Why do we need Joule-Lenz's law? Joule-Lenz law. Definition, formula, physical meaning
Physical law estimating thermal effect electric current. The Joule-Lenz law was discovered in 1841 by James Joule and in 1842, completely independently, by Emilius Lenz.
as we already know, when free electrons move along a conductor, it must overcome the resistance of the material. During this movement of charges, constant collisions of atoms and molecules of the substance occur. In this case, the energy of movement and resistance is converted into heat. Its dependence on current was first described by two independent scientists, James Joule and Emil Lenz. That is why the law received a double name.
Definition, the amount of heat released per unit time in a specific section of an electrical circuit is directly proportional to the product of the square of the current in a given section and its resistance.
Mathematically, the formula can be written as follows:
Q = а×I 2 ×R×t
Where Q– amount of heat generated, A– heat coefficient (usually it is taken equal to 1 and is not taken into account), I– current strength, R– material resistance, t– time of current flow through the conductor. If the heat coefficient a = 1, That Q measured in joules. If a = 0.24, That Q measured in small calories.
Any conductor always heats up if current flows through it. But overheating of conductors is very dangerous, because it can damage not only electronic equipment, but also cause a fire. For example, in the event of a short circuit, the overheating of the conductor material is enormous. Therefore, to protect against short circuits and large overheats in electronic circuits special radio components are added - fuses. For their manufacture, a material is used that quickly melts and de-energizes the supply circuit when the current reaches maximum values. Fuses must be selected depending on the cross-sectional area of the conductor.
The Joule-Lenz law is relevant for both direct and alternating current. According to it, many different heating devices work. After all, the thinner the conductor, the greater the current passes through it over a longer period of time, the greater the amount of heat released as a result.
I hope you remember to remember that current depends on voltage. The question arises, why does the laptop not heat up as much as an iron? Because at the base there is a spiral wire made of steel, which has low resistance. Plus a steel sole, so the iron heats up to high temperatures, and we can iron them.
And it has a voltage stabilizer that reduces 220 volts to 19 volts. Plus, the resistance of all circuits and components is quite high. Additionally for cooling there is a cooler and copper thermal radiators.
The work of the Joule-Lenz law is clearly visible in practice. The most famous example of its use is an ordinary incandescent lamp or, in which the filament glows due to the passage of a high voltage current through it.
Based on the Joule-Lenz law, and works, where the creation of a welded joint is accomplished by heating the metal, due to the current passing through it and deforming the parts being welded by compression.
Electric arc welding, also works on physical principles Joule-Lenz law. To carry out welding work, the electrodes are heated to such a state that a welding arc occurs between them. Effect voltaic arc discovered by the Russian scientist V.V. Petrov, using the Joule-Lenz principle.
In addition to the mathematical formula, this law also has a differential form. Let us assume that a current flows through a stationary conductor and all its work is spent only on heating. Then, according to the law of conservation of energy, we obtain the following mathematical expression.
Let's look at the Joule-Lenz Law and its application.
When electric current passes through a conductor, it heats up. This happens because those moving under the influence electric field free electrons in metals and ions in electrolyte solutions collide with molecules or atoms of conductors and transfer their energy to them. Thus, when work is performed by current the internal energy of the conductor increases , a certain amount of heat is released in it, equal to the work of the current, and the conductor heats up: Q = A or Q = IUt .
Considering that U = IR , as a result we get the formula:
Q = I 2 Rt, Where
Q
- amount of heat released (in Joules)
I
- current strength (in Amperes)
R
— conductor resistance (in Ohms)
t
— travel time (in seconds)
Joule–Lenz law : the amount of heat generated by a current-carrying conductor is equal to the product of the square of the current, the resistance of the conductor and the time the current travels.
Where does the Joule-Lenz law apply?
1. For example, in incandescent lamps and in electric heating devices the Joule-Lenz law applies. They use a heating element, which is a high-resistance conductor. Due to this element, it is possible to achieve localized heat release in a specific area. Heat generation will appear with increasing resistance, increasing the length of the conductor, or choosing a specific alloy.
2. One of the areas of application of the Joule-Lenz law is reduction of energy losses . The thermal effect of current leads to energy loss. When transmitting electricity, the transmitted power depends linearly on voltage and current, and the heating power depends on the current quadratically, so if you increase the voltage while lowering the current before supplying electricity, it will be more profitable. But an increase in voltage leads to a decrease in electrical safety. To increase the level of electrical safety, the load resistance is increased according to the increase in voltage in the network.
3. Also, the Joule-Lenz law affects selection of wires for circuits . Because if the wires are selected incorrectly, the conductor may become very hot and may catch fire. This occurs when the current exceeds the maximum permissible values and too much energy is released.
Electricity is an integral feature of our era. Absolutely everything around is tied to it. Any modern man, even without technical education, knows that electric current flowing through wires can in some cases heat them, often to very high temperatures. It would seem that this is known to everyone and is not worth mentioning. However, how to explain this phenomenon? Why and how does the conductor heat up?
Let's fast forward to the 19th century, the era of accumulation of knowledge and preparation for the technological leap of the 20th century. An era when all over the world various scientists and simply self-taught inventors discover something new almost every day, often spending a huge amount of time on research and, at the same time, not presenting the final result.
One of these people, the Russian scientist Emilius Christianovich Lenz, was fascinated by electricity, at the then primitive level, trying to calculate electrical circuits. In 1832, Emilius Lenz was “stuck” with calculations, since the parameters of his simulated circuit “energy source - conductor - energy consumer” varied greatly from experiment to experiment. In the winter of 1832-1833, the scientist discovered that the cause of the instability was a piece of platinum wire that he brought from the cold. When heating or cooling a conductor, Lenz also noticed that there was a certain relationship between the current strength, the electrical current and the temperature of the conductor.
At certain parameters of the electrical circuit, the conductor quickly thawed and even warmed up slightly. There were practically no measuring instruments in those days - it was impossible to accurately measure either current or resistance. But this was a Russian physicist, and he showed ingenuity. If this is an addiction, then why shouldn't it be reversible?
In order to measure the amount of heat generated by the conductor, the scientist designed a simple “heater” - a glass container in which there was an alcohol-containing solution and a platinum spiral conductor immersed in it. By applying different amounts of electric current to the wire, Lenz measured the time it took for the solution to heat up to a certain temperature. The sources in those days were too weak to heat the solution to a serious temperature, so it was not possible to visually determine the amount of solution that had evaporated. Because of this, the research process was very drawn out - thousands of options for selecting the parameters of the power source, conductor, long measurements and subsequent analysis.
Joule-Lenz formula
As a result, a decade later, in 1843, Emilius Lenz put the result of his experiments in the form of a law for public viewing by the scientific community. However, it turned out that he was ahead of him! A couple of years ago English physicist James Prescott Joule had already conducted similar experiments and also presented his results to the public. But, after carefully checking all the works of James Joule, the Russian scientist found out that own experiences much more accurate, developed larger volume research, therefore, Russian science has something to complement the English discovery.
The scientific community considered both research results and combined them into one, thereby renaming Joule's law to the Joule-Lenz law. The law states that the amount of heat released by a conductor when an electric current flows through it is equal to the product of the strength of this current squared, the resistance of the conductor and the time during which the current flows through the conductor. Or the formula:
Q=I 2 Rt
Where
Q - amount of heat generated (Joules)
I - current flowing through the conductor (Amps)
R - conductor resistance (Ohms)
t - time of passage of current through the conductor (Seconds)
Why does the conductor get hot?
How is the heating of the conductor explained? Why does it heat up and not remain neutral or cool down? Heating occurs due to the fact that free electrons moving in a conductor under the influence of an electric field bombard the atoms of metal molecules, thereby transferring to them their own energy, which turns into heat. To put it quite simply: when overcoming the material of the conductor, the electric current seems to “rub”, colliding with electrons against the molecules of the conductor. Well, as you know, any friction is accompanied by heating. Consequently, the conductor will heat up while electric current runs through it.
It also follows from the formula that the higher the resistivity of the conductor and the higher the current flowing through it, the higher the heating will be. For example, if you connect a copper conductor (resistivity 0.018 Ohm mm²/m) and an aluminum conductor (0.027 Ohm mm²/m) in series, then when electric current flows through the circuit, aluminum will heat up more than copper due to its higher resistance . Therefore, by the way, it is not recommended to twist copper and aluminum wires together in everyday life - there will be uneven heating at the point of twisting. The result is burning with subsequent loss of contact.
Application of the Joule-Lenz law in life
The discovery of the Joule-Lenz law had enormous consequences for practical application electric current. Already in the 19th century, it became possible to create more accurate measuring instruments based on the contraction of a wire spiral when heated by a flowing current of a certain magnitude - the first dial voltmeters and ammeters. The first prototypes of electric heaters, toasters, and melting furnaces appeared - a conductor with a high resistivity, which made it possible to obtain a fairly high temperature.
Fuses and bimetallic circuit breakers (analogues of modern thermal protection relays) were invented, based on the difference in heating of conductors with different resistivities. And, of course, having discovered that at a certain current strength a conductor with a high resistivity can heat up red hot, this effect used as a light source. The first light bulbs appeared.
A conductor (carbon stick, bamboo thread, platinum wire, etc.) was placed in a glass flask, air was pumped out to slow down the oxidation process and an undamped, clean and stable light source was obtained - an electric light bulb
Conclusion
Thus, we can say that almost all electrical and electrical engineering is based on the Joule-Lenz law. Having discovered this law, it became possible to predict in advance some future problems in the development of electricity. For example, due to the heating of the conductor, the transmission of electric current over a long distance is accompanied by losses of this current to heat. Accordingly, to compensate for these losses, it is necessary to reduce the transmitted current, compensating for this with a high voltage. And at the end consumer, lower the voltage and receive a higher current.
The Joule-Lenz law relentlessly follows from one era of technological development to another. Even today we constantly observe it in everyday life - the law appears everywhere, and people are not always happy about it. A very hot processor of a personal computer, loss of light due to a burnt copper-aluminum twist, a knocked-out fuse insert, electrical wiring burned out due to a high load - all this is the same Joule-Lenz law.
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Lesson 254. Joule-Lenz law. Work and power of electric current
Joule-Lenz law. Part 1
Lesson 255. Problems on work and power of electric current
Subtitles
Definitions
IN verbal formulation sounds like this
The power of heat released per unit volume of a medium during the flow of direct electric current is proportional to the product of the electric current density and the electric field strength.
Mathematically can be expressed in the following form:
w = j → ⋅ E → = σ E 2 (\displaystyle w=(\vec (j))\cdot (\vec (E))=\sigma E^(2))Where w (\displaystyle w)- heat generation power per unit volume, j → (\displaystyle (\vec (j)))- electric current density, E → (\displaystyle (\vec (E)))- electric field strength, σ is the conductivity of the medium, and the dot denotes the scalar product.
The law can also be formulated in integral form for the case of current flow in thin wires:
In integral form, this law has the form
d Q = I 2 R d t (\displaystyle dQ=I^(2)Rdt) Q = ∫ t 1 t 2 I 2 R d t (\displaystyle Q=\int \limits _(t_(1))^(t_(2))I^(2)Rdt)Where dQ- the amount of heat released over a period of time dt, I- current strength, R- resistance, Q- the total amount of heat released during the period of time from t 1 before t 2. In the case of constant current and resistance:
Q = I 2 R t (\displaystyle Q=I^(2)Rt)And applying Ohm's law, you can obtain the following equivalent formulas:
Q = V 2 t / R = I V t (\displaystyle Q=V^(2)t/R\ =IVt)Practical significance
Reduced energy loss
When transmitting electricity, the thermal effect of current in wires is undesirable, since it leads to energy losses. The supply wires and the load are connected in series, which means there is current in the network I (\displaystyle I) on wires and load is the same. The load power and wire resistance should not depend on the choice of source voltage. The power released on the wires and on the load is determined by the following formulas
Q w = R w ⋅ I 2 (\displaystyle Q_(w)=R_(w)\cdot I^(2)) Q c = V c ⋅ I (\displaystyle Q_(c)=V_(c)\cdot I)Whence it follows that Q w = R w ⋅ Q c 2 / V c 2 (\displaystyle Q_(w)=R_(w)\cdot Q_(c)^(2)/V_(c)^(2)). Since in each specific case the load power and wire resistance remain unchanged and the expression R w ⋅ Q c 2 (\displaystyle R_(w)\cdot Q_(c)^(2)) is a constant, then the heat generated on the wire is inversely proportional to the square of the voltage at the consumer. By increasing the voltage we reduce heat loss in the wires. This, however, reduces the electrical safety of power lines.
Choosing wires for circuits
The heat generated by a current-carrying conductor is released to varying degrees in environment. If the current strength in the selected conductor exceeds a certain maximum permissible value, such strong heating is possible that the conductor can cause a fire in objects near it or melt itself. As a rule, when choosing wires intended for assembling electrical circuits, it is enough to follow the accepted regulatory documents, which regulate the choice of conductor cross-section.
Electric heating devices
If the current strength is the same throughout the entire electrical circuit, then in any selected section the more heat will be generated, the higher the resistance of this section.
By deliberately increasing the resistance of a section of a circuit, localized heat generation can be achieved in that section. They work on this principle electric heating devices. They use a heating element- conductor with high resistance. Increasing the resistance is achieved (jointly or separately) by choosing an alloy with high resistivity (for example, nichrome, constantan), increasing the length of the conductor and reducing its cross-section. The lead wires have a generally low resistance and therefore their heating is usually unnoticeable.
Fuses
To protect electrical circuits from the flow of excessively high currents, a piece of conductor with special characteristics. This is a conductor with a relatively small cross-section and made of such an alloy that, at permissible currents, heating the conductor does not overheat it, but at excessively high currents, the overheating of the conductor is so significant that the conductor melts and opens the circuit.
The energy of the directed movement of charged particles is spent on heating the crystal lattice of the conductor.2. What is the amount of heat received by the crystal lattice of a conductor from directionally moving charged particles?
The amount of heat received by the crystal lattice is equal to the work done by the electric current.3. Formulate the Joule-Lenz law. Write down its mathematical expression.
The amount of heat released in the conductor is directly proportional to the square of the current strength, the resistance of the conductor andthe time it takes for current to flow through a conductor.
