What is the internal resistance of the source. Measuring emf and internal resistance of a current source
An electric current in a conductor arises under the influence of an electric field, causing free charged particles to move in a direction. Generating particle current is a serious problem. To build such a device that will maintain the field potential difference for a long time in one state is a task that was only possible for humanity to solve by 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”.
The accumulation of electric charge already took place 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 the series of chemical elements, the more significant 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, an amount of heat is released in conductors proportional to the resistance. If the amount of heat is denoted by Q int. , current strength I, its flow time t, then we get:
- Q internal = 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 a closed circuit, the EMF of the current source is directly proportional 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 drain them. 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 a decreasing current to a given 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 it for? The voltage, resistance, current (or rather, current strength) measured during the experiment are used further.
To determine the EMF of the 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.
The 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 significantly less than the external one.
The practical function of accumulators 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 of development of automotive technology.
Small, lightweight, high-capacity rechargeable batteries are also essential in mobile electronic devices. The amount of energy used in them is directly related to the performance of the devices.
Let's try to solve this problem using a 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, imagine that a serial circuit of an ideal voltage source 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.
8.5. Thermal effect of current
8.5.1. Current source power
Total power of the current source:
P total = P useful + P losses,
where P useful - useful power, P useful = I 2 R; P losses - power losses, P losses = I 2 r; I - current strength in the circuit; R - load resistance (external circuit); r is the internal resistance of the current source.
Total power can be calculated using one of three formulas:
P full = I 2 (R + r), P full = ℰ 2 R + r, P full = I ℰ,
where ℰ is the electromotive force (EMF) of the current source.
Net power- this is the power that is released in the external circuit, i.e. on a load (resistor), and can be used for some purposes.
Net power can be calculated using one of three formulas:
P useful = I 2 R, P useful = U 2 R, P useful = IU,
where I is the current strength in the circuit; U is the voltage at the terminals (clamps) of the current source; R - load resistance (external circuit).
Power loss is the power that is released in the current source, i.e. in the internal circuit, and is spent on processes taking place in the source itself; The power loss cannot be used for any other purposes.
Power loss is usually calculated using the formula
P losses = I 2 r,
where I is the current strength in the circuit; r is the internal resistance of the current source.
During a short circuit, the useful power goes to zero
P useful = 0,
since there is no load resistance in the event of a short circuit: R = 0.
The total power during a short circuit of the source coincides with the loss power and is calculated by the formula
P full = ℰ 2 r,
where ℰ is the electromotive force (EMF) of the current source; r is the internal resistance of the current source.
Useful power has maximum value in the case when the load resistance R is equal to the internal resistance r of the current source:
R = r.
Maximum useful power:
P useful max = 0.5 P full,
where Ptot is the total power of the current source;
P full = ℰ 2 / 2 r. Explicit formula for calculation maximum useful power
as follows:
P useful max = ℰ 2 4 r .
- To simplify the calculations, it is useful to remember two points: if with two load resistances R 1 and R 2 the same useful power is released in the circuit, then internal resistance
current source r is related to the indicated resistances by the formula
- r = R 1 R 2 ;
if the maximum useful power is released in the circuit, then the current strength I * in the circuit is half the strength of the short circuit current i:
I * = i 2 .
Example 15. When shorted to a resistance of 5.0 Ohms, a battery of cells produces a current of 2.0 A. The short circuit current of the battery is 12 A. Calculate the maximum useful power of the battery.
Solution . Let us analyze the condition of the problem.
1. When a battery is connected to a resistance R 1 = 5.0 Ohm, a current of strength I 1 = 2.0 A flows in the circuit, as shown in Fig. a, determined by Ohm’s law for the complete circuit:
I 1 = ℰ R 1 + r,
where ℰ - EMF of the current source; r is the internal resistance of the current source.
2. When the battery is short-circuited, a short-circuit current flows in the circuit, as shown in Fig. b. The short circuit current is determined by the formula
where i is the short circuit current, i = 12 A.
3. When a battery is connected to a resistance R 2 = r, a current of force I 2 flows in the circuit, as shown in Fig. in , determined by Ohm's law for the complete circuit:
I 2 = ℰ R 2 + r = ℰ 2 r;
in this case, the maximum useful power is released in the circuit:
P useful max = I 2 2 R 2 = I 2 2 r.
Thus, to calculate the maximum useful power, it is necessary to determine the internal resistance of the current source r and the current strength I 2.
In order to find the current strength I 2, we write the system of equations:
i = ℰ r, I 2 = ℰ 2 r)
and divide the equations:
i I 2 = 2 .
This implies:
I 2 = i 2 = 12 2 = 6.0 A.
I 1 = ℰ R 1 + r, i = ℰ r)
i = ℰ r, I 2 = ℰ 2 r)
I 1 i = r R 1 + r .
i I 2 = 2 .
r = I 1 R 1 i − I 1 = 2.0 ⋅ 5.0 12 − 2.0 = 1.0 Ohm.
Let's calculate the maximum useful power:
P useful max = I 2 2 r = 6.0 2 ⋅ 1.0 = 36 W.
Thus, the maximum usable power of the battery is 36 W.
EMF and voltage. Internal resistance of power supplies.
Educational program is such an educational program!
Ohm's law. That's what I mean.
We have already talked about Ohm's law. Let's talk again - from a slightly different angle. Without going into physical details and speaking in simple cat language, Ohm's law states: the greater the emf. (electromotive force), the greater the current, the greater the resistance, the less the current.
Translating this spell into the language of dry formulas we get:
I=E/R
where: I - current strength, E - E.M.F. - electromotive force R - resistance
Current is measured in amperes, emf. - in volts, and the resistance bears the proud name of Comrade Ohm. E.m.f. - this is a characteristic of an ideal generator, the internal resistance of which is considered to be infinitesimal. In real life, this rarely happens, so Ohm’s law for a series circuit (more familiar to us) comes into force:
I=U/R
where: U is the source voltage directly at its terminals.
Let's look at a simple example.
Let's imagine an ordinary battery in the form of an emf source. and a certain resistor connected in series with it, which will represent the internal resistance of the battery. Let's connect a voltmeter in parallel to the battery. Its input resistance is significantly greater than the internal resistance of the battery, but not infinitely large - that is, current will flow through it. The voltage value that the voltmeter shows will be less than the emf value. just by the amount of voltage drop across the internal imaginary resistor at a given current. But, nevertheless, it is precisely this value that is taken as the battery voltage.
The final stress formula will have the following form:
U(baht)=E-U(internal)
Since the internal resistance of all batteries increases over time, the voltage drop across the internal resistance also increases. In this case, the voltage at the battery terminals decreases. Meow!
Got it figured out!
What happens if you connect an ammeter to a battery instead of a voltmeter? Since the ammeter's internal resistance tends to zero, we will actually be measuring the current flowing through the internal resistance of the battery. Since the internal resistance of the source is very small, the current measured in this case can reach several amperes.
However, it should be noted that the internal resistance of the source is the same element of the circuit as all the others. Therefore, as the load current increases, the voltage drop across the internal resistance will also increase, which leads to a decrease in the voltage across the load. Or as we radio cats like to put it - a voltage drop.
In order for load changes to have as little effect on the output voltage of the source as possible, they try to minimize its internal resistance.
You can select the elements of a series circuit in such a way that at any of them you get a voltage that is reduced, compared to the original, by any number of times.
Let's say there is a simple electrical closed circuit that includes a current source, for example a generator, galvanic cell or battery, and a resistor with a resistance R. Since the current in the circuit is not interrupted anywhere, it flows inside the source.
In such a situation, we can say that any source has some internal resistance that prevents current flow. This internal resistance characterizes the current source and is designated by the letter r. For a battery, internal resistance is the resistance of the electrolyte solution and electrodes; for a generator, it is the resistance of the stator windings, etc.
Thus, the current source is characterized by both the magnitude of the EMF and the value of its own internal resistance r - both of these characteristics indicate the quality of the source.
Electrostatic high-voltage generators (like the Van de Graaff generator or the Wimshurst generator), for example, are distinguished by a huge EMF measured in millions of volts, while their internal resistance is measured in hundreds of megaohms, which is why they are unsuitable for producing large currents.
Galvanic elements (such as a battery), on the contrary, have an EMF of the order of 1 volt, although their internal resistance is of the order of fractions or, at most, tens of ohms, and therefore currents of units and tens of amperes can be obtained from galvanic elements.
This diagram shows a real source with an attached load. Its internal resistance, as well as the load resistance, are indicated here. According to, the current in this circuit will be equal to:
Since the section of the external circuit is homogeneous, the voltage across the load can be found from Ohm’s law:
Expressing the load resistance from the first equation and substituting its value into the second equation, we obtain the dependence of the load voltage on the current in a closed circuit:
In a closed loop, the EMF is equal to the sum of the voltage drops across the elements of the external circuit and the internal resistance of the source itself. The dependence of load voltage on load current is ideally linear.
The graph shows this, but experimental data on a real resistor (crosses near the graph) always differ from the ideal:
Experiments and logic show that at zero load current, the voltage on the external circuit is equal to the source emf, and at zero load voltage, the current in the circuit is equal to . This property of real circuits helps to experimentally find the emf and internal resistance of real sources.
Experimental determination of internal resistance
To experimentally determine these characteristics, plot the dependence of the voltage on the load on the current value, then extrapolate it to the intersection with the axes.
At the point of intersection of the graph with the voltage axis is the value of the source emf, and at the point of intersection with the current axis is the value of the short circuit current. As a result, the internal resistance is found by the formula:
The useful power developed by the source is released to the load. The dependence of this power on the load resistance is shown in the figure. This curve starts from the intersection of the coordinate axes at the zero point, then increases to the maximum power value, after which it drops to zero when the load resistance is equal to infinity.
To find the maximum load resistance at which the maximum power will theoretically develop at a given source, the derivative of the power formula with respect to R is taken and set equal to zero. Maximum power will develop when the external circuit resistance is equal to the internal resistance of the source:
This provision about the maximum power at R = r allows us to experimentally find the internal resistance of the source by plotting the dependence of the power released on the load on the value of the load resistance. Having found the real, and not theoretical, load resistance that provides maximum power, the real internal resistance of the power supply is determined.
The efficiency of a current source shows the ratio of the maximum power allocated to the load to the total power that is currently being developed
