The resistance of a conductor through heat. Joule–Lenz law

The Joule-Lenz law is a law of physics that determines the quantitative measure of thermal action electric current. This law was formulated in 1841 by the English scientist D. Joule and completely separately from him in 1842 by the famous Russian physicist E. Lenz. Therefore, he received his double name - the Joule-Lenz law.

Law definition and formula

The verbal formulation is as follows: the power of heat released in the conductor when flowing through it is proportional to the product of the density value electric field to the tension value.

Mathematically, the Joule-Lenz law is expressed as follows:

ω = j E = ϭ E²,

where ω is the amount of heat released in units. volume;

E and j are the strength and density, respectively, of the electric fields;

σ is the conductivity of the medium.

The physical meaning of the Joule-Lenz law

The law can be explained as follows: the current flowing through the conductor is a displacement electric charge under influence . In this way, electric field does some work. This work is spent on heating the conductor.

In other words, energy transforms into its other quality - heat.

But excessive heating of conductors with current and electrical equipment must not be allowed, as this can lead to their damage. Severe overheating is dangerous with wires, when sufficiently large currents can flow through the conductors.

In integral form for thin conductors Joule-Lenz law sounds like this: the amount of heat that is released per unit time in the section of the circuit under consideration is determined as the product of the square of the current strength and the resistance of the section.

Mathematically, this formulation is expressed as follows:

Q = ∫ k I² R t,

in this case, Q is the amount of released heat;

I is the current value;

R is the active resistance of the conductors;

t is the exposure time.

The value of the parameter k is usually called the thermal equivalent of work. The value of this parameter is determined depending on the digit capacity of the units in which the measurements of the values used in the formula are performed.

The Joule-Lenz law has enough general character, since it does not depend on the nature of the forces that generate the current.

From practice, it can be argued that it is valid for both electrolytes and conductors and semiconductors.

Application area

There are a huge number of areas of application in everyday life of the Joule Lenz law. For example, a tungsten filament in an incandescent lamp, an arc in electric welding, a heating filament in an electric heater, and more. etc. This is the most widely accepted physical law in Everyday life.

Simultaneously, but independently of each other, who discovered it in 1840) is a law that quantifies the thermal effect of an electric current.

When current flows through a conductor, a transformation occurs electrical energy into heat, and the amount of heat released will be equal to the work of electric forces:

Q = W

Joule-Lenz law: the amount of heat generated in a conductor is directly proportional to the square of the current strength, the resistance of the conductor and the time of its passage.

Practical value

Reduction of energy losses

When transmitting electricity, the thermal effect of the current is undesirable, since it leads to energy losses. Since the transmitted power depends linearly on both voltage and current strength, and the heating power depends quadratically on current strength, it is advantageous to increase the voltage before transmitting electricity, reducing the current strength as a result. Increasing the voltage reduces the electrical safety of power lines. In the case of using high voltage in the circuit, in order to maintain the same power of the consumer, it will be necessary to increase the resistance of the consumer (quadratic dependence. 10V, 1 Ohm = 20V, 4 Ohm). The supply wires and the consumer are connected in series. Wire resistance ( R w) is constant. But the resistance of the consumer ( R c) increases when a higher voltage is selected in the network. The ratio of the resistance of the consumer and the resistance of the wires is also growing. When the resistances are connected in series (wire - consumer - wire), the distribution of the released power ( Q) is proportional to the resistance of the connected resistances. ; ; ; the current in the network for all resistances is constant. Therefore, we have the relation Q c / Q w = R c / R w ; Q c And R w are constants (for each specific task). Let's define that . Consequently, the power released on the wires is inversely proportional to the resistance of the consumer, that is, it decreases with increasing voltage. because . (Q c- constant); We combine the last two formulas and derive that ; for each specific task is a constant. Therefore, the heat generated on the wire is inversely proportional to the square of the voltage at the consumer. The current passes evenly.

Selection of wires for circuits

The heat generated by a current-carrying conductor is, to one degree or another, released in environment. In the event that the current strength in the selected conductor exceeds a certain maximum permissible value, such strong heating is possible that the conductor can provoke a fire in objects near it or melt itself. As a rule, when assembling electrical circuits, it is enough to follow the accepted regulatory documents, which regulate, in particular, the choice of the cross section of conductors.

Electric heaters

If the current strength is the same throughout the electrical circuit, then in any selected area, the more heat will be released, the higher the resistance of this section.

By deliberately increasing the resistance of a circuit section, localized heat generation in this section can be achieved. This principle works electric heaters. They use a heating element - conductor with high resistance. An increase in resistance is achieved (jointly or separately) by choosing an alloy with high resistivity (e.g. nichrome, constantan), increasing the length of the conductor, and decreasing its cross section. The lead wires are usually low resistance and therefore their heating is usually imperceptible.

Fuses

To protect electrical circuits from the flow of excessively large currents, a piece of conductor with special characteristics is used. This is a conductor of relatively small cross section and made of such an alloy that, at allowable currents, heating the conductor does not overheat it, and at excessively large overheating of the conductor is so significant that the conductor melts and opens the circuit.

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Joule-Lenz law

Joule-Lenz law(after the English physicist James Joule and the Russian physicist Emil Lenz, who simultaneously, but independently of each other, discovered it in 1840) is a law that quantifies the thermal effect of an electric current.

When current flows through a conductor, electrical energy is converted into thermal energy, and the amount of heat released will be equal to the work of electrical forces:

Q = W

Joule-Lenz law: the amount of heat generated in a conductor is directly proportional to the square of the current strength, the resistance of the conductor and the time of its passage.

Practical value

Reduction of energy losses

When transmitting electricity, the thermal effect of the current is undesirable, since it leads to energy losses. Since the transmitted power depends linearly on both voltage and current, and the heating power depends quadratically on the current, it is advantageous to increase the voltage before transmitting electricity, thereby reducing the current. Increasing the voltage reduces the electrical safety of power lines. In the case of using high voltage in the circuit, in order to maintain the same power of the consumer, it will be necessary to increase the resistance of the consumer (quadratic dependence. 10V, 1 Ohm = 20V, 4 Ohm). The supply wires and the consumer are connected in series. Wire resistance ( R w) is constant. But the resistance of the consumer ( R c) increases when a higher voltage is selected in the network. The ratio of the resistance of the consumer and the resistance of the wires is also growing. When the resistances are connected in series (wire - consumer - wire), the distribution of the released power ( Q) is proportional to the resistance of the connected resistances. ; ; ; the current in the network for all resistances is constant. Therefore, we have the relation Q c / Q w = R c / R w ; Q c And R w these are constants (for each specific task). Let's define that . Consequently, the power released on the wires is inversely proportional to the resistance of the consumer, that is, it decreases with increasing voltage. because . (Q c- constant); We combine the last two formulas and derive that ; for each specific task is a constant. Therefore, the heat generated on the wire is inversely proportional to the square of the voltage at the consumer. The current passes evenly.

Selection of wires for circuits

The heat generated by a current-carrying conductor is, to one degree or another, released into the environment. In the event that the current strength in the selected conductor exceeds a certain maximum permissible value, such strong heating is possible that the conductor can provoke a fire in objects near it or melt itself. As a rule, when assembling electrical circuits, it is sufficient to follow the accepted regulatory documents, which regulate, in particular, the choice of the cross section of conductors.

Electric heaters

If the current strength is the same throughout the electrical circuit, then in any selected area, the more heat will be released, the higher the resistance of this section.

By deliberately increasing the resistance of a circuit section, localized heat generation in this section can be achieved. This principle works electric heaters. They use a heating element- conductor with high resistance. An increase in 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 are usually low resistance and therefore their heating is usually imperceptible.

Fuses

Main article: Fuse (electricity)

Joule-Lenz law

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

In addition, Emilius Lenz and the English physicist Joule, studying by experience the thermal effects of current, independently discovered the law according to which the amount of heat that is released in the conductor will be directly proportional to the square of the electric current that passes through the conductor, its resistance and the time during which the electric current is maintained unchanged in the conductor.

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

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

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, which has a resistance of 1 ohm, in one second a number of heat, which is equal to 0.24 kcal. Based on this, the amount of heat in calories released in the conductor can be calculated by the formula:

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

The Joule-Lenz law can be tested experimentally. For some time, a current is passed through a wire spiral immersed in a liquid poured into a calorimeter. Then the amount of heat released in the calorimeter is calculated. The resistance of the spiral is known in advance, the current is measured with an ammeter and the 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 formula expression for the Joule-Lenz law:

The formula Q \u003d l²Rt is convenient to use when calculating the amount of heat released in a series connection, because in this case the electric current in all conductors is the same. So when it happens serial connection several conductors, in each of them such an amount of heat will be released, which 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 nickel, since its resistivity is the greatest, it is stronger and heats up.

If the conductors are connected in parallel, then the electric current in them will be different, and 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 \u003d (U² / R) t.

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

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

Taking as a basis the Joule-Lenz law, they calculate various electric lighting installations, heating and heating electrical appliances. The conversion of electrical energy into heat energy is also widely used.

Joule-Lenz law

Consider a homogeneous conductor, to the ends of which a voltage U is applied . During the time dt, a charge is transferred through the conductor section dq = Idt . Since the current is the movement of charge dq under the action of an electric field, then, according to formula (84.6), the work of the current

(99.1)

If the conductor resistance R , then, using Ohm's law (98.1), we obtain

(99.2)

From (99.1) and (99.2) it follows that the current power

(99.3)

If current is expressed in amperes, voltage is in volts, resistance is in ohms, then the work of the current is expressed in joules, and the power is in watts. In practice, off-system units of current work are also used: watt-hour (Wh) and kilowatt-hour (kWh). 1 W×h - operation of a current with a power of 1 W for 1 hour; 1 Wh = 3600 Ws = 3.6-103 J; 1 kWh=103 Wh=3.6-106 J.

The amount of heat released per unit time per unit volume is called the specific heat power of the current. She is equal

(99.6)

Using the differential form of Ohm's law (j = gE) and the relation r = 1/g , we get

(99.7)

Formulas (99.6) and (99.7) are a generalized expression of the Joule-Lenz law in differential form, suitable for any conductor.

The thermal effect of the current is widely used in technology, which began with the discovery in 1873 by the Russian engineer A. N. Lodygin (1847-1923) of an incandescent lamp. The operation of electric muffle furnaces is based on heating conductors with electric current. electric arc(discovered by the Russian engineer V.V. Petrov (1761-1834)), contact electric welding, household electric heaters, etc.

Joule Lenz formula. briefly

Nina chill

Joule Lenz's law determines the amount of heat released in a section of an electrical circuit with finite resistance when current passes through it. A prerequisite is the fact that there should be no chemical transformations in this section of the chain. Consider a conductor with a voltage applied to its ends. Therefore, current flows through it. Thus, the electrostatic field and external forces do the work of moving the electric charge from one end of the conductor to the other.
If at the same time the conductor remains motionless and chemical transformations do not occur inside it. Then all the work expended by the external forces of the electrostatic field goes to increase internal energy conductor. That is, to warm it up.

Content:

The famous Russian physicist Lenz and the English physicist Joule, conducting experiments on the study of the thermal effects of electric current, independently derived the Joule-Lenz law. This law reflects the relationship between the amount of heat released in the conductor and the electric current passing through this conductor for a certain period of time.

Properties of electric current

When an electric current passes through a metal conductor, its electrons constantly collide with various foreign particles. These can be ordinary neutral molecules or molecules that have lost electrons. An electron in the process of movement can split off one more electron from a neutral molecule. As a result, its kinetic energy is lost, and instead of a molecule, a positive ion is formed. In other cases, the electron, on the contrary, combine with a positive ion and form a neutral molecule.

In the process of collisions of electrons and molecules, energy is consumed, which later turns into heat. The expenditure of a certain amount of energy is associated with all movements during which one has to overcome resistance. At this time, the work expended on overcoming frictional resistance is converted into thermal energy.

Joule Lenz's law formula and definition

According to the Lenz Joule law, an electric current passing through a conductor is accompanied by an amount of heat that is directly proportional to the square of the current and the resistance, as well as the time it takes for this current to flow through the conductor.

In the form of a formula, the Joule-Lenz law is expressed as follows: Q \u003d I 2 Rt, in which Q displays the amount of heat released, I - , R is the resistance of the conductor, t is the period of time. The value of "k" is the thermal equivalent of work and is used in cases where the amount of heat is measured in calories, current strength - , resistance - in ohms, and time - in seconds. The numerical value of k is 0.24, which corresponds to a current of 1 ampere, which, with a conductor resistance of 1 ohm, releases an amount of heat equal to 0.24 kcal for 1 second. Therefore, to calculate the amount of released heat in calories, the formula Q = 0.24I 2 Rt is used.

When using the SI system of units, the amount of heat is measured in joules, so the value of "k", in relation to the Joule-Lenz law, will be equal to 1, and the formula will look like: Q \u003d I 2 Rt. According to I = U/R. If this current value is substituted into the main formula, it will take the following form: Q \u003d (U 2 / R) t.

Basic Formula Q = I 2 Rt is very convenient to use when calculating the amount of heat that is released in the case of a series connection. The current strength in all conductors will be the same. When several conductors are connected in series at once, each of them will release so much heat, which will be proportional to the resistance of the conductor. If three identical wires of copper, iron and nickel are connected in series, then the maximum amount of heat will be released last. This is due to the highest specific resistance of nickeline and the stronger heating of this wire.

When the same conductors are connected in parallel, the value of the electric current in each of them will be different, and the voltage at the ends will be the same. In this case, the formula Q \u003d (U 2 / R) t is more suitable for calculations. The amount of heat released by a conductor will be inversely proportional to its conductivity. Thus, the Joule-Lenz law is widely used for calculating electric lighting installations, various heating and heating devices, as well as other devices associated with the conversion of electrical energy into heat.

Joule-Lenz law. Work and power of electric current

Hello. The Joule-Lenz law is unlikely when you need it, but it is included in basic course 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 great contribution to the development of thermodynamics and in 1842 Emil Khristianovich Lenz, a Russian scientist of German origin, who made a great contribution already 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 him, I said that electric current heats the conductors through which it flows. Joule and Lenz came up with a formula by which the amount of heat generated can be calculated.

So, initially, the formula looked like this:

The unit of measurement according to this formula was calories and the coefficient k, which is equal to 0.24, was “responsible” for this, 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 designation joule was adopted, the formula has 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 released, measured in Joules (SI designation - J);

I - current, measured in Amperes, A;

R - resistance, measured in Ohms, Ohms;

t is the time measured in seconds, s;

and U is the voltage, measured in volts, V.

Look carefully, does one part of this formula remind you of anything? And more specifically? But this is power, or rather the power formula from Ohm's law. And to be honest, I have not yet seen such a representation of the Joule-Lenz law on the Internet:

Now we recall the mnemonic table and obtain 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 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 a long-term permissible current flowing through wires. This is the current that the wire can handle. long time(that is, indefinitely), without destroying the wire (and the 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 section is used. Knowing the melting temperature of such a conductor, one can calculate the amount of heat that is necessary for the conductor to melt from the flow of large currents through it, and by calculating the current, one can calculate the resistance that such a conductor must have. In general, as you already understood, using the Joule-Lenz law, you can calculate the cross section or resistance (the values \u200b\u200bof interdependent) of a conductor for a 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 serial connection shines weaker. And you probably remember why: the voltage drop across the resistance is stronger, the lower the resistance. And since the power is, and the voltage drops very much, it turns out that a large resistance will emit a large number of heat, that is, the current will have to work harder to overcome a large resistance. And the amount of heat that the current will release in this case can be calculated using the Joule-Lenz law. If we take a series connection of resistances, then use better expression through the square of the current, that is, original view formulas:

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

You all use examples of the work 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 thickness ( transverse section) and the 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. According to the same law, the degree of possible heating of almost any electrical and electronic device is determined.

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, losses electrical power in thermal equivalent, etc.

You may ask how to convert Joules to Watts and that's pretty frequently asked question in the Internet. Although the question is somewhat wrong, reading 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 the consumed instantaneous power is measured in Watts, that is, the directly used circuit while the circuit is on. And the Joule determines the work of an electric current, that is, the power of the current 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) on yourself at a time, but how far, how quickly and how many times you can take them away is work . That is, there is no way 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 more easily remember it, and even if you suddenly forgot the basic formula, then remembering just Ohm's law, you can again get the Joule-Lenz law. And I say goodbye to you on this.