Internal resistance of the current source. Resistance - formula

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Internal resistance of the current source. Resistance - formula
Internal resistance of the current source. Resistance - formula
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Electric current in the conductor arises under the influence of an electric field, forcing free charged particles to come into directed motion. Creating a particle current is a serious problem. To build such a device that will maintain the potential difference of the field for a long time in one state is a task that mankind could solve only by the end of the 18th century.

current resistance formula
current resistance formula

First attempts

The first attempts to "accumulate electricity" for its further research and use were made in Holland. The German Ewald Jürgen von Kleist and the Dutchman Peter van Muschenbruk, who conducted their research in the town of Leiden, created the world's first capacitor, later called the "Leyden jar".

The accumulation of electric charge has already taken place under the action of mechanical friction. It was possible to use a discharge through a conductor for a certain, rather short, period of time.

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

Unfortunately, discharge (electrical current generated by a capacitor)lasted so short that it could not create a direct current. In addition, the voltage given by the capacitor is gradually reduced, which leaves no opportunity to receive a continuous current.

I should have looked for another way.

First source

current source internal resistance
current source internal resistance

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

However, another Italian, Alessandro Volta, refuted Galvani's conclusions. Interested in the possibility of obtaining electricity from animal organisms, he conducted a series of experiments with frogs. But his conclusion turned out to be the complete opposite of the 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 contract, indicating a potential difference. The source of the electric field was the contact of dissimilar metals. The farther apart they are in a series of chemical elements, the greater the effect.

Plates of dissimilar metals, laid with paper discs soaked in an electrolyte solution, created the necessary potential difference for a long time. And let it be low (1.1 V), but the electric current could be investigated for a long time. The main thing is that the voltage remained unchanged for just as long.

current resistance
current resistance

What's going on

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

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

In the simplest galvanic cells, oxidative reactions occur on one electrode, and reduction reactions occur on the other. Electrons come to the electrodes from the outside of the circuit. The electrolyte is the current conductor of the ions inside the source. The strength of resistance governs the duration of the process.

Copper-zinc element

The principle of operation of galvanic cells is interesting to consider using the example of a copper-zinc galvanic cell, the action of which is due to the energy of zinc and copper sulfate. In this source, a copper plate is placed in a copper sulfate solution, and a zinc electrode is immersed in a zinc sulfate solution. Solutions are separated by a porous spacer 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 the liquid, zinc atoms, having turned into ions, appear in the solution. Electrons are released on the electrode, which can take part in the generation of current.

Getting to the copper electrode, the electrons take part in the reduction reaction. Fromsolution, copper ions enter the surface layer, in the process of reduction they turn into copper atoms, depositing on the copper plate.

To summarize what is happening: the process of operation of a galvanic cell is accompanied by the transfer of electrons from the reducing agent to the oxidizing agent along the outer part of the circuit. Reactions take place on both electrodes. An ion current flows inside the source.

Difficulty of use

In principle, any of the possible redox reactions can be used in batteries. But there are not so many substances capable of working in technically valuable elements. Moreover, many reactions require 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 direct current.

resistance force
resistance force

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

The internal resistance of a current source is important.

A little about resistance

The use of electric current, no doubt, brought scientific and technological progress to a new level, gave him a giant boost. But the force of resistance to the flow of current gets in the way of such development.

definecurrent source internal resistance
definecurrent source internal resistance

On the one hand, electric current has invaluable properties used in everyday life and technology, on the other hand, there is significant opposition. Physics, as a science of nature, tries to strike a balance, to bring these circumstances into line.

Current resistance arises due to 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 resistance of the external part of the circuit are of a slightly different nature, but the same in these processes is the work done to move the charge.

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

Work current

In accordance with the Joule-Lenz law, the amount of heat released in conductors is proportional to the resistance. If we designate the amount of heat as Qint., the strength of the current I, the time of its flow t, then we get:

Qint=I2 · r t,

where r is the internal resistance of the sourcecurrent.

In the entire circuit, including both its internal and external parts, the total amount of heat will be released, the formula of which is:

Qfull=I2 · r t + I 2 R t=I2 (r +R) t,

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

Ohm's law for a complete circuit

Take into account that the main work is done by external forces inside the current source. Its value is equal to the product of the charge carried by the field and the electromotive force of the source:

q E=I2 (r + R) t.

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

E=I (r + R)

According to cause-and-effect relationships, Ohm's law has the form:

I=E: (r + R)

The current in a closed circuit is directly proportional to the EMF of the current source and inversely proportional to the total (total) resistance of the circuit.

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

Source discharge capacity

Discharge capacity can also be attributed to the main characteristics of the sources. The maximum amount of electricity that can be obtained when operating under certain conditions depends on the strength of the discharge current.

voltage resistance current
voltage resistance current

In the ideal case, when certain approximations are made, the discharge capacity can be considered constant.

KFor 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 100mA, then it works for 5 hours.

Methods for charging batteries

Exploitation of batteries leads to their discharge. Restoration of batteries, charging of small cells is carried out using a current whose strength value does not exceed one tenth of the source capacity.

resistance formula
resistance formula

The following charging methods are available:

  • using constant current for a specified time (about 16 hours current 0.1 battery capacity);
  • charging with a step-down current to a predetermined potential difference value;
  • use of unbalanced currents;
  • successive application of short pulses of charging and discharging, in 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 on 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. To do this, you need to know its EMF, the value of the resistance of the rheostat.

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

I=U: R,

where I is the current strength in the outer part of the circuit, measured with an ammeter; U - voltage on the externalresistance.

To improve the accuracy, measurements are taken at least 5 times. What is it for? The voltage, resistance, current (or rather, current strength) measured during the experiment are used below.

To determine the EMF of the current source, we use the fact that the voltage at its terminals with the key open is almost equal to the EMF.

Let's assemble a circuit from a battery, a rheostat, an ammeter, a key connected in series. We connect a voltmeter to the terminals of the current source. Having opened the key, we take its readings.

Internal resistance, the formula of which is obtained from Ohm's law for a complete circuit, 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 one.

The practical function of rechargeable batteries and batteries is widely used. The indisputable environmental safety of electric motors is beyond doubt, but creating a capacious, ergonomic battery is a problem of modern physics. Its solution will lead to a new round in the development of automotive technology.

Small, lightweight, high-capacity batteries are also essential in mobile electronic devices. The amount of energy used in them is directly related to the performance of the devices.

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