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# Joule-Lenz law

Emil Khristianovich Lentz (1804 – 1865) – Russianthe famous physicist. He is one of the founders of electromechanics. His name is associated with the discovery of a law that determines the direction of the induction current, and the law that determines the electric field in a conductor with a current.

In addition, Aemili Lenz and the English physicistJoule, studying the thermal effects of the current, independently of each other, 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 was called the law of Joule-Lentz, its formula is as follows:

Q = kl²Rt, (1)

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

If the amount of heat is measured in calories, the currentin amperes, resistance in Ohms, and time in seconds, then k is numerically equal to 0.24. This means that the current in 1a secures in the conductor, which has a resistance of 1 Ohm, per second, the heat number, which is 0.24 kcal. Proceeding from this, the amount of heat in calories released in the conductor can be calculated by the formula:

Q = 0.24l²Rt.

In the system of SI units, the energy, the amount of heat andThe work is measured in units – joules. Therefore, the proportionality coefficient in the Joule-Lenz law is unity. In this system the Joule-Lenz formula has the form:

Q = l²Rt. (2)

The law of Joule-Lenz can be verified by experience. A current is passed through a wire spiral immersed in a liquid poured into the calorimeter. Then the amount of heat released in the calorimeter is counted. The resistance of the spiral is known in advance, the current is measured by an ammeter and the time by a stopwatch. Changing the current in the circuit and using different spirals, one can verify the Joule-Lenz law.

Based on Ohm’s law

I = U / R,

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

Q = (U² / R) t.

It is convenient to use the formula Q = l2Rt for the calculationthe amount of heat released in a series connection, because in this case the electric current in all conductors is the same. Therefore, when a number of conductors are connected in series, each of them will be given a quantity 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, since its resistivity is greatest, it is stronger and warms up.

If the conductors are connected in parallel, thenThe electric current in them will be different, and the voltage at the ends of such conductors is the same. Calculation of the amount of heat that will be released at such a connection, it is better to conduct, using the formula Q = (U² / R) t.

This formula shows that, in a parallel connection, each conductor will allocate as much heat as will be inversely proportional to its conductivity.

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

Taking as a basis the law of Joule-Lenz, producecalculation of various electric lighting installations, heating and heating electrical appliances. Also, the conversion of the energy of electricity into heat is widely used.

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