Ohm's law- a physical law that determines the relationship between electrical quantities - voltage, resistance and current for conductors.
It was first discovered and described in 1826 by the German physicist Georg Ohm, who showed (using a galvanometer) quantitative relationship between electromotive force, electric current and the properties of the conductor, as a proportional relationship.
Subsequently, the properties of the conductor, capable of withstanding electric current based on this dependence, began to be called electrical resistance (Resistance), denoted in calculations and on diagrams by the letter R and measured in ohms in honor of the discoverer.
The source of electrical energy itself also has internal resistance, which is usually denoted by the letter r.

Ohm's brother, Martin Ohm, fought against the German education system. All of these factors made it difficult to accept Ohm's work, which was not fully accepted until the decade of the year. Luckily, Omu was recognized for his contributions to science before he died. This fluctuation, known as Johnson-Nyquist noise, is due to the discreteness of the load. Ohm's law is valid for average current for resistive materials. Ohm's work preceded Maxwell's equations, as well as any understanding of circuits alternating current. Modern developments in the field of electromagnetic theory and circuit analysis do not contradict Ohm's law when they are evaluated within the appropriate limits.

Ohm's law for a circuit section

So school course Physicists are well aware of the classical interpretation of Ohm's Law:

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

This means, if to the ends of the conductor resistance R= 1 ohm voltage applied U\u003d 1 Volt, then the current value I in the conductor will be equal to 1/1 \u003d 1 Ampere.

This is easy to understand by analyzing the circuit in which they are in series, a voltage source and a 6 ohm resistor. You can establish a relationship between the battery voltage, the value of the resistor, and the current that the battery supplies and circulates through the resistor. From the same formula, you can clear voltage as a function of current and resistance, then Ohm's Law. So more resistance has more slope.

To memorize the three expressions of Ohm's Law, he uses a triangle, which has much in common with the formulas above and can give three cases. An increase in voltage means an increase in current, and an increase in current means an increase in voltage. At a fixed voltage: an increase in current causes a decrease in resistance and an increase in resistance causes a decrease in current at DC: Voltage follows resistance. An increase in resistance causes an increase in voltage, and an increase in voltage causes an increase in resistance. At a fixed resistance value: current follows voltage. . In particular, this law studies the relationship between three concepts: flow, potential difference and electric.

Two more useful relations follow from this:

If a current of 1 ampere flows in a conductor with a resistance of 1 ohm, then the voltage at the ends of the conductor is 1 volt (voltage drop).

If there is a voltage of 1 volt at the ends of the conductor and a current of 1 ampere flows through it, then the resistance of the conductor is 1 ohm.

The above formulas in this form can be applied to alternating current only if the circuit consists only of active resistance R.
In addition, it should be remembered that Ohm's Law is valid only for linear circuit elements.

Ohm's law allows you to explain the phenomenon of electric current

In its simplest form, this law states that the current flowing through an electrical conductor is directly proportional to the potential difference and, in parallel, inversely proportional to the resistance. This is due to the passage of electrons from one point to another through a conduit, such as a copper wire. Thus, current intensity refers to the number of electrons passing through a conductor in a given time, and their measurement is amplifiers.

Potential difference, commonly known as electrical voltage, is the one that allows electrons to move through the conductor, and its unit is the volt. Finally, resistance is the greater or lesser opposition that some conductor presents to the passage of electric current.

A simple online calculator for practical calculations is offered.

Ohm's law. Calculation of voltage, resistance, current, power.
After reset, enter any two known parameters.

Ohm's law for a closed circuit

If an external circuit with resistance is connected to the power supply R, a current will flow in the circuit, taking into account the internal resistance of the source:

This simple formula explains how voltage, current, and resistance are related. The discovery of Ohm's Law occurred at the beginning of the nineteenth century, an era in which the generation of electric current was already known thanks to the research of Alexander Volta. The German scientist Georg Simon Ohm wanted to delve into the advances of the new fluid discovered by Volta and began experimenting on the properties of electricity using metallic bodies until he finally discovered the law that bears his name.

Ohm's law has definitely been improved by Maxwell's electromagnetic theory

Although Ohm's law was a key contribution to describing how electricity works, it should be noted that this law is not always followed because Georg Simon Ohm did not consider other laws that interfere with electricity, Kirchhoff's laws. Many electrical phenomena were not explained until the scientist James Clerk Maxwell combined electricity and the so-called Maxwell's laws.

I- The strength of the current in the circuit.
- Electromotive force (EMF) - the magnitude of the voltage of the power source independent of the external circuit (no load). Characterized potential energy source.
r- Internal resistance of the power supply.

For electromotive force, external resistance R and internal r connected in series, then the magnitude of the current in the circuit is determined by the value of the EMF and the sum of the resistances: I = /(R+r) .

Also known as voltage or voltage, but how do they relate both quantities? It was the physicist Georg Simon Ohm, a teacher high school, the first of which established this relationship, which we now know as Ohm's law. The current flowing through a conductor is directly proportional to the potential difference between its ends and inversely proportional to its electrical resistance.

Drivers who comply with Ohm's law

Ohm's law expression is also usually written as follows. This last expression is very important because it reflects a decrease or loss electrical potential between two points of resistance. The Ohm's law expression is widely used to analyze simple circuits. However, this is not applicable in most situations. As we previously studied in the section on electrical resistance, the resistance of a body depends on.

The voltage at the terminals of the external circuit will be determined based on the current strength and resistance R relation, which has already been discussed above: U=IR.
Voltage U, when connecting the load R, will always be less than the EMF by the value of the product I*r, which is called the voltage drop across the internal resistance of the power supply.
We encounter this phenomenon quite often when we see partially discharged batteries or accumulators in operation.
As they discharge, their internal resistance increases, therefore, the voltage drop inside the source increases, which means that the external voltage decreases. U = - I*r.
The lower the current and the internal resistance of the source, the closer the value of its EMF and the voltage at its terminals U.
If the current in the circuit is zero, then = U. The circuit is open, the EMF of the source is equal to the voltage at its terminals.

Therefore, Ohm's law only applies when the driver is within a certain temperature range. Ohm's law is valid only for some materials, called ohmic, but does not apply to samples of ionized gas and other conductors, called non-axial. The material that makes it up. . The most famous was the one made by the Dutchman Musbrok in the city of Leiden, which is known as the Leiden bottle.

The action of exposing the ends of the body to a potential difference causes a continuous and ordered movement of charges in one direction, which is called "electric current". The study of moving charges is called "electrodynamics". However, knowing the atomic structure, we know that its value is from negative to positive. So we say that a body is positively charged when it has lost electrons and negatively charged when it has picked up electrons.

In cases where the internal resistance of the source can be neglected ( r≈ 0), the voltage at the source terminals will be equal to the EMF ( ≈ U) regardless of the resistance of the external circuit R.
Such a power supply is called voltage source.

Ohm's law for alternating current

If there is inductance or capacitance in the AC circuit, their reactance must be taken into account.
In this case, Ohm's Law will be written as:

This is the flow of electrons circulating through a conductor. It can be obtained as the amount of charge flowing through the cross section of the conductor in a certain period of time. A device that measures intensity is called an ammeter. This is one where the flow of charges in a conductor always flows in the same direction. It is generated by batteries.

Each terminal is called a pole, which can be either positive or negative. This is the one where the flow of charges on the driver cyclically changes its direction in time. Effects of Electric Current Passing electric current through conductors has different effects depending on the nature of the conductors and the intensity of the current.

Here Z- total (complex) circuit resistance - impedance. It includes active R and reactive X components.
The reactance depends on the ratings of the reactive elements, on the frequency and shape of the current in the circuit.
You can get acquainted with the complex resistance in more detail on the page impedance.

This current acts directly on nervous system causing nerve contractions. When this happens, it is said to be an electric shock. As a result of these collisions, the atoms increase their vibrational energy and the material heats up. This effect is used in stoves, anafras, hair dryers, etc.

Thus, when the magnetic needle approaches the conductive current, the needle is observed to diverge sharply from its position. This effect is perhaps the most important in terms of technology. Electrical energy is converted into light energy such as fluorescent lights, discharge tubes, and light diodes.

Taking into account the phase shift φ , created by reactive elements, for a sinusoidal alternating current, Ohm's Law is usually written in complex form:

Complex current amplitude. = I amp e jφ
- complex voltage amplitude. = U amp e jφ
- complex resistance. Impedance.
φ - phase angle between current and voltage.
e is a constant, the base of the natural logarithm.
j is the imaginary unit.
I amp , U amp- amplitude values ​​of sinusoidal current and voltage.

For example, if a stream passes through acidic water, it decomposes into oxygen and hydrogen. voltage or electromotive force is the energy required for a charge to move through a conductor. It is also known as voltage or potential difference. It can be generated by a battery, accumulator or alternator.

A commonly used instrument is called a multimeter, which can be measured in addition to volts, amps, ohms, etc. Voltage = Voltage = Potential difference. This is the natural opposition of any material to the passage of electric current. In the case of a straight conductor, the electrical resistance depends on the length, area and resistivity of the material.

Nonlinear elements and circuits

Ohm's law is not a fundamental law of nature and may be applicable in limited cases, for example, for most conductors.
It cannot be used to calculate voltage and current in semiconductor or vacuum devices, where this dependence is not proportional and can only be determined using the current-voltage characteristic (CVC). This category of elements includes all semiconductor devices (diodes, transistors, zener diodes, thyristors, varicaps, etc.) and vacuum tubes.
Such elements and the circuits in which they are used are called non-linear.

Length: The resistance will be greater the longer the conductor is, as the number of electron impacts will also be greater. The nature of the material: due to the molecular composition, materials have different degrees of resistance, which is represented by the resistivity coefficient, which is represented by the Greek letter ρ.

The table shows the values ​​of the specific electrical resistance some substances. Comparing the above factors, we can establish that. The constant of proportionality corresponds to the coefficient of resistivity, and its value is characteristic of each substance. AT international system it is expressed in Ω. m.

In 1826, the German scientist Georg Ohm made a discovery and described
an empirical law on the relationship between such indicators as current strength, voltage and features of the conductor in the circuit. Subsequently, by the name of the scientist, he began to be called Ohm's law.

Later it turned out that these features are nothing but the resistance of the conductor that occurs in the process of its contact with electricity. This is the external resistance (R). There is also an internal resistance (r) specific to the current source.

The thermal mixing of the conductor particles is increased either by heat supplied from outside or by the impacts themselves between electrons and atoms. Due to this increase in collisions, free electrons will stop more often, so the current will decrease.

The α coefficients depend on each material. Example 1 - Calculation of resistivity. Determine resistivity a conductor having a length of 4 km, a section of 16 mm2 and a resistance of 20 ohms. Solution: We apply the formula. From this we refine the resistivity ρ.

Ohm's law for a circuit section

According to the generalized Ohm's law for a certain section of the circuit, the current strength in the circuit section is directly proportional to the voltage at the ends of the section and inversely proportional to the resistance.

Where U is the voltage of the ends of the section, I is the current strength, R is the resistance of the conductor.

Taking into account the above formula, it is possible to find unknown values ​​of U and R by doing simple mathematical operations.

Example 2 - Calculation of the length of a conductor. Calculate the length of an iron-nickel wire with a diameter of 6 mm and a resistance of 500 ohms. Solution. First, calculate the cross section from the diameter. The German physicist George Ohm decided that in order for an electric current to pass through a conductor, there must be an electrical voltage at its ends; therefore, there must be a relationship between the voltage at which the circuit passes and the current passing through it.

Having established an analogy between electric current and fluid current, Ohm found that the current was directly proportional to the voltage, whether it was a complete circuit or, in the case of a conductor, the potential difference between its ends; something similar to what happens in a water pipe, where the flow is proportional to the pressure difference between the ends of the part in question.

The formulas given above are valid only when the network experiences one resistance.

Ohm's law for a closed circuit

Current strength complete chain equal to the EMF divided by the sum of the resistances of the homogeneous and inhomogeneous sections of the circuit.

A closed network has both internal and external resistances. Therefore, the relation formulas will be different.

Then cleanup of the proposed expression should. Calculate the resistance of an electrical device if it is subjected to a voltage of 12 V and a current of 20 mA circulates. Pay attention to the resistance of the furnace, which draws 3 amps at 120 volts.

Solution: We apply Ohm's law. What potential difference must be applied to a 30 ohm rheostat to circulate 5 amps through it? It is the association of conductive elements that makes the circulation of electric current possible. At any electrical circuit consumption or resistance are the elements that transform electrical energy into some other type of energy.

Where E is the electromotive force (EMF), R is the external resistance of the source, r is the internal resistance of the source.

Ohm's law for an inhomogeneous section of a chain

A closed electrical network contains sections of a linear and non-linear nature. Sections that do not have a current source and do not depend on external influences are linear, and sections containing a source are non-linear.

Ohm's law for a section of a network of a homogeneous nature was stated above. The law on a non-linear section will have the following form:

I = U/ R = f1 – f2 + E/ R

Where f1 - f2 is the potential difference at the end points of the considered network section

R is the total resistance of the non-linear section of the circuit

The emf of a non-linear section of the circuit is greater than zero or less. If the direction of movement of the current coming from the source with the movement of current in the electrical network is the same, the movement of positive charges will prevail and the EMF will be positive. In case of coincidence of directions, traffic will be increased in the network negative charges created by the EMF.

Ohm's law for alternating current

With the capacitance or inertia available in the network, it is necessary to take into account in the calculations that they give out their resistance, from the action of which the current becomes variable.

Ohm's law for alternating current looks like this:

where Z is the resistance along the entire length of the electrical network. Also called impedance. The impedance is made up of active and reactive resistances.

Ohm's law is not a basic scientific law, but only an empirical relation, and in some conditions it may not be observed:

  • When the network has a high frequency, the electromagnetic field changes from high speed, and in calculations it is necessary to take into account the inertia of charge carriers;
  • Under conditions of low temperature with substances that have superconductivity;
  • When the conductor is strongly heated by the passing voltage, the ratio of current to voltage becomes variable and may not follow the general law;
  • When a conductor or dielectric is under high voltage;
  • In LED lamps;
  • Semiconductors and semiconductor devices.

In turn, elements and conductors that obey Ohm's law are called ohmic.

Ohm's law can provide an explanation for some natural phenomena. For example, when we see birds sitting on high-voltage wires, we have a question - why are they not affected by electricity? This is explained quite simply. Birds, sitting on the wires, are a kind of conductors. Most of the tension falls on the gaps between the birds, and the share that falls on the "guides" themselves does not pose a danger to them.

But this rule works only with a single contact. If a bird touches a wire or a telegraph pole with its beak or wing, it will inevitably die from the huge amount of stress that these areas carry. Such cases happen all over the place. Therefore, for security reasons, some settlements special devices have been installed to protect birds from dangerous voltage. On such perches, the birds are completely safe.

Ohm's law is also widely applied in practice. Electricity is deadly to a person with just one touch to a bare wire. But in some cases resistance human body may be different.

So, for example, dry and intact skin has a greater resistance to electricity than a wound or skin covered with sweat. Due to fatigue, nervous tension and intoxication, even with a small voltage, a person can get a strong electric shock.

On average, the resistance of the human body is 700 ohms, which means that a voltage of 35 V is safe for a person. Working with high voltage, experts use.