Constant electric current. EMF of the current source and internal resistance of the current source. Internal resistance of the current source. Resistance - formula

In the age of electricity, there is probably no person who does not know about the existence of electric current. But few people remember more from a school physics course than the names of quantities: current, voltage, resistance, Ohm’s law. And only very few remember what the meaning of these words is.

In this article, we will discuss how electric current occurs, how it is transmitted through a circuit, and how to use this quantity in calculations. But before moving on to the main part, let us turn to the history of the discovery of electric current and its sources, as well as the definition of what electromotive force is.

Story

Electricity as a source of energy has been known since ancient times, because nature itself generates it in huge volumes. A striking example is lightning or an electric ramp. Despite such closeness to humans, it was possible to curb this energy only in the middle of the seventeenth century: Otto von Guericke, the burgomaster of Magdeburg, created a machine that allowed the generation of an electrostatic charge. In the mid-eighteenth century, Peter von Muschenbroek, a scientist from Holland, created the world's first electric capacitor, named the Leyden jar in honor of the university where he worked.

Perhaps, the era of real discoveries dedicated to electricity begins with the work of Luigi Galvani and Alessandro Volta, who studied, respectively, electrical currents in muscles and the emergence of current in so-called galvanic cells. Further research opened our eyes to the connection between electricity and magnetism, as well as to several very useful phenomena (such as electromagnetic induction), without which it is impossible to imagine our lives today.

But we will not delve into magnetic phenomena and will focus only on electrical ones. So, let's look at how electricity arises in galvanic cells and what it is all about.

What is a galvanic cell?

We can say that it produces electricity due to chemical reactions occurring between its components. The simplest galvanic cell was invented by Alessandro Volta and named after him as a voltaic column. It consists of several layers, alternating with each other: a copper plate, a conductive gasket (in the home version of the design, cotton wool moistened with salt water is used) and a zinc plate.

What reactions take place in it?

Let's take a closer look at the processes that allow us to generate electricity using a galvanic cell. There are only two such transformations: oxidation and reduction. When one element, the reducing agent, is oxidized, it gives up electrons to another element, the oxidizing agent. The oxidizing agent, in turn, is reduced by accepting electrons. In this way, charged particles move from one plate to another, and this, as is known, is called electric current.

And now let’s move smoothly to the main topic of this article - the EMF of the current source. And first, let's look at what this electromotive force (EMF) is.

What is EMF?

This quantity can be represented as the work of forces (namely “work”) performed when a charge moves along a closed electrical circuit. Very often they also make clarifications that the charge must necessarily be positive and unit. And this is an essential addition, since only under these conditions can electromotive force be considered an accurate measurable quantity. By the way, it is measured in the same units as voltage: volts (V).

EMF of current source

As you know, each battery or battery has its own resistance value that they are capable of delivering. This value, the emf of the current source, shows how much work is done by external forces to move charge along the circuit in which the battery or accumulator is connected.

It is also worth clarifying what type of current the source produces: direct, alternating or pulsed. Galvanic cells, including accumulators and batteries, always produce only constant electric current. The EMF of the current source in this case will be equal in magnitude to the output voltage at the contacts of the source.

Now it’s time to figure out why such a quantity as EMF is needed in general, how to use it when calculating other quantities electrical circuit.

EMF formula

We have already found out that the EMF of the current source is equal to the work of external forces to move the charge. For greater clarity, we decided to write down the formula for this quantity: E=A external forces /q, where A is work, and q is the charge on which work was done. Please note that the total charge is taken, not the unit charge. This is done because we consider the work done by forces to move all charges in a conductor. And this work to charge ratio will always be constant for this source, since no matter how many charged particles you take, the specific amount of work for each of them will be the same.

As you can see, the formula for electromotive force is not so complicated and consists of only two quantities. It's time to move on to one of the main questions arising from this article.

Why is EMF needed?

It has already been said that EMF and voltage are actually the same quantities. If we know the values of the EMF and the internal resistance of the current source, then it will not be difficult to substitute them into Ohm’s law for a complete circuit, which looks like this: I=e/(R+r), where I is the current strength, e is the EMF, R is circuit resistance, r - internal resistance of the current source. From here we can find two characteristics of the chain: I and R. It should be noted that all these arguments and formulas are valid only for the chain DC. In the case of formula variables will be completely different, since it obeys its own oscillatory laws.

But it still remains unclear what application the EMF of a current source has. In a circuit, as a rule, there are a lot of elements that perform their function. In any phone there is a board, which is also nothing more than an electrical circuit. And each such circuit requires a current source to operate. And it is very important that its EMF matches the parameters for all elements of the circuit. Otherwise, the circuit will either stop working or burn out due to high voltage inside her.

Conclusion

We think this article was useful for many. After all, in modern world It is very important to know as much as possible about what surrounds us. Including essential knowledge about the nature of electric current and its behavior inside circuits. And if you think that such a thing as an electrical circuit is used only in laboratories and you are far from it, then you are very mistaken: all devices that consume electricity actually consist of circuits. And each of them has its own current source, which creates an EMF.

Let's try to solve this problem on specific example. The electromotive force of the power source is 4.5 V. A load was connected to it, and a current equal to 0.26 A flowed through it. The voltage then became equal to 3.7 V. First of all, let’s imagine that there is a hidden series circuit from ideal source voltage of 4.5 V, the internal resistance of which is zero, as well as a resistor, the value of which needs to be found. It is clear that in reality this is not the case, but for calculations the analogy is quite suitable.

Step 2

Remember that the letter U only denotes voltage under load. To designate the electromotive force, another letter is reserved - E. It is impossible to measure it absolutely accurately, because you will need a voltmeter with infinite input resistance. Even with an electrostatic voltmeter (electrometer), it is huge, but not infinite. But it’s one thing to be absolutely accurate, and another to have an accuracy acceptable in practice. The second is quite feasible: it is only necessary that the internal resistance of the source be negligible compared to the internal resistance of the voltmeter. In the meantime, let's calculate the difference between the EMF of the source and its voltage under a load consuming a current of 260 mA. E-U = 4.5-3.7 = 0.8. This will be the voltage drop across that “virtual resistor”.

Step 3

Well, then everything is simple, because the classical Ohm’s law comes into play. We remember that the current through the load and the “virtual resistor” is the same, because they are connected in series. The voltage drop across the latter (0.8 V) is divided by the current (0.26 A) and we get 3.08 Ohms. Here is the answer! You can also calculate how much power is dissipated at the load and how much is useless at the source. Dissipation at load: 3.7*0.26=0.962 W. At the source: 0.8*0.26=0.208 W. Calculate the percentage ratio between them yourself. But this is not the only type of problem to find the internal resistance of a source. There are also those in which the load resistance is indicated instead of the current strength, and the rest of the initial data is the same. Then you need to do one more calculation first. The voltage under load (not EMF!) given in the condition is divided by the load resistance. And you get the current strength in the circuit. After which, as physicists say, “the problem is reduced to the previous one”! Try to create such a problem and solve it.

Electric current in a conductor occurs under the influence electric field, causing free charged particles to come into directed motion. Generating particle current is a serious problem. Build a device that will maintain the field potential difference long time in one state - a task whose solution turned out to be within the power of humanity only towards the end of the 18th century.

First attempts

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

Accumulation electric charge has already passed under the influence of mechanical friction. It was possible to use a discharge through a conductor for a certain, fairly short 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 created by the capacitor) lasted so short that it could not be created. In addition, the voltage supplied by the capacitor gradually decreases, which leaves no possibility of receiving long-term current.

It was necessary to look for another way.

First source

The Italian Galvani's experiments on "animal electricity" 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 grid, he drew attention to the characteristic reaction of the nerve endings.

However, Galvani's conclusions were refuted by another Italian, Alessandro Volta. 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 previous hypotheses.

Volta noticed that a living organism is only an indicator of an electrical discharge. When current passes, the muscles of the paws contract, indicating a potential difference. The source of the electric field turned out to be the contact of dissimilar metals. The farther apart they are in a row chemical elements, the greater the effect.

Plates of dissimilar metals, lined with paper disks soaked in an electrolyte solution, created the necessary potential difference for a long time. And even though it was low (1.1 V), the electric current could be studied for a long time. The main thing is that the tension remained unchanged for just as long.

What's happening

Why does this effect occur in sources called “galvanic cells”?

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

In the simplest galvanic cells, oxidation reactions occur on one electrode, reduction reactions on the other. Electrons come to the electrodes from the outer part of the circuit. The electrolyte is a conductor of ion current inside the source. The force of resistance controls the duration of the process.

Copper-zinc element

It is interesting to consider the principle of operation of galvanic cells using the example of a copper-zinc galvanic cell, the action of which comes from the energy of zinc and copper sulfate. In this source, a copper plate is placed in a solution and a zinc electrode is immersed in a zinc sulfate solution. The solutions are separated by a porous spacer to avoid mixing, but they must come into contact.

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

Once on the copper electrode, electrons take part in the reduction reaction. Copper ions come from the solution to the surface layer; during the reduction process, they turn into copper atoms, depositing on the copper plate.

Let's summarize what is happening: the process of operation of a galvanic cell is accompanied by the transition of electrons from the reducing agent to the oxidizing agent along the external part of the circuit. Reactions occur 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 body. Such design features simplify the structure and reduce the cost of batteries.

Any galvanic cell is capable of producing direct current.

The current resistance does not allow all the ions to simultaneously appear on the electrodes, so the element operates for a long time. The chemical reactions of ion formation sooner or later stop, and the element is discharged.

The current source is of great importance.

A little about resistance

The use of electric current, undoubtedly, brought scientific and technological progress to a new level and gave it a gigantic impetus. But the force of resistance to the flow of current gets in the way of such development.

On the one hand, electric current has invaluable properties used in everyday life and technology, on the other hand, there is significant resistance. Physics, as a science of nature, tries to establish a balance and 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 current source and the resistance of the external part of the circuit have 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 filling: 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 its length and decreases with increasing cross-sectional area. When solving the problem of how to reduce resistance, physics recommends using specialized materials.

Current work

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

Q inside. = I 2 r t,

where r is the internal resistance of the current source.

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

Q total = I 2 r t + I 2 R t = I 2 (r +R) t,

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

Ohm's law for a complete circuit

Let us take into account that the main work is performed by external forces inside the current source. Its value is equal to the product of the charge transferred by the field and the electromotive force of the source:

q · E = I 2 · (r + R) · t.

Understanding that the charge is equal to the product of the current strength and the time it flows, we have:

E = I (r + R).

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

I = E: (r + R).

IN closed circuit is directly proportional to the EMF of the current source and inversely proportional to the total (impact) resistance of the circuit.

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

Source discharge capacity

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

In the ideal case, when certain approximations are made, the discharge capacity 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, it works for 5 hours.

Methods for charging batteries

Using batteries will result in their discharge. charging of small-sized elements is carried out using a current whose strength does not exceed one tenth of the source capacity.

The following charging methods are available:

using constant current for a given time (about 16 hours with a current of 0.1 battery capacity);
charging with reduced current up to set value potential difference;
use of asymmetrical currents;
sequential application of short pulses of charging and discharging, in which the time of the first exceeds the time of the second.

Practical work

A task is proposed: determine the internal resistance of the current source and the emf.

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

Use will allow you to determine the internal resistance of the current source. To do this, you need to know its EMF and the value of the rheostat resistance.

The calculation formula for the current resistance in the external 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 external part of the circuit, measured with an ammeter; U is the voltage across the external resistance.

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

To determine the EMF of a current source, we take advantage of the fact that the voltage at its terminals when the switch is open is almost equal to the EMF.

Let's assemble a circuit of a battery, a rheostat, an ammeter, and 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 derived from Ohm's law for complete chain, we determine by mathematical calculations:

I = E: (r + R).
r = E: I - U: I.

Measurements show that the internal resistance is significantly less than the external one.

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

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

At the ends of the conductor, and therefore the current, the presence of external forces of a non-electrical nature is necessary, with the help of which the separation of electrical charges occurs.

By outside forces are any forces acting on electrically charged particles in a circuit, with the exception of electrostatic (i.e., Coulomb).

Third-party forces set in motion charged particles inside all current sources: in generators, power plants, galvanic cells, batteries, etc.

When a circuit is closed, an electric field is created in all conductors of the circuit. Inside the current source, charges move under the influence of external forces against Coulomb forces (electrons move from a positively charged electrode to a negative one), and throughout the rest of the circuit they are driven by an electric field (see figure above).

In current sources, during the process of separating charged particles, a transformation occurs different types energy into electricity. Based on the type of converted energy, the following types of electromotive force are distinguished:

- electrostatic- in an electrophore machine, in which mechanical energy is converted into electrical energy by friction;

- thermoelectric- in a thermoelement - the internal energy of the heated junction of two wires made of different metals is converted into electrical energy;

- photovoltaic- in a photocell. Here the conversion of light energy into electrical energy occurs: when certain substances are illuminated, for example, selenium, copper (I) oxide, silicon, a loss of negative electrical charge is observed;

- chemical- in galvanic cells, batteries and other sources in which chemical energy is converted into electrical energy.

Electromotive force (EMF)— characteristics of current sources. The concept of EMF was introduced by G. Ohm in 1827 for direct current circuits. In 1857, Kirchhoff defined EMF as the work of external forces during the transfer of a unit electric charge along a closed circuit:

ɛ = A st /q,

Where ɛ — EMF of the current source, A st- work of outside forces, q- amount of transferred charge.

Electromotive force is expressed in volts.

We can talk about electromotive force at any part of the circuit. This is the specific work of external forces (work to move a single charge) not throughout the entire circuit, but only in a given area.

Internal resistance of the current source.

Let there be a simple closed circuit consisting of a current source (for example, a galvanic cell, battery or generator) and a resistor with a resistance R. The current in a closed circuit is not interrupted anywhere, therefore, it also exists inside the current source. Any source represents some resistance to current. It's called internal resistance of the current source and is designated by the letter r.

In the generator r- this is the winding resistance, in a galvanic cell - the resistance of the electrolyte solution and electrodes.

Thus, the current source is characterized by the values of EMF and internal resistance, which determine its quality. For example, electrostatic machines have a very high EMF (up to tens of thousands of volts), but at the same time their internal resistance is enormous (up to hundreds of megohms). Therefore, they are unsuitable for generating high currents. Galvanic cells have an EMF of only approximately 1 V, but the internal resistance is also low (approximately 1 Ohm or less). This allows them to obtain currents measured in amperes.

Ohm's law for a complete circuit, the definition of which concerns the value of electric current in real circuits, depends on the current source and the load resistance. This law also has another name - Ohm's law for closed circuits. The operating principle of this law is as follows.

As the most simple example, electric lamp, which is a consumer of electric current, together with the current source is nothing more than a closed one. This electrical circuit is clearly shown in the figure.

An electric current passing through a light bulb also passes through the current source itself. Thus, while passing through the circuit, the current will experience the resistance of not only the conductor, but also the resistance, directly, of the current source itself. In the source, resistance is created by the electrolyte located between the plates and the boundary layers of the plates and electrolyte. It follows that in a closed circuit, its total resistance will consist of the sum of the resistances of the light bulb and the current source.

External and internal resistance

Load resistance, in in this case of a light bulb connected to a current source is called external resistance. The direct resistance of the current source is called internal resistance. For a more visual representation of the process, all values must be designated conventionally. I - , R - external resistance, r - internal resistance. When current flows through an electrical circuit, in order to maintain it, there must be a potential difference between the ends of the external circuit, which has the value IxR. However, current flow is also observed in the internal circuit. This means that in order to maintain electric current in the internal circuit, a potential difference at the ends of the resistance r is also necessary. The value of this potential difference is equal to Iхr.

Battery electromotive force

The battery must have next value electromotive force capable of maintaining the required current in the circuit: E=IxR+Ixr. From the formula it can be seen that the electromotive force of the battery is the sum of external and internal. The current value must be taken out of brackets: E=I(r+R). Otherwise, you can imagine: I=E/(r+R) . The last two formulas express Ohm's law for a complete circuit, the definition of which is as follows: in a closed circuit, the current strength is directly proportional to the electromotive force and inversely proportional to the sum of the resistances of this circuit.