elements (the sum of the voltage drops) is equal to the output voltage of the power source. Each individual element has its own voltage applied and depends on the current strength and resistance of the particular one:

U el =I*R element

The resistance of a circuit section for parallel-connected elements is calculated by the formula:

1/R=1/R1+1/R2

For a mixed connection, you need to reduce the chain to an equivalent form. For example, if one resistor is connected to two parallel-connected resistors, then first calculate the resistance of the parallel-connected ones. You will get the total resistance of two resistors and all you have to do is add it to the third one, which is connected in series with them.

Ohm's law for a complete circuit

A complete circuit requires a power source. Ideal source power supply is a device that has a single characteristic:

• voltage, if it is a source of EMF;
• current strength, if it is a current source;

Such a power source is capable of delivering any power with unchanged output parameters. In a real power source, there are also such parameters as power and internal resistance. In essence, internal resistance is an imaginary resistor installed in series with the EMF source.

Ohm's Law formula for complete chain looks similar, but adds internal IP resistance. For a complete chain it is written by the formula:

I=ε/(R+r)

Where ε is the EMF in Volts, R is the load resistance, r is the internal resistance of the power source.

In practice, the internal resistance is fractions of an Ohm, and for galvanic sources it increases significantly. Have you seen this when two batteries (new and dead) have the same voltage, but one produces required current and works properly, but the second one does not work, because... sags at the slightest load.

Ohm's law in differential and integral form

For a homogeneous section of the circuit, the above formulas are valid; for a non-uniform conductor, it is necessary to divide it into the shortest segments so that changes in its dimensions are minimized within this segment. This is called Ohm's Law in differential form.

In other words: the current density is directly proportional to the voltage and conductivity for an infinitely small section of the conductor.

In integral form:

Ohm's law for alternating current

When calculating alternating current circuits, instead of the concept of resistance, the concept of “impedance” is introduced. Impedance is denoted by the letter Z and includes active resistance load R a and reactance X (or R r). This is due to the shape of the sinusoidal current (and currents of any other shapes) and the parameters of the inductive elements, as well as the laws of commutation:

1. The current in a circuit with inductance cannot change instantly.
2. The voltage in a circuit with a capacitor cannot change instantly.

Thus, the current begins to lag or advance the voltage, and full power divided into active and reactive.

X L and X C are the reactive components of the load.

In this regard, the value cosФ is introduced:

Here – Q – re active power, caused by alternating current and inductive-capacitive components, P – active power (distributed on active components), S – apparent power, cosФ – power factor.

You may have noticed that the formula and its presentation overlaps with the Pythagorean theorem. This is indeed true, and the angle Ф depends on how large the reactive component of the load is - the greater it is, the greater it is. In practice, this leads to the fact that the current actually flowing in the network is greater than that recorded by the household meter, while enterprises pay for full power.

In this case, resistance is presented in complex form:

Here j is the imaginary unit, which is typical for the complex form of equations. It is less often denoted as i, but in electrical engineering the effective value of alternating current is also denoted, therefore, in order not to be confused, it is better to use j.

The imaginary unit is equal to √-1. It is logical that there is no such number when squared that can result in a negative result of “-1”.

How to remember Ohm's law

To remember Ohm's Law, you can memorize the wording in simple words type:

The greater the voltage, the greater the current; the greater the resistance, the less current.

Or use mnemonic pictures and rules. The first is the presentation of Ohm's law in the form of a pyramid - briefly and clearly.

A mnemonic rule is a simplified form of a concept for simple and easy understanding and study. Can be either in verbal form or in graphic form. To correctly find the required formula, cover the desired quantity with your finger and get the answer in the form of a product or quotient. Here's how it works:

The second is a caricature representation. It is shown here: the more Ohm tries, the more difficult it is for Ampere to pass, and the more Volts, the easier it is for Ampere to pass.

Ohm's law is one of the fundamental ones in electrical engineering; without its knowledge, most calculations are impossible. And in everyday work it is often necessary to convert or determine current by resistance. It is not at all necessary to understand its derivation and the origin of all quantities - but the final formulas are required to be mastered. In conclusion, I would like to note that there is an old joke saying among electricians: “If you don’t know Om, stay at home.” And if every joke has a grain of truth, then here this grain of truth is 100%. Explore theoretical foundations, if you want to become a professional in practice, and other articles from our site will help you with this.

Like( 0 ) I don't like it( 0 )

Depends on the magnitude of the effect that the current can have on the conductor, be it 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 strength in the circuit will be. An electric field is characterized by a quantity called voltage. Therefore, we come to the conclusion that the current depends on the voltage.

Indeed, it was experimentally possible to establish 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 factor as the voltage was changed.

Connection with resistance

However, any circuit or section of a circuit is characterized by another important quantity called resistance to electric current. Resistance is inversely proportional to current. If you change the resistance value in 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 value of resistance, then the current strength will increase by the same amount. And, conversely, as the resistance increases, the current decreases proportionally.

Ohm's law formula for a section of a circuit

By comparing these two dependencies, one can come to the same conclusion that the German scientist Georg Ohm came to in 1827. He connected together the three above-mentioned physical quantities and derived a law that was named after him. Ohm's law for a section of a circuit states:

The current strength in a section of a circuit 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 – resistance.

Application of Ohm's Law

Ohm's law is one of fundamental laws of physics. Its discovery at one time allowed us to make a huge leap in science. Currently, it is impossible to imagine any very elementary calculation of basic electrical quantities for any circuit without using Ohm's law. The idea of ​​this law is not the exclusive domain of electronics 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 an 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. Calculation of the required resistance value when designing and assembling a circuit can be done according to Ohm’s law, based on the expected values ​​of current and voltage that will be passed through a given section of the circuit.

Abstract

Ohm's law. History of discovery. Various types Ohm's law.

1. General view Ohm's law.

2. The history of the discovery of Ohm’s law, a brief biography of the scientist.

3. Types of Ohm's laws.

Ohm's law establishes the relationship between current strength I in the conductor and potential difference (voltage) U between two fixed points (sections) of this conductor:

Georg Simon Ohm was born on March 16, 1787 in Erlangen, in the family of a hereditary mechanic. After graduating from school, Georg entered the city gymnasium. The Erlangen Gymnasium was supervised by the university. Classes at the gymnasium were taught by four professors. Georg, having graduated from high school, in the spring of 1805 began studying mathematics, physics and philosophy at the Faculty of Philosophy of the University of Erlangen.

After studying for three semesters, he accepted an invitation to take the place of a mathematics teacher in a private school in the Swiss town of Gottstadt.

In 1811 he returned to Erlangen, graduated from the university and received a Ph.D. Immediately after graduating from the university, he was offered the position of private assistant professor in the department of mathematics of the same university.

In 1812 Ohm was appointed teacher of mathematics and physics at a school in Bamberg. In 1817, he published his first printed work, dedicated to the methodology of teaching “The Most best option teaching geometry in preparatory classes." Ohm began researching electricity. Ohm based his electrical measuring instrument on the design of Coulomb's torsion balances. Ohm compiled the results of his research in the form of an article entitled "Preliminary report on the law according to which metals conduct contact electricity." The article was published in 1825 in the Journal of Physics and Chemistry, published by Schweigger. However, the expression found and published by Ohm turned out to be incorrect, which was one of the reasons for its long-term non-recognition. Having taken all precautions, eliminating all possible sources of error in advance, Ohm proceeded. new dimensions.

His famous article “Definition of the law according to which metals conduct contact electricity, together with an outline of the theory of the voltaic apparatus and the Schweigger multiplier,” published in 1826 in the Journal of Physics and Chemistry, appears.

In May 1827, “Theoretical Studies of Electric Circuits” volume of 245 pages, which contained Ohm’s now theoretical reasoning on electric circuits. In this work, the scientist proposed to characterize the electrical properties of a conductor by its resistance and introduced this term into scientific use. Om found more simple formula for the law of a section of an electrical circuit that does not contain an EMF: “The magnitude of the current in a galvanic circuit is directly proportional to the sum of all voltages and inversely proportional to the sum of the reduced lengths. In this case, the total reduced length is defined as the sum of all individual reduced lengths for homogeneous sections having different conductivity and different transverse section".

In 1829, his article “An Experimental Study of the Operation of an Electromagnetic Multiplier” appeared, in which the foundations of the theory of electrical measuring instruments were laid. Here Ohm proposed a unit of resistance, for which he chose resistance copper wire 1 foot long and 1 square line in cross section.

In 1830, Ohm's new study, “An Attempt to Create an Approximate Theory of Unipolar Conductivity,” appeared.

It was not until 1841 that Ohm's work was translated into English language, in 1847 - into Italian, in 1860 - into French.

On February 16, 1833, seven years after the publication of the article in which his discovery was published, Ohm was offered a position as professor of physics at the newly organized Polytechnic School of Nuremberg. The scientist begins research in the field of acoustics. Ohm formulated the results of his acoustic research in the form of a law, which later became known as Ohm's acoustic law.

The Russian physicists Lenz and Jacobi were the first to recognize Ohm's law among foreign scientists. They also helped his international recognition. With the participation of Russian physicists, on May 5, 1842, the Royal Society of London awarded Ohm a gold medal and elected him as a member.

In 1845 he was elected a full member of the Bavarian Academy of Sciences. In 1849, the scientist was invited to the University of Munich to the position of extraordinary professor. In the same year, he was appointed custodian of the state collection of physical and mathematical instruments, while simultaneously delivering lectures on physics and mathematics. In 1852, Ohm received the position of full professor. Ohm died on July 6, 1854. In 1881, at the electrical engineering congress in Paris, scientists unanimously approved the name of the resistance unit - 1 Ohm.

In general, the relationship between I And U nonlinear, but in practice it is always possible to consider it linear in a certain voltage range and apply Ohm’s law; for metals and their alloys this range is practically unlimited.

Ohm's law in the form (1) is valid for sections of the circuit that do not contain sources of emf. In the presence of such sources (batteries, thermocouples, generators, etc.), Ohm’s law takes the form:

Ohm's law can be written in differential form, relating the current density at each point of the conductor j with full tension electric field. Potential. electric field strength E, created in conductors by microscopic charges (electrons, ions) of the conductors themselves, cannot support the stationary movement of free charges (current), since the work of this field on a closed path is zero. The current is maintained by non-electrostatic forces of various origins (induction, chemical, thermal, etc.), which act in EMF sources and which can be represented as some equivalent non-potential field with intensity E ST, called third party. The total field strength acting on charges inside the conductor is, in general, equal to E + E ST . Accordingly, Ohm's differential law has the form:

Ohm's law in complex form is also valid for sinusoidal quasi-stationary currents.

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 when 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 circuit section states: current is directly proportional to voltage and inversely proportional to resistance.

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

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

To express Ohm's law most simply mathematically, it is believed that The resistance of a conductor that carries a current of 1 A at a voltage of 1 V is 1 ohm.

The current in amperes 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 symbols will give the formula for calculating it. By the way, Ohm's law is called only one formula from the triangle - the one that reflects the dependence of current on voltage and resistance. The other two formulas, although they are its consequences, have no physical meaning.

Calculations performed using Ohm's law for a section of a circuit will be correct when the voltage is expressed in volts, resistance in ohms and current in amperes. If multiple units of measurement 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 Ohm's law formula for a section of a circuit 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 kilo-ohms and mega-ohms, respectively.

Other articles about electricity in a simple and accessible presentation:

Calculating voltage using Ohm's law can be illustrated with the following example. Let a current of 5 mA pass through a section of a circuit with a resistance of 10 kOhm and you need to determine the voltage in this section.

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

IN electronic devices Current is usually expressed in milliamps and resistance in kilo-ohms. Therefore, it is convenient to use these units of measurement in calculations according to Ohm’s law.

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

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

The formula for determining resistance should not be understood to mean that the resistance of a given conductor depends on the outflow and voltage. It is known that it depends on the length, cross-sectional area and material of the conductor. By appearance The formula for determining resistance is similar to 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 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 values.

When the same current passes in two sections of a 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, different currents pass in two different sections of the circuit, then the smaller current will always be in the section that has greater resistance. All this follows from the basic formulation of Ohm’s law for a section of a circuit, i.e., from the fact that the greater the current, the greater the voltage and the lower the resistance.

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

Ohm's law can be clearly represented as the so-called current-voltage characteristics. As you know, a direct proportional relationship between two quantities is a straight line passing through the origin. This dependence is usually called linear.

In Fig. Figure 2 shows as an example a graph of Ohm's law for a section of a circuit with a resistance of 100 Ohms. The horizontal axis represents voltage in volts, and the vertical axis represents current in amperes. The scale of current and voltage can be chosen as desired. A straight line is drawn so that for any point the ratio of voltage to current is 100 Ohms. For example, if U = 50 V, then I = 0.5 A and R = 50: 0.5 = 100 Ohm.

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

The graph of Ohm's law for negative values ​​of current and voltage has the same appearance. This indicates 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 is.

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

There are also devices in which the resistance changes when the voltage or current changes. Then the relationship between current and voltage is expressed not according to Ohm’s law, but in a more complex way. For such devices, the current-voltage characteristic will not be a straight line passing through the origin of coordinates, but will be either a curve or a broken line. These devices are called nonlinear.

Mnemonic diagram for Ohm's law

Hello, dear readers of the Electrician's Notes website..

I'm opening today new section on a site called .

In this section I will try to explain electrical engineering issues to you in a clear and simple manner. I will say right away that we will not delve too far into theoretical knowledge, but we will get to know the basics in sufficient order.

The first thing I want to introduce you to is Ohm's law for a section of a chain. This is the most basic law that everyone should know.

Knowledge of this law will allow us to easily and accurately determine the values ​​of current, voltage (potential difference) and resistance in a section of the circuit.

Who is Om? A little history

Ohm's law was discovered by the famous German physicist Georg Simon Ohm in 1826. This is what he looked like.

I will not tell you the entire biography of Georg Ohm. You can find out more about this on other resources.

I will only say the most important things.

The most basic law of electrical engineering is named after him, which we actively use in complex calculations in design, in production and in everyday life.

Ohm's law for a homogeneous section of a chain is as follows:

I – the value of the current flowing through a section of the circuit (measured in amperes)

U – voltage value on a section of the circuit (measured in volts)

R – resistance value of the circuit section (measured in Ohms)

If the formula is explained in words, it turns out that the current strength proportional to voltage and is inversely proportional to the resistance of the circuit section.

Let's conduct an experiment

To understand the formula not in words, but in deeds, you need to assemble the following diagram:

The purpose of this article is to show clearly how to use Ohm's law for a section of a circuit. Therefore, I assembled this circuit on my workbench. See below what she looks like.

Using the control (selection) key, you can select either constant voltage or alternating voltage on the way out. In our case, constant voltage is used. I change the voltage level using a laboratory autotransformer (LATR).

In our experiment, I will use a voltage across a section of the circuit equal to 220 (V). We check the output voltage using a voltmeter.

Now we are completely ready to conduct our own experiment and test Ohm’s law in reality.

Below I will give 3 examples. In each example, we will determine the required value using 2 methods: using a formula and in a practical way.

Example #1

In the first example, we need to find the current (I) in the circuit, knowing the magnitude of the source DC voltage and resistance value LED light bulb.

The DC voltage source voltage is U = 220 (V). The resistance of an LED light bulb is R = 40740 (Ohm).

Using the formula, we find the current in the circuit:

I = U/R = 220 / 40740 = 0.0054 (A)

We connect in series with the LED light bulb, switched on in ammeter mode, and measure the current in the circuit.

The multimeter display shows the circuit current. Its value is 5.4 (mA) or 0.0054 (A), which corresponds to the current found by the formula.

Example No. 2

In the second example, we need to find the voltage (U) of a section of the circuit, knowing the amount of current in the circuit and the resistance value of the LED light bulb.

I = 0.0054 (A)

R = 40740 (Ohm)

Using the formula, we find the voltage of the circuit section:

U = I*R = 0.0054 *40740 = 219.9 (V) = 220 (V)

Now let’s check the result obtained in a practical way.

We connect a multimeter switched on in voltmeter mode in parallel to the LED light bulb and measure the voltage.

The multimeter display shows the measured voltage. Its value is 220 (V), which corresponds to the voltage found using the formula of Ohm's law for a section of the circuit.

Example No. 3

In the third example, we need to find the resistance (R) of a circuit section, knowing the magnitude of the current in the circuit and the voltage value of the circuit section.

I = 0.0054 (A)

U = 220 (V)

Again, let's use the formula and find the resistance of the circuit section:

R = U/I = 220/0.0054 = 40740.7 (Ohm)

Now let’s check the result obtained in a practical way.

We measure the resistance of an LED light bulb using a multimeter.

The resulting value was R = 40740 (Ohm), which corresponds to the resistance found by the formula.

How easy it is to remember Ohm's Law for a section of a circuit!!!

In order not to get confused and to easily remember the formula, you can use a small hint that you can do yourself.

Draw a triangle and enter the parameters of the electrical circuit into it, according to the figure below. You should get it like this.

How to use it?

Using the hint triangle is very easy and simple. Close with your finger the circuit parameter that needs to be found.

If the remaining parameters on the triangle are located at the same level, then they need to be multiplied.

If the remaining parameters on the triangle are located at different levels, then it is necessary to divide the upper parameter by the lower one.

With the help of a hint triangle, you will not get confused in the formula. But it’s better to learn it like the multiplication table.

Conclusions

At the end of the article I will draw a conclusion.

Electric current is a directed flow of electrons from point B with a minus potential to point A with a plus potential. And the higher the potential difference between these points, the more electrons will move from point B to point A, i.e. The current in the circuit will increase, provided that the circuit resistance remains unchanged.

But the resistance of the light bulb opposes the flow of electric current. And the greater the resistance in the circuit ( serial connection several light bulbs), the lower the current in the circuit will be, at a constant mains voltage.

P.S. Here on the Internet I found a funny but explanatory cartoon on the topic of Ohm’s law for a section of a circuit.