Lenz's law formula. Joule-Lenz law: its formulation and application

Hello. You are unlikely to ever need the Joule-Lenz law, but it is included in the basic course of electrical engineering, and therefore now I will tell you about this law.

The Joule-Lenz law was discovered by two great scientists independently of each other: in 1841, James Prescott Joule, an English scientist who made a major contribution to the development of thermodynamics and in 1842, Emilius Christianovich Lenz, a Russian scientist of German origin, who made a great contribution to electrical engineering. Since the discovery of both scientists occurred almost simultaneously and independently of each other, it was decided to call the law a double name, or rather, surnames.

Remember when, and not only that, I said that electric current heats the conductors through which it flows. Joule and Lenz determined a formula that can be used to calculate the amount of heat released.

So, initially, the formula looked like this:

The unit of measurement according to this formula was calories and the coefficient k was responsible for this, which is equal to 0.24, that is, the formula for obtaining data in calories looks like this:

But since in the SI measurement system, in view of the large number of measured quantities and to avoid confusion, the notation joule was adopted, the formula changed somewhat. k became equal to one, and therefore the coefficient was no longer written in the formula and it began to look like this:

Here: Q is the amount of heat generated, measured in Joules (SI symbol - J);

I – current, measured in Amperes, A;

R – resistance, measured in Ohms, Ohm;

t – time measured in seconds, s;

and U – voltage, measured in volts, V.

Look carefully, doesn’t one part of this formula remind you of anything? And specifically? But this is power, or rather the power formula from Ohm’s law. And to be honest, I have never seen such a representation of the Joule-Lenz law on the Internet:

Now we recall the mnemonic table and get at least three formulaic expressions of the Joule-Lenz law, depending on what quantities we know:

It would seem that everything is very simple, but it seems so to us only when we already know this law, and then both great scientists discovered it not theoretically, but experimentally and then were able to substantiate it theoretically.

Where can this Joule-Lenz law come in handy?

In electrical engineering there is the concept of long-term permissible current flowing through wires. This is a current that the wire can withstand for a long time (that is, indefinitely), without destroying the wire (and insulation, if any, because the wire can be without insulation). Of course, you can now take the data from the PUE (Electrical Installation Rules), but you received this data solely on the basis of the Joule-Lenz law.

In electrical engineering, fuses are also used. Their main quality is reliability. For this, a conductor of a certain cross-section is used. Knowing the melting point of such a conductor, you can calculate the amount of heat that is necessary for the conductor to melt from the flow of large current values ​​through it, and by calculating the current, you can calculate the resistance that such a conductor must have. In general, as you already understand, using the Joule-Lenz law you can calculate the cross-section or resistance (the values ​​are interdependent) of the conductor for the fuse.

And also, remember, we talked about. There, using the example of a light bulb, I told the paradox that a more powerful lamp in a series connection shines weaker. And you probably remember why: the lower the resistance, the greater the voltage drop across the resistance. And since power is , and the voltage drops very much, it turns out that a large resistance will generate a large amount of heat, that is, the current will have to work harder to overcome the large resistance. And the amount of heat that the current will release can be calculated using the Joule-Lenz law. If we take a series connection of resistances, then it is better to use an expression in terms of the square of the current, that is, the original form of the formula:

And for a parallel connection of resistances, since the current in parallel branches depends on the resistance, while the voltage on each parallel branch is the same, the formula is best represented in terms of voltage:

You all use examples of the Joule-Lenz law in everyday life - first of all, these are all kinds of heating devices. As a rule, they use nichrome wire and the thickness (cross-section) and length of the conductor are selected taking into account that prolonged thermal exposure does not lead to rapid destruction of the wire. In exactly the same way, a tungsten filament glows in an incandescent lamp. The same law determines the degree of possible heating of almost any electrical and electronic device.

In general, despite its apparent simplicity, the Joule-Lenz law plays a very important role in our lives. This law gave a great impetus to theoretical calculations: heat generation by currents, calculation of the specific temperature of the arc, conductor and any other electrically conductive material, loss of electrical power in thermal equivalent, etc.

You may ask how to convert Joules to Watts and this is a fairly common question on the Internet. Although the question is somewhat misleading, as you read on you will understand why. The answer is quite simple: 1 J = 0.000278 Watt*hour, while 1 Watt*hour = 3600 Joules. Let me remind you that instantaneous power consumption is measured in Watts, that is, directly used while the circuit is turned on. And Joule determines the work of an electric current, that is, the current power over a period of time. Remember, in Ohm's law I gave an allegorical situation. Current is money, voltage is a store, resistance is a sense of proportion and money, power is the amount of products that you can carry (take away) at one time, but how far, how quickly and how many times you can take them away is work . That is, it is impossible to compare work and power, but it can be expressed in units that are more understandable to us: Watts and hours.

I think that now it will not be difficult for you to apply the Joule-Lenz law in practice and theory, if necessary, and even convert Joules to Watts and vice versa. And thanks to the understanding that the Joule-Lenz law is the product of electrical power and time, you can remember it more easily, and even if you suddenly forgot the basic formula, then remembering just Ohm’s law you can again obtain the Joule-Lenz law. And with this I say goodbye to you.

It is quite difficult to imagine the life of a modern person without electricity. It has become one of the main and most valuable attributes of modern existence. In fact, anyone who has ever worked with electricity knows that when current passes through wires, they tend to heat up. Why does this depend?

What is current

Current is the ordered movement of charged particles called electrons. And if current flows through a conductor, then various physical processes begin to occur in it, namely, electrons collide with molecules.

Molecules are neutral or those that have lost their negatively charged particle. As a result of collisions, either electrons can become neutral molecules, or an electron is knocked out of another similar molecule, forming a positively charged ion. During these collisions, the kinetic energy of the charged particles is consumed. It is this energy that becomes heat.

Thermal heating of the conductor can also be affected by resistance. For example, you can take a certain body and drag it along the ground. The earth in this case is resistance. What will happen to him? That's right, a frictional force will occur between the body and the surface, which, in turn, heats the body. The current behaves exactly the same in this case.

Addiction

And, taking into account all of the above, scientists were able to determine this relationship between current strength, resistance and amount of heat. This dependence is called the Joule-Lenz law, the formula of which is known to all physicists. In 1832-1833, the Russian physicist Emilius Lentz discovered that when metal conductors were exposed to heat, their conductivity changed dramatically. This actually complicated the scientist’s work and made it difficult to calculate electrical circuits.

At the same time, the young scientist came up with the idea that perhaps there was some kind of relationship between the current strength and the temperature of the conductor. But what to do? At that time, there were no precise electrical instruments that could measure current strength, resistance, and there was not even a source of stable EMF. This did not stop Lenz; he decided to conduct an experiment.

Experiments of a Russian physicist

The essence of this experiment was so simple, like everything ingenious, that even a schoolboy could repeat it. The scientist designed a special device that served to measure the amount of heat generated by the conductor. This device turned out to be an ordinary vessel, into which Lenz poured a solution of diluted alcohol and placed a conductor - a platinum wire, to which an electric current was supplied.

After the device was created, the scientist began conducting experiments. He measured the exact amount of time required for the alcohol in the vessel to be heated to 10 o C. Many not only months, but also years were spent on this. And in 1843, 10 years later, a law was published, the essence of which was that the heating of a conductor by current is proportional to the square of the current used for heating.

Joule and Lenz

But that was not the case! It turns out that several years ago the English physicist James Prescott Joule conducted similar experiments and already published his observations. What should I do? Lenz did not give up and carefully studied Joule's work and came to the conclusion that, even though they performed the same experiments, Lenz's experiments were much more accurate. In connection with this, the scientific community added Lenz amendments to Joule’s work and this law became known as the Joule-Lenz law. The mathematical formulation of the law looks like this:

Q = I *U*t, where:

• I - current strength, A;
• U - voltage, V;
• t is the time it takes the current to pass through the conductor, s.

The law itself sounds like this: the amount of thermal energy released in a conductor through which an electric current flows is equal to the product of the current strength, the voltage and the time the current passes through the conductor.

Ohm's law

However, will this statement always be true? You can try to derive it using Ohm's law. Judging by it, U = I*R, where R is resistance, Ohm.

Taking into account Ohm's law, you can substitute the value into the formula Q = I*U*t = I 2 *R*t. From this we can conclude that the amount of heat directly depends on the resistance of the conductor. Also for the Joule-Lenz law this statement will be true: I = Q = I*U*t.

All three formulas will be correct, but Q = I 2 *R*t will be true for all situations. The other two are also correct, but under certain circumstances.

Conductors

Now about the conductors. Initially, in their experiments, Joule and Lenz used platinum wires, as mentioned above. In all similar experiments, scientists of that time used mainly metal conductors, since they were quite inexpensive and stable. It is not surprising, because until now metal conductors are the main type of conductors, and therefore it was initially believed that the Joule-Lenz law was applicable only to them. However, a little later it was discovered that this law applies not only to metal conductors. It is true for any of them. The conductors themselves according to classification can be divided into:

• Metal (copper, iron, silver, etc.). The main role in them is played by negatively charged particles (electrons) that flow through the conductor.
• Liquid. In them, ions are responsible for the movement of charges - these are atoms in which there are either too many or too few electrons.
• Gaseous. Unlike their counterparts, in such conductors the current is determined by the movement of both ions and electrons.

And despite the differences, in any case, as the current or resistance increases, the amount of heat will also increase.

Application of the law by other physicists

The discovery of the Joule-Lenz law held great promise. After all, in fact, this law made it possible to create various kinds of electric heating devices and elements. For example, a little later after the discovery of the law, scientists noticed that when certain elements are heated, they begin to glow. They wanted to experiment with them using different conductors, and in 1874, Russian engineer Alexander Nikolaevich Lodygin invented the modern incandescent lamp, the filament of which was made of tungsten.

The Joule-Lenz law is also applied in electrical engineering - for example, when creating fuses. A fuse is a certain element of an electrical circuit, the design of which is made in such a way that when a current flows through it above the permissible value (for example, during a short circuit), it overheats, melts and opens the power circuit. Even an ordinary electric kettle or microwave oven, which virtually everyone has, works according to this law.

Conclusion

It is quite difficult to determine the contribution of these scientists to modern electronics and electrical engineering, but one thing is for sure - the emergence of the Joule-Lenz law turned people’s understanding of electricity upside down and gave more specific knowledge of what an electric field is in a conductor with current.

Without a doubt, the law discovered by these great physicists became a defining step in all science, and it was thanks to this discovery that other more or less grandiose achievements of other scientists were subsequently made. All science is a close interweaving of discoveries, some solved and unresolved problems. The law discussed in this article in a certain way influenced many studies and left an indelible and quite distinct mark on science.

Electricity is an integral feature of our era. Absolutely everything around is tied to it. Any modern person, 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 the 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 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 already conducted similar experiments and also presented his results to the public. But, having carefully checked all the works of James Joule, the Russian scientist found out that his own experiments were much more accurate, a larger volume of research had been accumulated, therefore, Russian science had 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 their own energy to them, 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 the practical applications of 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 was used, 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 was 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 follows relentlessly 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.

Emilius Christianovich Lenz (1804 - 1865) - famous Russian physicist. He is one of the founders of electromechanics. His name is associated with the discovery of the law that determines the direction and the law that determines the electric field in a conductor carrying current.

In addition, Emilius Lenz and the English physicist Joule, independently studying each other experimentally, discovered the law according to which the amount of heat released in a conductor will be directly proportional to the square of the electric current that passes through the conductor, its resistance and time, in the flow of electric current is maintained constant in a conductor.

This law is called the Joule-Lenz law, its formula is expressed as follows:

where Q is the amount of heat released, l is current, R is conductor resistance, t is time; the quantity k is called the thermal equivalent of work. The numerical value of this quantity depends on the choice of units in which the other quantities included in the formula are measured.

If the amount of heat is measured in calories, current in amperes, resistance in Ohms, and time in seconds, then k is numerically equal to 0.24. This means that a current of 1A releases in a conductor that has a resistance of 1 Ohm, in one second, a heat amount that is equal to 0.24 kcal. Based on this, the amount of heat in calories released in the conductor can be calculated using the formula:

In the SI system of units, energy, heat and work are measured in units - joules. Therefore, the proportionality coefficient in the Joule-Lenz law is equal to one. In this system, the Joule-Lenz formula looks like:

The Joule-Lenz law can be verified experimentally. A current is passed through a wire spiral immersed in a liquid poured into the calorimeter for some time. Then the amount of heat released in the calorimeter is calculated. The resistance of the coil is known in advance, the current is measured with an ammeter and time with a stopwatch. By changing the current in the circuit and using different spirals, you can check the Joule-Lenz law.

Based on Ohm's law

Substituting the current value into formula (2), we obtain a new expression for the Joule-Lenz law:

The formula Q = l²Rt is convenient to use when calculating the amount of heat released during a series connection, because in this case it is the same in all conductors. Therefore, when several conductors occur, each of them will release an amount of heat that is proportional to the resistance of the conductor. If, for example, three wires of the same size are connected in series - copper, iron and nickel, then the greatest amount of heat will be released from the nickel wire, since it is the largest, it heats up stronger.

If then the electric current in them will be different, but the voltage at the ends of such conductors is the same. It is better to calculate the amount of heat that will be released during such a connection using the formula Q = (U²/R)t.

This formula shows that when connected in parallel, each conductor will release an amount of heat that will be inversely proportional to its conductivity.

If you connect three wires of equal thickness - copper, iron and nickel - in parallel with each other and pass current through them, then the greatest amount of heat will be released into it and will heat up more than the rest.

Taking the Joule-Lenz law as a basis, calculations are made for various electric lighting installations, heating and heating electrical appliances. The conversion of electrical energy into thermal energy is also widely used.

The amount of heat released per unit time in the section of the circuit under consideration is proportional to the product of the square of the current in this section and the resistance of the section

Joule Lenz's law in integral form in thin wires:

If the current strength changes over time, the conductor is stationary and there are no chemical transformations in it, then heat is generated in the conductor.

The conversion of electrical energy into heat is widely used in electric furnaces and various electric heating devices. The same effect in electrical machines and devices leads to involuntary energy expenditure (energy loss and reduced efficiency). Heat, by causing these devices to heat up, limits their load; When overloaded, the temperature rise may damage the insulation or shorten the service life of the installation.

In the formula we used:

Amount of heat

Current work

Conductor voltage

Current strength in the conductor

Time lapse