• Formula for internal resistance of emf source. Constant electric current. EMF of the current source and internal resistance of the current source

    Purpose of the work: study the method of measuring EMF and internal resistance of a current source using an ammeter and voltmeter.

    Equipment: metal tablet, current source, ammeter, voltmeter, resistor, key, clamps, connecting wires.

    To measure the EMF and internal resistance of the current source, an electrical circuit is assembled, the diagram of which is shown in Figure 1.

    An ammeter, resistance and switch connected in series are connected to the current source. In addition, a voltmeter is also connected directly to the output jacks of the source.

    EMF is measured by reading a voltmeter with the switch open. This method of determining EMF is based on a corollary from Ohm’s law for complete chain, according to which, with an infinitely large resistance of the external circuit, the voltage at the source terminals is equal to its emf. (See the paragraph "Ohm's Law for a Complete Circuit" in the Physics 10 textbook).

    To determine the internal resistance of the source, key K is closed. In this case, two sections can be roughly distinguished in the circuit: external (the one that is connected to the source) and internal (the one that is located inside the current source). Since the source EMF is equal to the sum of the voltage drops in the internal and external sections of the circuit:

    ε = Ur+UR, ThatUr = ε -UR (1)

    According to Ohm's law for a section of the chain U r = I · r(2). Substituting equality (2) into (1) we get:

    I· r = ε - Ur , whence r = (ε - UR)/ J

    Therefore, to find out internal resistance current source, you must first determine its EMF, then close the switch and measure the voltage drop across the external resistance, as well as the current strength in it.

    Work progress

    1. Prepare a table to record the results of measurements and calculations:

    ε ,V

    U r , B

    i,a

    r , Ohm

      Draw a diagram in your notebook to measure the EMF and internal resistance of the source.

      After checking the circuit, assemble the electrical circuit. Unlock the key.

      Measure the magnitude of the source emf.

      Close the key and determine the readings of the ammeter and voltmeter.

      Calculate the internal resistance of the source.

    1. Determination of emf and internal resistance of a current source by graphical method

    Purpose of the work: study the measurements of emf, internal resistance and short circuit current of the current source, based on the analysis of the graph of the dependence of the voltage at the output of the source on the current in the circuit.

    Equipment: galvanic cell, ammeter, voltmeter, resistor R 1 , variable resistor, key, clamps, metal tablet, connecting wires.

    From Ohm’s law for a complete circuit it follows that the voltage at the output of the current source depends in direct proportion to the current in the circuit:

    since I =E/(R+r), then IR + Ir = E, but IR = U, whence U + Ir = E or U = E – Ir (1).

    If you plot the dependence of U on I, then from its points of intersection with the coordinate axes you can determine E, I K.Z. - current strength short circuit(the current that will flow in the source circuit when the external resistance R becomes zero).

    EMF is determined by the point of intersection of the graph with the voltage axis. This point on the graph corresponds to the state of the circuit in which there is no current in it and, therefore, U = E.

    The strength of the short circuit current is determined by the point of intersection of the graph with the current axis. In this case, the external resistance R = 0 and, therefore, the voltage at the source output U = 0.

    The internal resistance of the source is found by the tangent of the angle of inclination of the graph relative to the current axis. (Compare formula (1) with a mathematical function of the form Y = AX + B and remember the meaning of the coefficient for X).

    Work progress

      To record the measurement results, prepare a table:

    1. After the teacher checks the circuit, assemble the electrical circuit. Set the variable resistor slider to the position at which the resistance of the circuit connected to the current source is maximum.

      2. Determine the current in the circuit and the voltage at the source terminals at the maximum resistance value of the variable resistor. Enter the measurement data into the table.

      Repeat current and voltage measurements several times, decreasing the value each time variable resistance so that the voltage at the source terminals decreases by 0.1V. Stop measurements when the current in the circuit reaches 1A.

      Plot the points obtained in the experiment on a graph. Plot voltage along the vertical axis, and current along the horizontal axis. Draw a straight line through the points.

      Continue the graph until it intersects with the coordinate axes and determine the values ​​of E and I K.Z.

      Measure the EMF of the source by connecting a voltmeter to its terminals with the external circuit open. Compare the EMF values ​​obtained by the two methods and indicate the reason for the possible discrepancy in the results.

      Determine the internal resistance of the current source. To do this, calculate the tangent of the angle of inclination of the constructed graph to the current axis. Since the tangent of an angle in a right triangle is equal to the ratio of the opposite side to the adjacent side, this can practically be done by finding the ratio E / I K.Z

    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, 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, 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 outside forces by charge movement. 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 there's such a thing as 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.

    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 is 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 using 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 P is full - full power current source; P full = ℰ 2 / 2 r.

    Explicit formula for calculation maximum useful power looks like this:

    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 .

    It follows from this:

    I 2 = i 2 = 12 2 = 6.0 A.

    In order to find the internal resistance of the source r, we write the system of equations:

    I 1 = ℰ R 1 + r, i = ℰ r)

    and divide the equations:

    I 1 i = r R 1 + r .

    It follows from this:

    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.

    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 direct current circuits. In 1857, Kirchhoff defined EMF as the work of external forces when transferring a single 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.

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