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 dependence was called the "Joule-Lenz Law". The Englishman established the dependence a year earlier than the Russian, but the law got its name from the names of both scientists, because their research was independent. The law is not theoretical, but it is of great practical importance. And so let's briefly and clearly find out the definition of the Joule-Lenz law and where it is applied.
Content:
- The wording
- FAQ
- Let's move on to practice
- Joule-Lenz law for the transmission of electricity over a distance
- Fuses and fuses
The wording
In a real conductor, when current flows through it, work is performed against friction forces. Electrons move through the wire and collide with other electrons, atoms, and other particles. As a result, heat is generated. 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:
The current is indicated by the letter I and is expressed in Amperes, the Resistance is R in Ohms, and the time t is in seconds. The unit of measurement for heat 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 in order to increase its temperature by 1 degree.
This writing of the formula is valid for a section of a circuit when the conductors are connected in series, when one value of current flows in them, but a different voltage drops at the ends. The product of the current squared by the resistance equals the 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 parallel connection, the Joule-Lenz law can be written in the form:
In differential form, it looks like this:
Where j is the current density A / cm2, E is the electric field strength, sigma is the resistivity of the conductor.
It should be noted 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 stands out on the one that has the greatest resistance, which can be concluded by analyzing the formula of the Law Joule-Lenz.
FAQ
How do I find the time? This refers to 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 the resistance, a formula is used, which is often called "rail", that is:
Here the letter "Ro" denotes the 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.
Resistivity is a tabular value and for each metal it has its own. Copper has orders of magnitude less than high-resistance alloys such as tungsten or nichrome. For what it is used, we will consider below.
Let's move on to practice
The Joule-Lenz law is of great importance for electrical calculations. First of all, you can apply it when calculating heating devices. A conductor is most often used as a heating element, but not a simple one (such as copper), but with a high resistance. Most often it is nichrome or kanthal, 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 power of heat for a heating device, you need to determine which body is in what volumes do you need to heat, take into account the amount of required heat and how long it needs to be transferred body. After calculations and transformations, you will receive the resistance and current strength in this circuit. Based on the data obtained on the resistivity, select the material of the conductor, its cross-section and length.
Joule-Lenz law for the transmission of electricity over a distance
At transmission of electricity over distances a significant problem arises - losses on transmission lines (power lines). The Joule-Lenz law describes the amount of heat generated by a conductor as a current flows. Power transmission lines power entire enterprises and cities, and this requires a lot of power, as a result of a large 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 designed to raise cables to a safe height above the ground in order to avoid electric shock.
Therefore, you need to reduce the current in order to do this, increase 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 with using transformer substations (KTP) or a number of KTP gradually lowering 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 applies to fuse sizes. These are elements that protect an electrical or electronic device from excessive currents for it, which may arise as a result of a surge in the supply voltage, short circuit on the board or windings (in the case of motors) to protect against further damage to the electrical system as a whole and fire. They consist of a housing, an insulator and a thin wire. The wire is selected with such a cross-section so that the rated current flows through it, and when it is exceeded, the amount of heat generated will burn it out.
As a result of the above, we conclude that the Joule-Lenz Law has found the widest application and is very important for electrical engineering. Thanks to the information about the amount of heat, which gives the performance of calculations according to the formulas indicated above, we can learn about the modes operation of devices, select the necessary materials and cross-section to increase the safety, reliability and durability of the device or circuit in the whole.
This concludes our article. We hope the information provided was useful and interesting for you. Finally, we recommend watching the video, which discusses this issue in more detail:
You probably don't know:
- The dependence of the resistance of the conductor on temperature
- The gimlet's rule in simple words
- What is dielectric loss
- How to become an electrician from scratch
