How to calculate the internal resistance of a power supply. What is internal resistance

Ohm's law for complete chain, the definition of which concerns the meaning 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 is clear 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.

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 internal resistance 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.

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 some substances are illuminated, for example, selenium, copper (I) oxide, silicon, a loss of negative electric charge;

- 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 circuits DC. 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.

The need to introduce the term can be illustrated by the following example. Let's compare two chemical DC sources with the same voltage:

• Car lead-acid battery with a voltage of 12 volts and a capacity of 55 Ah
• Eight AA batteries connected in series. The total voltage of such a battery is also 12 volts, the capacity is much smaller - approximately 1 Ah

Despite the same voltage, these sources differ significantly when operating at the same load. So, car battery capable of giving load high current(the car engine starts from the battery, while the starter consumes a current of 250 amperes), but from a chain of batteries the starter does not rotate at all. The relatively small capacity of the batteries is not the reason: one amp-hour in the batteries would be enough to rotate the starter for 14 seconds (at a current of 250 amps).

Thus, for two-terminal networks containing sources (that is, voltage generators and current generators), it is necessary to talk specifically about internal resistance (or impedance). If the two-terminal network does not contain sources, then “ internal resistance" for such a two-terminal network means the same as Just"resistance".

Related terms

If in any system it is possible to distinguish an input and/or an output, then the following terms are often used:

Physical principles

Despite the fact that in the equivalent circuit the internal resistance is presented as one passive element (and active resistance, that is, a resistor is necessarily present in it), the internal resistance is not concentrated in any one element. Two-terminal network only externally behaves as if it had a concentrated internal impedance and a voltage generator. In reality, internal resistance is an external manifestation of a set of physical effects:

• If in a two-terminal network there is only energy source without any electrical circuit (for example, a galvanic cell), then the internal resistance is almost purely active (unless we are talking about very high frequencies), it is due to physical effects that do not allow the power supplied by this source to the load to exceed a certain limit. The simplest example of such an effect is the non-zero resistance of the conductors of an electrical circuit. But, as a rule, the greatest contribution to power limitation comes from the effects non-electric nature. So, for example, in power it can be limited by the contact area of ​​the substances participating in the reaction, in a hydroelectric power station generator - by limited water pressure, etc.
• In the case of a two-terminal network containing inside electrical diagram , the internal resistance is “dispersed” in the circuit elements (in addition to the mechanisms listed above in the source).

This also implies some features of internal resistance:

The influence of internal resistance on the properties of a two-terminal network

The effect of internal resistance is an integral property of any active two-terminal network. The main result of the presence of internal resistance is the limitation electrical power, which can be obtained in a load powered from this two-terminal network.

Let there be a two-terminal network, which can be described by the above equivalent circuit. A two-terminal network has two unknown parameters that need to be found:

• EMF voltage generator U
• Internal resistance r

In general, to determine two unknowns, it is necessary to make two measurements: measure the voltage at the output of the two-terminal network (that is, the potential difference U out = φ 2 − φ 1) at two different load currents. Then the unknown parameters can be found from the system of equations:

Where U out1 I 1, Uout2- output voltage at current I 2. By solving the system of equations, we find the unknown unknowns:

Typically, more than simple technique: the voltage is in the no-load mode and the current is in the short-circuit mode of the two-terminal network. In this case, system () is written as follows:

Where U oc- output voltage in mode idle speed(English) open circuit), that is, at zero load current; Isc- load current in mode short circuit(English) short circuit), that is, under a load with zero resistance. It is taken into account here that the output current in no-load mode and the output voltage in short-circuit mode are zero. From the last equations we immediately get:

Measurement

Concept measurement applicable to real device(but not to the diagram). Direct measurement with an ohmmeter is impossible, since it is impossible to connect the probes of the device to the internal resistance terminals. Therefore, indirect measurement is necessary, which is not fundamentally different from calculation - voltages across the load are also required at two different current values. However, it is not always possible to use the simplified formula (2), since not every real two-terminal network allows operation in short circuit mode.

Sometimes the following simple measurement method is used, which does not require calculations:

• Open circuit voltage is measured
• A variable resistor is connected as a load and its resistance is selected so that the voltage across it is half the open circuit voltage.

After the described procedures, the resistance of the load resistor must be measured with an ohmmeter - it will be equal to the internal resistance of the two-terminal network.

Whatever measurement method is used, one should be wary of overloading the two-terminal circuit with excessive current, that is, the current should not exceed the maximum permissible values for this two-terminal network.

Reactive internal resistance

If the equivalent circuit of a two-terminal network contains reactive elements - capacitors and/or inductors, then calculation Reactive internal resistance is carried out in the same way as active resistance, but instead of resistor resistances, the complex impedances of the elements included in the circuit are taken, and instead of voltages and currents, their complex amplitudes are taken, that is, the calculation is made by the complex amplitude method.

Measurement reactance has some special features because it is a complex-valued function rather than a scalar value:

• You can search for various parameters of a complex value: modulus, argument, only the real or imaginary part, as well as the entire complex number. Accordingly, the measurement technique will depend on what we want to obtain.
• Any of the listed parameters depends on frequency. Theoretically, to obtain by measurement full information about internal reactive resistance, it is necessary to remove addiction on frequency, that is, carry out measurements at everyone frequencies that the source of a given two-terminal network can generate.

Application

In most cases, we should not talk about application internal resistance, and about accounting his negative influence, since internal resistance is rather a negative effect. However, in some systems a nominal internal resistance is essential.

Simplification of equivalent circuits

The representation of a two-terminal network as a combination of a voltage generator and internal resistance is the simplest and most frequently used equivalent circuit of a two-terminal network.

Source-Load Matching

Matching the source and load is the choice of the ratio of the load resistance and the internal resistance of the source in order to achieve the specified properties of the resulting system (as a rule, they try to achieve maximum value any parameter for this source). Most commonly used following types approvals:

Current and power matching should be used with caution as there is a risk of overloading the source.

High Voltage Reduction

Sometimes it is artificially added to the source high resistance(it is added to the internal resistance of the source) in order to significantly reduce the voltage received from it. However, adding a resistor as additional resistance (the so-called quenching resistor) leads to useless power being allocated to it. To avoid wasting energy, AC systems use reactive damping impedances, most often capacitors. This is how capacitor power supplies are built. Similarly, using a capacitive tap from a high-voltage power line, you can obtain small voltages to power any autonomous devices.

Minimizing noise

When amplified weak signals The problem often arises of minimizing the noise introduced by the amplifier into the signal. For this purpose special low noise amplifiers, however, they are designed in such a way that the lowest noise figure is achieved only within a certain range of the output impedance of the signal source. For example, a low noise amplifier provides minimal noise only over the source output impedance range of 1 kΩ to 10 kΩ; if the signal source has a lower output impedance (for example, a microphone with an output impedance of 30 Ohms), then a step-up transformer should be used between the source and the amplifier, which will increase the output impedance (as well as the signal voltage) to the required value.

Restrictions

The concept of internal resistance is introduced through an equivalent circuit, so the same restrictions apply as for the applicability of equivalent circuits.

Examples

Internal resistance values ​​are relative: what is considered small, for example, for a galvanic cell, is very large for powerful battery. Below are examples of two-terminal networks and the values ​​of their internal resistance r. Trivial cases of two-terminal networks no sources are specifically stated.

Low internal resistance

High internal resistance

Negative internal resistance

There are two-terminal networks whose internal resistance has negative meaning. In normal active resistance, energy dissipation occurs, in reactive In resistance, energy is stored and then released back to the source. The peculiarity of negative resistance is that it itself is a source of energy. Therefore, negative resistance does not occur in its pure form; it can only be simulated electronic circuit, which necessarily contains a source of energy. Negative internal resistance can be achieved in circuits by using:

• elements with negative differential resistance, such as tunnel diodes

Systems with negative resistance are potentially unstable and therefore can be used to build self-oscillators.

See also

Links

Literature

• Zernov N.V., Karpov V.G. Theory radio circuits. - M. - L.: Energy, 1965. - 892 p.
• Jones M.H. Electronics - practical course. - M.: Tekhnosphere, 2006. - 512 p. ISBN 5-94836-086-5

Notes

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In the age of electricity, there is probably no such person who would 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, burgomaster from Magdeburg, created a machine that allows generating 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 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 the 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 it can produce. 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: constant, alternating or pulsed. Galvanic cells, including accumulators and batteries, always produce only direct 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, and how to use it when calculating other quantities of an 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 ratio of work to charge will always be constant for a given 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 circuit: I and R. It should be noted that all these arguments and formulas are valid only for a direct current circuit. 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.