As a result of experiments, it was found that the amount of heat generated by current when passing through a conductor depends on the resistance of the conductor itself, the current and the time of its passage.

This physical law was first established in 1841 by the English physicist Joule, and somewhat later (in 1844) independently by the Russian academician Emil Christianovich Lenz (1804 - 1865).

The quantitative relationships that occur when a conductor is heated by current are called the Joule-Lenz law.

It was stated above:

Since 1 cal = 0.472 kgm, then

Thus,

1 J = 0.24 cal.

The energy of electric current is determined by the formula

A = I 2× r × t J.

Since the current energy is used for heating, the amount of heat generated by the current in the conductor is equal to:

Q= 0.24 × I 2× r × t cal.

This formula, expressing the Joule-Lenz law, shows and defines the law that the amount of heat in calories generated by a current passing through a conductor is equal to a factor of 0.24 multiplied by the square of the current in amperes, the resistance in ohms and the time in seconds.

Video - "Joule-Lenz Law, 8th grade physics":

Example 1. Determine how much heat a current of 6 A will generate when passing through a conductor with a resistance of 2 Ohms for 3 minutes.

Q= 0.24 × I 2× r × t= 0.24 × 36 × 2 × 180 = 3110.4 cal.

The formula for the Joule-Lenz law can be written as follows:

Q= 0.24 × I × I × r × t ,

and since I × r = U, then you can write:

Q= 0.24 × I × U× t cal.

Example 2. The electric stove is connected to a 120 V network. The current flowing through the spiral of the stove is 5 A. It is necessary to determine how much heat the current will release in 2 hours.

Q= 0.24 × I × U× t= 0.24 × 5 × 120 × 7200 = 1,036,800 cal = 1036.8 kcal.

Video - "Heating conductors with electric current":

E. H. Lenz generalized the experiments of electromagnetic induction, presenting this generalization in the form of the “Lenz rule”. In his works on the theory of electrical machines, Lenz studied the phenomenon of “armature reaction” in direct current machines and proved the principle of reversibility of electric machines. Lenz, working with Jacobi, studied the force of attraction of electromagnets and established the dependence of the magnetic moment on the magnetizing force.

Lenz was a member of the St. Petersburg Academy of Sciences and rector of St. Petersburg University.

In 1841 and 1842, independently of each other, English and Russian physicists established the dependence of the amount of heat on the flow of current in a conductor. This relationship was called the “Joule-Lenz Law”. The Englishman established the dependence a year earlier than the Russian, but the law received its name from the names of both scientists, because their research was independent. The law is not theoretical in nature, but has great practical significance. And so let's briefly and clearly find out the definition of the Joule-Lenz law and where it is applied.

Formulation

In a real conductor, when current flows through it, work is done against frictional forces. Electrons move through the wire and collide with other electrons, atoms and other particles. As a result, heat is released. The Joule-Lenz law describes the amount of heat generated when current flows through a conductor. It is directly proportional to the current strength, resistance and flow time.

In integral form, the Joule-Lenz Law looks like this:

Current strength is denoted by the letter I and is expressed in Amperes, Resistance is R in Ohms, and time t is in seconds. The unit of heat measurement Q is Joule, to convert to calories you need to multiply the result by 0.24. In this case, 1 calorie is equal to the amount of heat that needs to be supplied to clean water to increase its temperature by 1 degree.

This formula entry is valid for a section of a circuit with a series connection of conductors, when the same amount of current flows in them, but different voltages drop at the ends. The product of current squared and resistance equals power. At the same time, power is directly proportional to the square of the voltage and inversely proportional to the resistance. Then for an electrical circuit with a parallel connection, the Joule-Lenz Law can be written as:

In differential form it looks like this:

Where j is the current density A/cm 2, E is the electric field strength, sigma is the resistivity of the conductor.

It is worth noting that for a homogeneous section of the circuit, the resistance of the elements will be the same. If the circuit contains conductors with different resistances, a situation arises when the maximum amount of heat is released on the one that has the highest resistance, which can be concluded by analyzing the formula of the Joule-Lenz Law.

FAQ

How to find time? Here we mean the period of current flow through the conductor, that is, when the circuit is closed.

How to find the resistance of a conductor? To determine resistance, a formula is used, which is often called “rail”, that is:

Here the letter “Ro” denotes resistivity, it is measured in Ohm*m/cm2, l and S are the length and cross-sectional area. When calculating, square meters and centimeters are reduced and Ohms remain.

Specific resistance is a tabular value and is different for each metal. Copper has orders of magnitude less than high-resistivity alloys such as tungsten or nichrome. We will look at what this is used for below.

Let's move on to practice

The Joule-Lenz law is of great importance for electrical calculations. First of all, you can use it when calculating heating devices. A conductor is most often used as a heating element, but not a simple one (like copper), but with a high resistance. Most often it is nichrome or kantal, fechral.

They have high resistivity. You can use copper, but then you will waste a lot of cable (sarcasm, copper is not used for this purpose). To calculate the heat power for a heating device, you need to determine which body and in what volumes you need to heat, take into account the amount of heat required and how long it takes to transfer it to the body. After calculations and conversions, you will get the resistance and current in this circuit. Based on the data obtained on resistivity, you select the conductor material, its cross-section and length.

Joule-Lenz law for transmitting electricity over a distance

When a significant problem arises - losses on transmission lines (power lines). The Joule-Lenz law describes the amount of heat generated by a conductor when current flows. Power lines power entire enterprises and cities, and this requires high power and, as a consequence, high current. Since the amount of heat depends on the resistance of the conductor and the current, so that the cables do not heat up, you need to reduce the amount of heat. It is not always possible to increase the cross-section of the wires, because... this is costly in terms of the cost of the copper itself and the weight of the cable, which entails an increase in the cost of the supporting structure. High voltage power lines are shown below. These are massive metal structures created to raise the cable to a safe height above the ground, in order to avoid electric shock.

Therefore, you need to reduce the current to do this by increasing the voltage. Between cities, power lines usually have a voltage of 220 or 110 kV, and at the consumer it is reduced to the required value using transformer substations (TSP) or a whole series of PTS, gradually lowering it to values ​​that are safer for transmission, for example 6 kV.

Thus, with the same power consumption at a voltage of 380/220 V, the current will decrease hundreds and thousands of times lower. And according to the Joule-Lenz law, the amount of heat in this case is determined by the power that is lost on the cable.

Fuses and fuses

The Joule-Lenz law is applied when calculating fuses. These are elements that protect an electrical or electronic device from excessive currents that may arise as a result of a surge in supply voltage,

The Joule–Lenz law is a law of physics that defines a quantitative measure of the thermal effect of 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, it received its double name - the Joule-Lenz law.

Law definition and formula

The verbal formulation has the following form: the power of heat generated in a conductor when flowing through it is proportional to the product of the electric field density value and the intensity 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 intensity and density, respectively, of the electric fields;

σ is the conductivity of the medium.

Physical meaning of the Joule–Lenz law

The law can be explained as follows: current flowing through a conductor represents the movement of an electric charge under the influence. Thus, the electric field does some work. This work is spent on heating the conductor.

In other words, energy transforms into another quality – heat.

But excessive heating of current-carrying conductors and electrical equipment should not be allowed, as this can lead to damage. Severe overheating of the wires is dangerous when quite 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 defined 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 heat released;

I – current value;

R - active resistance of conductors;

t – 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 bit depth of the units in which the values ​​used in the formula are measured.

The Joule-Lenz law is quite general in nature, since it does not depend on the nature of the forces generating the current.

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

Application area

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

In the 19th century, independently of each other, the Englishman J. Joule and the Russian E. H. Lenz studied the heating of conductors by electric current and experimentally established a pattern: the amount of heat released in a current-carrying conductor is directly proportional to the square of the current, the resistance of the conductor and the time it takes for the current to pass.
Later it was found that this statement is true for any conductors: solid, liquid, gaseous. Therefore, the open pattern is called Joule-Lenz law:

The figure shows an installation diagram with which you can experimentally verify the Joule-Lenz law. By dividing the current by the voltage, the resistance is calculated using the formula R=U/I. The thermometer measures the increase in water temperature. By formulas Q=I2Rt And Q=cmDt° calculate the amounts of heat that, according to the results of the experiment, should coincide.
For those who are more deeply interested in physics, we specifically note that the Joule-Lenz law can be obtained not only experimentally, but also derived theoretically. Let's do it.


The resulting formula A=I2Rt is similar to the formula of the Joule-Lenz law, but on the left side it is the work of the current, and not the amount of heat. What gives us the right to consider these quantities equal? Let's write it down first law of thermodynamics(see § 6-h) and express the work from it:
DU = Q + A, therefore A =DU-Q.
Let's remember that DU- this is a change in the internal energy of a conductor heated by current; Q- the amount of heat given off by the conductor (this is indicated by the “-” sign in front); A- work done on the conductor. Let's find out what kind of work this is.
The conductor itself is motionless, but electrons move inside it, constantly colliding with the ions of the crystal lattice and transferring part of their kinetic energy to them. To prevent the flow of electrons from weakening, work is constantly done on them by the forces of the electric field created by the source of electricity. Therefore, A is the work done by the electric field forces to move electrons inside the conductor.
Let us now discuss the quantity DU(change in internal energy) applied to a conductor in which current begins to flow.
The conductor will gradually heat up, which means it internal energy will increase. As it heats up, the difference between the temperatures of the conductor and the environment will increase. According to Newton's law (see § 6-k), the heat transfer power of the conductor will increase. After some time, this will cause the temperature of the conductor to stop increasing. From now on the internal energy of the conductor will cease to change, that is, the value DU will become equal to zero.
Then the first law of thermodynamics for this state will be: A = -Q. That is If the internal energy of the conductor does not change, then the work done by the current is completely converted into heat. Using this conclusion, we write all three formulas for calculating the work of the current in a different form:

For now we will consider these formulas to be equal. Later we will discuss that the right formula is always valid (that’s why it is called the law), and the two left ones are only valid under certain conditions, which we will formulate when studying physics in high school.

Q = a*I*2R*t, where
Q - amount of heat released (in Joules)
a - proportionality coefficient
I - current strength (in Amperes)
R - Conductor resistance (in Ohms)
t - Travel time (in seconds)

The Joule-Lenz law explains that electric current is a charge that moves under the influence of an electric field. In this case, the field does work, and the current has power and energy is released. When this energy passes through a stationary metal conductor, it becomes thermal energy, since it is aimed at heating the conductor.

In differential form, the Joule-Lenz law is expressed as the volumetric thermal power density of the current in the conductor will be equal to the product of the electrical conductivity and the square of the electric field strength.

Application of the Joule-Lenz law

One area of ​​application of the Joule-Lenz law is to reduce 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.

Also, the Joule-Lenz law affects the choice of wires for circuits. If the wires are selected incorrectly, the conductor, as well as it, can become very hot. This occurs when the current exceeds the maximum permissible values ​​and too much energy is released. When selecting the correct wires, you should follow the regulatory documents.

Sources:

• Physical encyclopedia

There is a directly proportional relationship between current and voltage, described by Ohm's law. This law determines the relationship between current, voltage and resistance in a section of an electrical circuit.

Instructions

Remember current and voltage.
- Electric current is an ordered flow of charged particles (electrons). For quantitative determination, the value I is used, called current strength.
- Voltage U is the potential difference at the ends of a section of an electrical circuit. It is this difference that causes the electrons to move, like a fluid flowing.

Current strength is measured in amperes. In electrical circuits, the current strength is determined by an ammeter. The unit of voltage is , you can measure the voltage in a circuit using a voltmeter. Assemble a simple electrical circuit from a current source, a resistor, an ammeter and a voltmeter.

When a circuit is closed and current flows through it, record the instrument readings. Change the voltage at the ends of the resistance. You will see that the ammeter reading will increase as the voltage increases and vice versa. This experience demonstrates a directly proportional relationship between current and voltage.