Laboratory work No. 10. "Studying Ohm's law for a complete circuit - 3rd method." Purpose of the work: to study Ohm's law for a complete circuit. Objectives of the work:  determination of the EMF and internal resistance of a direct current source according to its current-voltage characteristic;  study of the graphical dependence of the power released in the external circuit on the magnitude of the electric current P  f I  . Equipment: DC source, ammeter, voltmeter, connecting wires, key, rheostat. Theory and method of doing work: Ohm's law I  Rr for a complete circuit I  Rr. Let us transform    I  R  r   I  R  I  r  U  I  r    U  I  r  U    I  r . expression Consequently, the dependence of the voltage at the output of a direct current source on the magnitude of the current (volt-ampere characteristic) has the form (see Fig. 1): fig. 1 Analysis of the current-voltage characteristic of a direct current source: 1) for point C: I=0, then U    0  r   2) for point D: U=0, then 0    I  r    I  r  I  3) tg  U   r I I short circuit   I short circuit r The expression for the power released in the external electrical circuit has the form P  I  U  I     I  r   I    I 2  r . Therefore, the graphical dependence P  f I  is a parabola, the branches of which are directed downward (see Fig. 2). rice. 2 Analysis of the graphical dependence P  f I  (see Fig. 3): fig. 3 1) for t.B: P=0, then 0  I   I 2  r  0    I  r  I   r  I short. , i.e. The abscissa t.B corresponds to the short circuit current; 2) because the parabola is symmetrical, then the abscissa t.A is half the short circuit current I  3) because in point A I  I k.z.   , and the ordinate corresponds to the maximum power value; 2 2r  Rr and I  2r , then after transformations we obtain R=r – the condition under which the power released in the external circuit with a direct current source takes on the maximum value; 2     r  4) maximum power value P  I 2  R   .  4r 2r 2 Procedure: 1. Connect a voltmeter to the terminals of the DC source (see Fig. 4). The voltage shown by the voltmeter is taken as the value of the EMF of the direct current source and considered as a reference for this laboratory work. Write the result in the form: (U±U) V. Take the absolute error equal to the division value of the voltmeter. rice. 4 2. Assemble the experimental setup according to the diagram shown in Figure 5: fig. 5 3. Carry out a series of 5-10 experiments, with smooth movement of the rheostat slider, recording the measurement results in the table: Current Strength Voltage I U A V 4. Based on the experimental data obtained, construct the current-voltage characteristic of the direct current source. 5. Determine the possible value of the EMF of the direct current source and the short circuit current. 6. Apply the technique of graphical processing of experimental data and calculations to calculate the internal resistance of a direct current source. 7. Present the calculation results in the form:  EMF of a direct current source: (av±av) V;  internal resistance of the direct current source: r=(rср±рср) Ohm. 8. Construct a graphical relationship U  f I  in Microsoft Excel, using the chart wizard, adding a trend line and specifying the equation of the line. Using the main parameters of the equation, determine the possible value of the EMF of the direct current source, short circuit current and internal resistance. 9. On the numerical axes, indicate the range of values ​​of the emf, the internal resistance of the direct current source and the short circuit current, obtained by various determination methods. 10. Investigate the power released in the external circuit from the magnitude of the electric current. To do this, fill out the table and construct a graphical dependence P  f I : Current Power I P A W 11. Using the constructed graph, determine the maximum power value, short circuit current, internal resistance of the current source and EMF. 12. It is possible to construct a graphical relationship P  f I  in Microsoft Excel using the chart wizard by adding a polynomial trend line with degree 2, intersecting the curve with the OY (P) axis at the origin and indicating the equation on the chart. Using the main parameters of the equation, determine the maximum power value, short circuit current, internal resistance of the current source and EMF. 13. Formulate a general conclusion about the work.

When designing and repairing circuits for various purposes, Ohm's law for a complete circuit must be taken into account. Therefore, those who are going to do this need to know this law to better understand the processes. Ohm's laws are divided into two categories:

• for a separate section of the electrical circuit;
• for a complete closed circuit.

In both cases, the internal resistance in the power supply structure is taken into account. In computational calculations, Ohm's law for a closed circuit and other definitions are used.

The simplest circuit with an EMF source

To understand Ohm's law for a complete circuit, for clarity of study, the simplest circuit with a minimum number of elements, EMF and active resistive load is considered. You can add connecting wires to the kit. A 12V car battery is ideal for power supply; it is considered as a source of EMF with its own resistance in the structural elements.

The role of the load is played by an ordinary incandescent lamp with a tungsten filament, which has a resistance of several tens of ohms. This load converts electrical energy into thermal energy. Only a few percent are spent on emitting a stream of light. When calculating such circuits, Ohm's law for a closed circuit is used.

Principle of proportionality

Experimental studies in the process of measuring quantities at different values ​​of the parameters of the complete circuit:

• Current strength – I A;
• The sums of the battery and load resistances – R+r are measured in ohms;
• EMF is a current source, denoted as E. measured in volts

it was noticed that the current strength has a directly proportional relationship with respect to the emf and an inverse proportional relationship with respect to the sum of the resistances that are closed in series in the circuit circuit. We formulate this algebraically as follows:

The considered example of a circuit with a closed loop circuit is with one power source and one external load resistance element in the form of an incandescent lamp. When calculating complex circuits with multiple circuits and many load elements, Ohm's law and other rules are applied for the entire circuit. In particular, you need to know Kirgoff’s laws, understand what two-terminal networks, four-terminal networks, branch nodes and individual branches are. This requires detailed consideration in a separate article; previously, this course of TERC (theory of electrical and radio engineering circuits) was taught in institutes for at least two years. Therefore, we limit ourselves to a simple definition only for the complete electrical circuit.

Features of resistance in power supplies

Important! If we see the resistance of the spiral on the lamp in the diagram and in the actual design, then the internal resistance in the design of the galvanic battery, or accumulator, is not visible. In real life, even if you disassemble the battery, it is impossible to find the resistance; it does not exist as a separate part; sometimes it is displayed on diagrams.

Internal resistance is created at the molecular level. The conductive materials of a battery or other generator power source with a current rectifier are not 100% conductive. There are always elements with particles of dielectric or metals of other conductivity, this creates current and voltage losses in the battery. Accumulators and batteries most clearly display the influence of the resistance of structural elements on the value of voltage and current at the output. The ability of the source to produce maximum current is determined by the purity of the composition of the conductive elements and electrolyte. The purer the materials, the lower the value of r, the emf source produces more current. And, conversely, in the presence of impurities, the current is less, r increases.

In our example, the battery has an EMF of 12V, a light bulb capable of consuming 21 W of power is connected to it, in this mode the lamp’s spiral heats up to the maximum permissible heat. The formulation of the current passing through it is written as:

I = P\U = 21 W / 12V = 1.75 A.

In this case, the lamp filament burns at half incandescence; let’s find out the reason for this phenomenon. For calculations of total load resistance (R + r) apply Ohm's laws for individual sections of circuits and principles of proportionality:

(R + r) = 12\ 1.75 = 6.85 Ohm.

The question arises of how to extract the value r from the sum of resistances. An acceptable option is to measure the resistance of the lamp spiral with a multimeter, subtract it from the total and obtain the value r - EMF. This method will not be accurate - when the coil heats up, the resistance changes its value significantly. Obviously, the lamp does not consume the power stated in its characteristics. It is clear that the voltage and current for filament of the coil are small. To find out the reason, let's measure the voltage drop across the battery with a connected load, for example, it will be 8 Volts. Let's assume that the helix resistance is calculated using the principles of proportionality:

U/I = 12V/1.75A = 6.85 Ohm.

When the voltage drops, the lamp resistance remains constant, in this case:

• I = U/R = 8V/6.85 Ohm = 1.16 A with the required 1.75A;
• Current loss = (1.75 -1.16) = 0.59A;
• By voltage = 12V – 8V = 4V.

The power consumption will be P = UxI = 8V x 1.16A = 9.28 W instead of the required 21 W. Let's find out where the energy goes. It cannot go beyond the closed loop; only the wires and the design of the EMF source remain.

EMF resistance –rcan be calculated using the lost voltage and current values:

r = 4V/0.59A = 6.7 Ohm.

It turns out that the internal resistance of the power source “eats up” half of the released energy, and this, of course, is not normal.

This happens in old, expired or defective batteries. Now manufacturers are trying to monitor the quality and purity of the current-carrying materials used in order to reduce losses. In order for maximum power to be delivered to the load, EMF source manufacturing technologies control that the value does not exceed 0.25 Ohm.

Knowing Ohm's law for a closed circuit, using the postulates of proportionality, you can easily calculate the necessary parameters for electrical circuits to identify faulty elements or design new circuits for various purposes.

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Creative laboratory on the topic “Graphical study of Ohm’s law for a complete circuit”

Materials provided by: Yuri Maksimov

email: [email protected]

Lesson objectives:

• didactic – create conditions for mastering new educational material using the research method of teaching;
• educational - form concepts about EMF, internal resistance and short circuit current.
• developing – develop students’ graphic skills, develop skills in handling current sources.
• educational – instill a culture of mental work.

Lesson type : a lesson in learning new material.

Equipment: set “Electricity-1 and 2” from the set of equipment “L - micro”, current source – flat battery.

DURING THE CLASSES.

1.Organizational moment (1-2 min.)

2.Updating knowledge (5 min.)

To achieve the goals of today's lesson, we need to remember the material we studied earlier. While answering questions, we will write down the main conclusions and formulas in notebooks and on the board.

• Ohm's law for a section of a circuit and its graph.
• The concept of volt-ampere characteristics.
• The concept of EMF, internal resistance, short circuit current Ohm's law for a closed circuit.
• Formula for calculating internal resistance.
• Formula for calculating EMF through current and resistor resistance (task 2 on p. 40 after §11)
• Formula for calculating EMF through voltage and resistor resistance.

Setting a learning task. Formulation of the topic and purpose of the lesson.

1. Measures EMF, internal resistance and short circuit current in several ways.
2. Study the physical meaning of EMF.
3. Find the most accurate way to determine EMF

Completing of the work.

First way – direct measurement of EMF.

Based on Ohm's law for a closed circuit, after transforming it we get the following formula:

U= E - I r.

When I=0 we get the calculation formula EMF: E=U . A voltmeter connected to the terminals of the current source shows the EMF value.

According to the voltmeter reading, we write down the EMF value: E = 4.9 V and short circuit current: Is.c = 2.6 A

We calculate the internal resistance using the formula:

r = (E – U) / I = 1.8 ohms

Second way – indirect calculation

1.according to ammeter readings.

Let's assemble an electrical circuit consisting of a series-connected current source, an ammeter, a resistor (first 2 Ohms, then 3 Ohms) and a key, as shown in the figure.

According to the formula: r = (I2R2 – I1R1) / (I1 – I2) Let's calculate the internal resistance: r = 3 Ohm

According to the formula: E = I1R1 – I1 r we find the EMF: E = 6 V.

According to the formula Ikz. = E/r We determine the short circuit current: Is = 2 A.

2.according to voltmeter readings.

Based on the voltmeter readings and taking into account the resistor resistance values, we obtain the following results:

r = 1 Ohm, E = 3.8 V. Is = 3.8 A.

Third way – graphic definition.

In problem 5 (p. 40) of the homework, you are asked to construct graphs of current strength versus resistance and electrical voltage versus resistance. This problem leads to the idea of ​​studying Ohm's law for a complete circuit through a graph of the reciprocal of current versus external resistance.

Let's rewrite this formula in another form:

1 / I = (R+ r) / E.

From this entry it is clear that the dependence of 1/I on R is a linear function, i.e. The graph is a straight line.

Let's assemble an electrical circuit consisting of a current source, an ammeter, a resistor and a switch connected in series. Changing the resistors, we write down their values ​​​​and the ammeter readings in the table. We calculate the reciprocal of the current.

Let's plot the dependence of the reciprocal of the current on the external resistance and continue it until it intersects with the R axis.

Analysis of the resulting graph.

• Point A on the graph corresponds to the condition 1 / I = 0, or R= ∞, which is possible with R= r
• Point B was obtained with resistance R=0, i.e. it shows the short circuit current.
• The blood pressure segment is equal to the sum of the resistances R+ r
• The CD segment is 1/I.

From the formula transformed at the beginning of the work: 1 / I = (R+ r) / E, we find:

1 / E = (1 / I) / (R + r) = tan α

From here we find the EMF:

E = сtg α = (BP) / (CD)

Calculation results:

r = 1.9 Ohm, E = 4.92 V. Is = 2.82 A.

Generalization of measurement results.

Main conclusions and analysis of results.

• The EMF of the current source is equal to the sum of the voltage drops on the external and internal sections of the circuit: E = IR + Ir = Uext + Uint.
• EMF is measured with a high-resistance voltmeter without an external load: U = E at R.
• Short circuit current is dangerous if the internal resistance of the current source is low.
• More accurate results are obtained with direct measurement and graphical determination.
• When choosing a power source, it is necessary to take into account a number of factors determined by operating conditions, load properties, and discharge time.

Creative laboratory on the topic “Graphical study of Ohm’s law for a complete circuit”

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Topic: “Study of Ohm’s law for a section of a circuit”

Goal of the work: establish experimentally the dependence of current on voltage and resistance.

Equipment: laboratory ammeter, laboratory voltmeter, power supply, set of three resistors with resistances of 1 Ohm, 2 Ohm, 4 Ohm, rheostat, current switch, connecting wires.

Progress.

Brief theoretical information

Electricity -ordered movement of charged particles

A quantitative measure of electric current is current strength I

Current strength -– scalar physical quantity equal to the ratio of the charge q transferred through the cross section of the conductor during the time interval t to this time interval:

In the International System of Units (SI) current is measured in amperes [A].

Current measuring device Ammeter. Included in the circuit sequentially

Voltage– this is a physical quantity that characterizes the action of an electric field on charged particles, numerically equal to the work of the electric field to move a charge from a point with potentialφ 1 to a point with potentialφ 2

U 12 = φ 1 – φ 2

U- voltage

A – current work

q – electric charge

Unit of voltage – Volt [V]

Voltage measuring device – Voltmeter. It is connected to the circuit parallel to the section of the circuit on which the potential difference is measured.

On electrical circuit diagrams, the ammeter is designated .

The quantity characterizing the resistance to electric current in a conductor, which is determined by the internal structure of the conductor and the chaotic movement of its particles, is calledelectrical resistance of the conductor.

The electrical resistance of a conductor depends onsizes And conductor shapes and from material, from which the conductor is made.

S – cross-sectional area of ​​the conductor

l – conductor length

ρ – conductor resistivity

The SI unit of electrical resistance of conductors is ohm[Ohm].

Graphical dependency amperage I from voltage U - volt-ampere characteristics

Ohm's law for a homogeneous section of a chain: The current in a conductor is directly proportional to the applied voltage and inversely proportional to the resistance of the conductor.

Named after its discoverer Georg Ohm.

Practical part

1. To complete the work, assemble an electrical circuit from a current source, an ammeter, a rheostat, a 2-ohm wirewound resistor and a key. Connect a voltmeter in parallel to the wirewound resistor (see diagram).

2. Experience 1.

Table 1. Section resistance 2 ohms

3.

4. Experience 2.

Table 2.

5.

6. Answer the security questions.

Control questions

1. What is electric current?

2. Define current strength. How is it designated? What is the formula?

3. What is the unit of current?

4. What device measures current strength? How is it included in an electrical circuit?

5. Define voltage. How is it designated? What is the formula?

6. What is the unit of voltage?

7. What device measures voltage? How is it included in an electrical circuit?

8. Define resistance. How is it designated? What is the formula?

9. What is the unit of resistance?

10. Formulate Ohm's law for a section of the circuit.

Measurement option.

Experience 1. Study of the dependence of current on voltage in a given section of the circuit. Turn on the current. Using a rheostat, increase the voltage at the terminals of the wire resistor to 1 V, then to 2 V and to 3 V. Each time, measure the current and write the results in the table. 1.

Table 1. Section resistance 2 ohms

Based on the experimental data, construct a graph of current versus voltage. Draw a conclusion.

Experience 2. Study of the dependence of current on the resistance of a section of a circuit at a constant voltage at its ends. Connect a wirewound resistor with a resistance of 1 Ohm, then 2 Ohms and 4 Ohms, into the circuit according to the same circuit. Using a rheostat, set the same voltage at the ends of the section each time, for example, 2 V. Measure the current strength and record the results in Table 2.

Table 2.Constant voltage in the area 2 V

Based on the experimental data, construct a graph of current versus resistance. Draw a conclusion.

Presentation: "Laboratory work: "Study of Ohm's law for a section of a circuit."

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