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Creative laboratory on the topic “Graphical study of Ohm’s law for complete chain »

Materials provided by: Yuri Maksimov

email: [email protected]

Lesson objectives:

• didactic – create conditions for learning new things educational material using research method training;
• 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.

PROGRESS OF THE LESSON.

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.

Staging educational task. Formulation of the topic and purpose of the lesson.

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

Getting the job done.

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 current source, an ammeter, a resistor (first 2 Ohms, then 3 Ohms) and a switch connected in series, 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) homework You are asked to construct graphs of current versus resistance and electrical voltage versus resistance. This task leads to the idea of ​​studying Ohm's law for a complete circuit through a graph of the magnitude, retroactive effect current from 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 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.

I (Ohm)

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.

Measuring method	Internal resistance	EMF value	Short circuit current

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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Subject: Checking Ohm's Law for a Complete Circuit

Purpose of the work: determine the internal resistance of the current source and its EMF.

Equipment:
Explanations for work

Electric current in conductors is caused by so-called direct current sources. The forces that cause the movement of electric charges inside a direct current source against the direction of action of the electrostatic field forces are called outside forces. Work attitude A side , performed by external forces to move the charge  Q along the chain, to the value of this charge is called electromotive force  source (EMF):

The emf of the source is measured with a voltmeter, the current strength is measured with an ammeter.

According to Ohm's law, the current strength in a closed circuit with one source is determined by the expression:

Thus, the current strength in the circuit is equal to the ratio of the electromotive force of the source to the sum of the resistances of the external and internal sections of the circuit. Let the current values ​​I 1 and I 2 and the voltage drops across the rheostat U 1 and U 2 be known. For EMF we can write:
= I 1 (R 1 + r) and

I 2 (R 2 + r)

Equating the right-hand sides of these two equalities, we get

I 1 (R 1 + r) = I 2 (R 2 + r)

I 1 R 1 + I 1 r = I 2 R 2 + I 2 r

I 1  r – I 2 r = I 2 R 2 - I 1 R 1

Because I 1 R 1 = U 1 and I 2 R 2 = U 2, then the last equality can be written as follows

r(I 1 – I 2) = U 2 – U 1,

Quests

Figure 1

1. 
   Using a multimeter, determine the voltage on the battery with the key open. This will be the emf of the battery
2. 
   Close the key and measure the current I 1 and voltage U 1 on the rheostat. Record instrument readings.
3. 
   Change the resistance of the rheostat and write down other values ​​for the current I 2 and voltage U 2 .
4. 
   Repeat the current and voltage measurements for 4 more different positions of the rheostat slider and record the resulting values ​​in the table:

Experience no.

1. 
   Calculate internal resistance using the formula:

1. 
   Determine the absolute and relative error of EMF measurement (∆ℇ and δ
2. 
   ) and internal resistance (∆r and δ r) of the battery.
3. 
   
4. 
   

Security questions

1. 
   State Ohm's law for the complete circuit.
2. 
   What is the emf of the source when the circuit is open?
3. 
   What causes the internal resistance of a current source?
4. 
   How is the short circuit current of a battery determined?

Literature

1. 
   
2. 
   
3. 
   

The work lasts 2 hours

Laboratory work № 8

Subject: Determination of EMF and internal resistance of a voltage source

Purpose of the work: measure the EMF and internal resistance of the current source.

Equipment: power supply, wirewound resistor, ammeter, key, voltmeter, connecting wires.

Explanations for work

The electrical circuit diagram is shown in Figure 1. The circuit uses an accumulator or battery as a current source.

Figure 1

When the switch is open, the emf of the current source is equal to the voltage on the external circuit. In the experiment, the current source is connected to a voltmeter, the resistance of which should be much greater than the internal resistance of the current source r. Usually the resistance of the current source is low, so to measure the voltage you can use a voltmeter with a scale of 0–6 V and a resistance R V = 900 Ohms. Since the source resistance is usually small, then indeed R is in r. In this case, the difference between E and U does not exceed tenths of a percent, so the error in measuring the EMF is equal to the error in measuring the voltage.

The internal resistance of a current source can be measured indirectly by taking ammeter and voltmeter readings with the switch closed.

Indeed, from Ohm’s Law for a closed circuit we obtain: E=U+Ir, where U=IR is the voltage on the external circuit. That's why

To measure the current in a circuit, you can use an ammeter with a scale of 0 - 5 A.
Quests

1. 
   
2. 
   Assemble the electrical circuit according to Figure 1.
3. 
   Measure the EMF of the current source with a voltmeter when the switch is open:

E=U

1. 
   Write down the accuracy class of the voltmeter k v and the measurement limit U max of its scale.
2. 
   Find absolute error measuring the emf of the current source:

1. 
   Write down the final result of measuring the emf of the current source:

1. 
   Turn off the voltmeter. Lock the key. Measure the current I in the circuit with an ammeter.
2. 
   Write down the accuracy class of the ammeter k A and the measurement limit I max of its scale.
3. 
   Find the absolute error in current measurement:

1. 
   Calculate the internal resistance of the current source using the formula:

1. 
   Find the absolute error in measuring the internal resistance of the current source:

1. 
   Write down the final result of measuring the internal resistance of the current source:

1. 
   Enter the results of measurements and calculations into the table:

Measuring the EMF of a current source					Measuring the internal resistance of a current source
E=U,B	k v ,V	Umax,V	∆E,%	E+∆E,%	I,A	k A ,A	I max ,A	R,Ohm	∆R,Ohm	∆r,Ohm	r+∆r,Ohm

1. 
   Prepare a report, it should contain: the name of the topic and purpose of the work, a list of necessary equipment, formulas for the desired quantities and their errors, a table with the results of measurements and calculations, a conclusion on the work.
2. 
   Answer the test questions orally.

Security questions

1. 
   Why are the voltmeter readings different when the key is open and when the switch is closed?
2. 
   How to improve the accuracy of measuring the EMF of a current source?
3. 
   What resistance is called internal resistance?
4. 
   What determines the potential difference between the poles of a current source?

Literature

1. 
   Dmitrieva V. F. Physics for professions and technical specialties: a textbook for educational institutions beginning and Wednesday prof. education. - M.: Publishing Center "Academy", 2014;
2. 
   Samoilenko P.I. Physics for professions and specialties of socio-economic profile: a textbook for educational institutions of primary and secondary professional. education. - M.: Publishing Center "Academy", 2013;
3. 
   Kasyanov V.D. Notebook for laboratory work. 10th grade. - M.: Bustard, 2014.

The work lasts 2 hours

Laboratory work No. 9

Subject: Study of the phenomenon of electromagnetic induction

Purpose of the work: study the phenomenon of electromagnetic induction and the properties of vortex electric field, establish and formulate a rule for determining induced current.

Equipment: milliammeter, coil-coil, arc-shaped magnet, power source, coil with an iron core from a dismountable electromagnet, key, connecting wires.

Explanations for work

Electromagnetic induction is the occurrence of an electromotive force in a conductor when it moves in a magnetic field in a closed conducting circuit due to its movement in a magnetic field or a change in the field itself. This electromotive force is called the electromotive force of electromagnetic induction. Under its influence, in a closed conductor there arises electric current, called induced current.

Law of electromagnetic induction (Faraday-Maxwell's law): The EMF of electromagnetic induction in a circuit is proportional and opposite in sign to the rate of change of magnetic flux through a surface stretched over the circuit:

The minus sign on the right side of the law of electromagnetic induction corresponds to Lenz's rule: with any change in the magnetic flux through a surface stretched over a closed conducting circuit, an induced current appears in the circuit in such a direction that its own magnetic field counteracts the change in magnetic flux that caused the induced current.
Quests

1. 
   Study the guidelines for performing laboratory work yourself.
2. 
   Connect the coil to the clamps of the milliammeter.
3. 
   While observing the readings of the milliammeter, bring one of the poles of the magnet to the coil, then stop the magnet for a few seconds, and then bring it closer to the coil again, pushing it into it.
4. 
   Write down whether you have changed magnetic flux piercing the coil while the magnet moves? During his stop?
5. 
   Based on your answers to the previous question, draw and write down a conclusion about the condition under which an induced current occurs in the coil.
6. 
   The direction of the current in the coil can be judged by the direction in which the milliammeter needle deviates from the zero division. Check whether the direction of the induction current in the coil will be the same or different when the same magnet pole approaches it and moves away from it.
7. 
   Approach the magnet pole to the coil at such a speed that the milliammeter needle deviates by no more than half the limit value of its scale.
8. 
   Repeat the same experiment, but at a higher speed of the magnet than in the first case. At a higher or lower speed of movement of the magnet relative to the coil, does the magnetic flux passing through this coil change faster? With a rapid or slow change in the magnetic flux through the coil, did a larger current arise in it? Based on your answer to the last question, draw and write down a conclusion about how the modulus of the strength of the induction current arising in the coil depends on the rate of change of the magnetic flux passing through this coil.
9. 
   Assemble the electrical circuit:

Figure 1

1. 
   Check whether an induced current occurs in coil 1 in the following cases:

a) when closing and opening the circuit in which coil 2 is connected;

b) when direct current flows through coil 2;

c) when the current flowing through coil 2 increases and decreases by moving the rheostat slider to the corresponding side.

11. In which of the cases listed in paragraph 9 does the magnetic flux passing through coil 1 change? Why is it changing?

12. Prepare a report, it should contain: the name of the topic and purpose of the work, a list of necessary equipment, experimental schemes, conclusion on the work.

13. Answer the test questions orally.
Security questions

1. 
   Why is it better to take a closed conductor in the form of a coil, and not in the form of a single turn of wire, to detect induction current?
2. 
   Formulate the law of electromagnetic induction.
3. 
   Name the instruments and devices whose operation is based on induction currents.
4. 
   What is the phenomenon of electromagnetic induction?
5. 
   Change which physical quantities can lead to a change in magnetic flux?

Literature

1. 
   Dmitrieva V.F. Physics for professions and technical specialties: a textbook for educational institutions beginning. and Wednesday prof. education. - M.: Publishing Center "Academy", 2014;
2. 
   Samoilenko P.I. Physics for professions and specialties of socio-economic profile: a textbook for educational institutions of primary and secondary professional. education. - M.: Publishing Center "Academy", 2013;
3. 
   Kasyanov V.D. Notebook for laboratory work. 10th grade. - M.: Bustard, 2014.

The work lasts 2 hours

Laboratory work No. 10

Ohm's law for a complete circuit is an empirical (derived from experiment) law that establishes the relationship between current strength, electromotive force (EMF) and external and internal resistance in a circuit.

When conducting actual studies of the electrical characteristics of DC circuits, it is necessary to take into account the resistance of the current source itself. Thus, in physics, a transition is made from an ideal current source to a real current source, which has its own resistance (see Fig. 1).

Rice. 1. Image of ideal and real current sources

Consideration of a current source with its own resistance requires the use of Ohm's law for the complete circuit.

Let us formulate Ohm's law for a complete circuit as follows (see Fig. 2): the current strength in a complete circuit is directly proportional to the emf and inversely proportional to the total resistance of the circuit, where total resistance is understood as the sum of external and internal resistances.

Rice. 2. Diagram of Ohm's law for a complete circuit.

• R – external resistance [Ohm];
• r – resistance of the EMF source (internal) [Ohm];
• I – current strength [A];
• ε – EMF of the current source [V].

Let's look at some problems on this topic. Problems on Ohm's law for a complete circuit are usually given to 10th grade students so that they can better understand the specified topic.

I. Determine the current in a circuit with a light bulb, a resistance of 2.4 Ohms and a current source whose emf is 10 V and the internal resistance is 0.1 Ohms.

By definition of Ohm's law for a complete circuit, the current strength is equal to:

II. Determine the internal resistance of a current source with an emf of 52 V. If it is known that when this current source is connected to a circuit with a resistance of 10 Ohms, the ammeter shows a value of 5 A.

Let's write Ohm's law for the complete circuit and express the internal resistance from it:

III. One day a schoolboy asked his physics teacher: “Why does the battery run out?” How to correctly answer this question?

We already know that a real source has its own resistance, which is determined either by the resistance of electrolyte solutions for galvanic cells and batteries, or the resistance of conductors for generators. According to Ohm's law for a complete circuit:

therefore, the current in the circuit may decrease either due to a decrease in emf or due to an increase in internal resistance. The battery's emf value is almost constant. Consequently, the current in the circuit decreases due to an increase in internal resistance. So, the “battery” runs out, as its internal resistance increases.

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 minimum quantity elements, EMF and active resistive load. 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 meanings full circuit parameters:

• 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 direct proportional dependence relative to the EMF and an inverse proportional relationship relative 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 multiple load elements, Ohm's law applies to the entire circuit and other rules. 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 simple definition only for a 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 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 less value 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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