Internal resistance of the current source. Resistance is the formula

The electric current in the conductor arises under the influence of an electric field, which forces the free charged particles to come into directional motion. Creating a particle current is a serious problem. To build such a device, which will maintain the potential difference of the field for a long time in one state - a task whose solution was under the power of mankind only towards the end of the 18th century.

First attempts

The first attempts to "save electricity" for further research and use were made in Holland. German Ewald Jurgen von Kleist and Dutchman Peter van Mushenbrook, who conducted their research in the town of Leiden, created the world's first condenser, later called a "Leiden jar."

The accumulation of electric charge was already under the influence of mechanical friction. The discharge through the conductor could be used for a short enough period of time.

The victory of the human mind over such an ephemeral substance as electricity turned out to be revolutionary.

Unfortunately, the discharge (electric current generated by the capacitor) lasted so short that it could not create a constant current . In addition, the voltage given by the capacitor gradually decreases, which does not leave the possibility of obtaining a continuous current.

It was necessary to look for another way.

The first source

The experiments of the Italian Galvani on the study of "animal electricity" were an original attempt to find a natural source of current in nature. Hanging the legs of the prepared frogs on the metal hooks of the iron grid, he drew attention to the characteristic reaction of the nerve endings.

However, Galvani's conclusions were denied by another Italian - Alessandro Volta. Interested in the possibility of receiving electricity from animal organisms, he conducted a series of experiments with frogs. But his conclusion was the complete opposite of previous hypotheses.

Volta drew attention to the fact that a living organism is only an indicator of an electrical discharge. When the current passes, the muscles of the legs are shortened, indicating the potential difference. The source of the electric field was the contact of dissimilar metals. The further apart they are in a series of chemical elements, the more significant the effect.

Plates of dissimilar metals, padded with paper discs impregnated with electrolyte solution, created a long time the necessary difference in potentials. And let it was low (1.1 V), but the electric current could be investigated for a long time. The main thing is that the tension remained unchanged for as long.

What's happening

Why do the sources called "galvanic cells" cause such an effect?

Two metal electrodes placed in a dielectric play different roles. One supplies electrons, the other takes them. The process of oxidation-reduction reaction leads to the appearance of an excess of electrons on one electrode, which is called a negative pole, and a defect on the second, which we denote as the positive pole of the source.

In the simplest galvanic cells, oxidative reactions occur on one electrode, reducing reactions on the other. Electrons come to the electrodes from the outside of the circuit. Electrolyte is a conductor of the ion current inside the source. The strength of resistance guides the duration of the process.

Copper-zinc element

The principle of the action of galvanic cells is interesting to consider on the example of a copper-zinc galvanic cell, whose action is taken into account the energy of zinc and copper sulfate. In this source, a copper plate is placed in a solution of copper sulfate, and the zinc electrode is immersed in a solution of zinc sulfate. The solutions are separated by a porous gasket to prevent mixing, but must be in contact.

If the circuit is closed, the surface layer of zinc is oxidized. In the process of interaction with a liquid, zinc atoms, having turned into ions, appear in solution. Electrons are liberated on the electrode, which can take part in the formation of current.

Getting on a copper electrode, electrons take part in the recovery reaction. Copper ions come from the solution to the surface layer, they are converted into copper atoms during the reduction process, depositing on a copper plate.

Summarize what is happening: the process of operation of the galvanic cell is accompanied by the transition of the electrons of the reducing agent to the oxidizer along the outer part of the chain. Reactions go on both electrodes. Inside the source, ion current flows.

Difficulties of use

In principle, any of the possible oxidation-reduction reactions can be used in batteries. But there are not so many substances that can work in valuable technical elements. Moreover, many reactions require the cost of expensive substances.

Modern batteries have a simpler structure. Two electrodes placed in one electrolyte fill the vessel - the battery case. Such design features simplify the structure and reduce the cost of batteries.

Any galvanic cell is capable of producing a constant current.

The current resistance does not allow all ions to be on the electrodes at the same time, so the element works long enough. Chemical reactions of the formation of ions sooner or later cease, the element is discharged.

The internal resistance of the current source is of great importance.

A little bit about resistance

The use of electric current, undoubtedly, brought scientific and technical progress to a new level, gave him a tremendous push. But the strength of resistance to the flow of current becomes in the way of such development.

On the one hand, the electric current has invaluable properties used in everyday life and technology, on the other - there is considerable opposition. Physics as a science of nature is trying to establish a balance, to reconcile these circumstances.

The resistance of the current arises from the interaction of electrically charged particles with the substance through which they move. It is impossible to exclude this process under normal temperature conditions.

Resistance

The internal resistance of the current source and the counteraction of the outer part of the circuit have a somewhat different nature, but the same in these processes is the accomplishment of work on charge transfer.

The work itself depends only on the properties of the source and its filling: the qualities of the electrodes and electrolyte, as well as for the outer parts of the circuit whose resistance depends on the geometric parameters and chemical characteristics of the material. For example, the resistance of a metal wire increases with increasing length and decreases with the expansion of the cross-sectional area. When solving the problem of how to reduce resistance, physics recommends the use of specialized materials.

Current Operation

According to the Joule-Lenz law, the amount of heat in the conductors is proportional to the resistance. If the quantity of heat is Q _internal. , The current I, the time it flows, t, we get:

• Q _int. = I ^{2 ·} R · t,

Where r is the internal resistance of the current source.

In the whole chain, which includes both the internal and external parts of it, the total amount of heat will be released, the formula of which has the form:

• Q _total = I ^{2 ·} R · t + I ^{2 ·} R · t = I ^{2 ·} (R + R) t,

It is known how the resistance in physics is denoted: the external circuit (all elements except the source) has resistance R.

Ohm's law for the complete chain

We will take into account that the main work is done by outside forces inside the current source. Its magnitude is equal to the product of the charge carried by the field and the electromotive force of the source:

• Q · E = I ² · (R + R) t.

Realizing that the charge is equal to the product of the current strength at the time of its flow, we have:

• E = I · (r + R).

In accordance with the cause-effect relations, Ohm's law has the form:

• I = E: (r + R).

The current in the closed circuit is directly proportional to the emf of the current source and is inversely proportional to the total impedance of the circuit.

Based on this pattern, it is possible to determine the internal resistance of the current source.

Discharge capacity of the source

The main characteristics of the sources include the discharge capacity. The maximum amount of electricity received during operation under certain conditions depends on the strength of the discharge current.

In the ideal case, when certain approximations are performed, the discharge capacitance can be considered constant.

For example, a standard battery with a potential difference of 1.5 V has a discharge capacity of 0.5 Ah. If the discharge current is 100 mA, then it works for 5 hours.

Methods of charging batteries

Operation of the batteries leads to their discharge. Restoration of accumulators, charging of small-sized elements is carried out by means of a current, the force value of which does not exceed one tenth of the source's capacity.

The following charging methods are available:

• The use of an unchanging current for a given time (about 16 hours with a current of 0.1 of the battery capacity);
• Charging with a down-current to a predetermined value of the potential difference;
• Use of unbalanced currents;
• Consecutive application of short charge and discharge pulses, at which the time of the first exceeds the time of the second.

Practical work

The task is proposed: to determine the internal resistance of the current source and EMF.

To perform it, you need to stock up a current source, an ammeter, a voltmeter, a slider rheostat, a key, a set of conductors.

Using Ohm's law for a closed circuit will determine the internal resistance of the current source. For this it is necessary to know its EMF, the resistance value of the rheostat.

The calculated current resistance formula in the outer part of the circuit can be determined from the Ohm's law for the chain section:

• I = U: R,

Where I is the current in the outer part of the circuit, measured by an ammeter; U is the voltage at the external resistance.

To increase the accuracy of the measurements are made at least 5 times. What is it for? Measured in the course of the experiment, the voltage, resistance, current (or rather, current) are used later.

To determine the EMF of the current source, let's use the fact that the voltage at its terminals with an open key is practically equal to the EMF.

We will assemble a chain of batteries, a rheostat, an ammeter, and a key in series. Connect the voltmeter to the terminals of the current source. Having opened the key, we take off his testimony.

The internal resistance, the formula of which is obtained from Ohm's law for the complete chain, is determined by mathematical calculations:

• I = E: (r + R).
• R = E: I - U: I.

Measurements show that the internal resistance is much less than the external resistance.

The practical function of batteries and batteries is widely used. Indisputable environmental safety of electric motors is not in doubt, but to create a capacious, ergonomic battery - the problem of modern physics. Its decision will lead to a new round of development of automotive equipment.

Small, lightweight, capacious batteries are also essential in mobile electronic devices. The stock of energy used in them is directly related to the operability of the devices.