How to give definition to the law of Ohm for a complete chain

How to give definition to the law of Ohm for a complete chain

The law of Ohm for a complete chain considers resistance to electric current in its source. For understanding of the full law of Ohm himself needs to understand an essence of internal resistance of a source of current and its electromotive force.

The formulation of Ohm's law for subcircuit, as they say, is transparent. That is, it is clear without additional explanations: current of the site's I chain, R having electrical resistance, is equal to tension on it of U divided into the size of its resistance: I = U/R (1)

But here the wording of the law of Ohm for a complete chain: current is equal in a chain to electromotive force (e. of page) its source, external chain of R, divided into the sum of resistance, and internal resistance of a source of current of r:

I = E/(R + r) (2), quite often causes difficulties in understanding. It is not clear that it e. of page, than it differs from tension from where the internal resistance of a source of current undertakes and that it means. Explanations are necessary because the law of Ohm for a complete chain ("full Ohm", on a professional slang of electricians) makes deep physical meaning.

Meaning of "full Ohm"

The law of Ohm for a complete chain is inseparably linked with the most fundamental law of the nature: law of energy conservation. If the source of current had no internal resistance, then it in an external chain, that is to consumers of the electric power, it could give as much as big current and, respectively, as much as big power.E. of page is the difference of electric potentials on source terminals without loading. It is similar to a water pressure in the lifted tank. While there is no expense (current), water level stands still. Opened the crane – level without pumping falls. In the giving pipe water tests resistance to its current, as well as electric charges in a wire. If there is no loading, terminals are opened, then E and U coincide in size. At short circuit of a chain, for example, inclusion of a bulb, a part e. of page creates tension on it and performs useful work. Other part of energy of a source dissipates on its internal resistance, turns into heat and dissipates. These are losses. If resistance of the consumer is shown less internal resistance of a source of current, then on it the most part of power is allocated. At the same time share e. with for an external chain falls, but on its internal resistance the main part of energy of current is emitted and lost in vain. The nature does not allow to take from it more, than it can give. In it the meaning of conservation laws is also concluded. Intuitively, but the inhabitants of old "Khruschev's" apartments who put at themselves conditioners, but stinted conducting replacement well understand the meaning of internal resistance. The counter "winds as mad", the socket, a wall is heated where under plaster there takes place old aluminum conducting, and the conditioner hardly cools.

R nature

"The full Ohm" is badly understood most often because the internal resistance of a source in most cases has not the electric nature. Let's explain on the example of the ordinary salt battery. More precisely, an element as the electric battery is formed from several elements. An example of the ready battery – "Krone". It consists of 7 elements in the general case. The scheme of a chain from one element and a bulb is shown in the drawing. How does the battery develop current? Let's address the left position of the drawing in the beginning. With the liquid (electrolyte) installing electrical equipment 1 are placed in a vessel a coal core 2 in a cover from compounds of manganese 3. The core with a manganese cover is made by a positive electrode, or the anode. The coal core in this case works just as the slip ring. A negative electrode (cathode) 4 – metal zinc. In selling batteries electrolyte gel, but not liquid. The cathode – a zinc glass in which the anode is placed and is poured electrolyte. The secret of the battery is that own, the nature the set, electric potential of manganese is less, than at zinc. Therefore the cathode attracts to itself electrons, and in exchange pushes away from itself to the anode positive ions of zinc. Because of it the cathode is gradually spent. All know that if not to replace the sat-down battery, it will begin to flow: electrolyte will flow out through the corroded zinc glass. Owing to the movement of charges in electrolyte on a coal core with manganese the positive charge, and on zinc – negative collects. Therefore they are also called the anode and the cathode respectively though from within the battery look on the contrary. The difference of charges will also create e. of page of the battery. The movement of charges in electrolyte will stop when size e. of page will become the equal difference of own potentials of materials of electrodes; forces of an attraction will be equal to pushing away forces. Now we will close a chain: let's connect to the battery a bulb. Charges through it will come back home everyone to themselves, having made useful business – the bulb will light up. And in the battery the electrons with ions "run" again as charges left poles outside, and attraction/pushing away appeared again. In effect, the battery gives current and the bulb shines, due to consumption of zinc which at the same time turns into other chemical compounds. Again to extract from them pure zinc, it is necessary to spend, on the law of energy conservation, it, but not electric there is, so much, how many the battery gave to a bulb, yet did not begin to flow. And now, at last, we will be able to understand r nature. In the battery – this resistance to the movement first of all big and heavy ions in electrolyte. Electrons without ions will not move as there will be no force of their attraction. In industrial electric generators the emergence of r is caused not only the electrical resistance of their windings. External causes also contribute to its size. For example, in hydroelectric power station (hydroelectric power station) the turbine efficiency, resistance to water current in a conduit influence loss its value, in mechanical transfer from the turbine to the generator. Even water temperature behind a dam and its zailennost.

Example of calculation for the law of Ohm for a complete chain

To understand to itself it is final that "the full Ohm" in practice means, we will calculate the chain described above from the battery and a bulb. For this purpose it is necessary to address the right part of the drawing where it is presented in more "electrified" form. Here already clearly it is visible that even in the simplest chain there are actually two loops of current: one, useful, through R bulb resistance, and another, "parasitic", through the internal resistance of a source of r. There is an important point: the parasitic chain is never as electrolyte has own broken off. If nothing is connected to the battery, in it small current of a self-discharge all the same flows. Therefore to reserve batteries for the future there is no sense: will just begin to flow. It is possible to store about half a year in the fridge under the freezer. Before use it is necessary to allow to get warm up to the external temperature. But we will return to calculations. Internal resistance of the cheap salt battery is about 2 Ohms. AA. of page of couple zinc-manganese – 1.5 V. Poprobuyem to connect to the battery a bulb on 1.5 V and 200 mA, that is 0.2 A. We will determine its resistance from Ohm's law for subcircuit: R = U/I (3) Is substituted: R = 1.5 B/0.2 And = 7.5 Ohms. Full resistance of a chain of R+r then will be 2 + 7.5 = 9.5 Ohms. Let's divide into it e. of page, and on a formula (2) we will receive current in a chain: 1.5 B/9.5 Ohms = 0.158 A or 158 mA. Tension on a bulb at the same time will be U = IR = 0.158 A*7.5 Ohms = 1.185 V, and in the battery in vain there will be 1.5 V - 1.185 V = 0.315 V. Lampochk burns obviously with "nedokaly".

Not everything is so bad

The law of Ohm for a complete chain not only shows where energy losses are concealed. He also prompts ways of fight against them. For example, in the case described above it is not absolutely correct to reduce battery r: it will turn out very expensive and with a high self-discharge. And here if to make a hair of a bulb thinner and to fill its cylinder not with nitrogen, but inert gas xenon, then it will shine also brightly at three times smaller current. Then almost all e. of page of the battery will be attached to a bulb and losses will be small.

Author: «MirrorInfo» Dream Team