Objective:
Deepening knowledge about Ohm's law for chain sections and Ohm's law for a complete chain. Application of Kirchhoff's rules for the calculation of DC circuits.
Equipment : training and laboratory stand "Laws of direct current", a multimeter, three or four resistors with known resistances, two galvanic cells of different types, connecting wires.
Introduction
Statement of the problem of calculating the DC circuit: “Knowing the values of the emf acting in the circuit, the internal resistances of the current sources and the resistances of all elements of the circuit, calculate the current strengths in each section of the circuit and the voltage drop in each element.”
When solving this problem, we use:
Ohm's law for a circuit section
I- current strength, U- voltage in the circuit section, R- section resistance;
Ohm's law for a complete circuit
I- current strength, e - emf current source, R is the resistance of the external circuit, r is the internal resistance of the current source.
The direct calculation of branched circuits containing several closed circuits and several current sources is performed using two Kichhoff rules.
Any point in a branched circuit where at least three current-carrying conductors converge is called node. In this case, the current entering the node is considered positive, and the current leaving the node is considered negative.
Kirchhoff's first rule: the algebraic strength of the currents converging in the node is zero:
Kirchhoff's second rule: in any closed circuit, arbitrarily chosen in a branched circuit, the algebraic sum of the products of the current forces and the resistances of the corresponding sections of this circuit is equal to the algebraic sum of the emfs encountered in the circuit:
(4)
Description of the stand "Laws of direct current"
The work uses a stand consisting of two current sources (galvanic cells), a set of four resistors with known resistances, a multimeter and a set of connecting wires.
1. When assembling electrical circuits, it is necessary to ensure good contact in each connection.
2. Connecting wires are twisted under the terminals clockwise .
3. When measuring currents and voltages, the multimeter probes must be tightly pressed to the terminals.
4. Measurements are made when the circuit is short-circuited with a button.
5. Do not leave the chain assembled for a long time.
First of all, learn the rules for measuring with a universal electrical measuring instrument - a multimeter.
Measurement, processing and presentation of measurement results
Exercise 1.
emf current source can be measured directly with a voltmeter with a fairly high degree of accuracy. But it should be borne in mind that in this case the measured voltage is less than the true value of the emf. the magnitude of the voltage drop across the current source itself.
, (5)
where U- voltmeter readings.
The difference between the true value of emf. and the measured voltage is equal to:
. (6)
In this case, the relative error in the measurement of emf. is equal to:
(7)
Usually the resistance of the current source (galvanic cell) is several Ohm(For example, 1ohm). Even if the resistance of the voltmeter is small (for example, 100 ohm), then in this case the error of direct measurement of emf totals » 1%. A good voltmeter, including those used in a multimeter, has a resistance of the order 10 6 ohm. It is clear that when using such a voltmeter, we can assume that the reading of the voltmeter is practically equal to the measured emf from the current source.
1. Prepare the multimeter for DC voltage measurement until 2 V .
2. Without removing the galvanic cells from the fixtures, measure and record their emf. accurate to hundredths of a volt.
3. E.f.s. the value is always positive. Observe the polarity when connecting the multimeter to power sources. The red probe of the multimeter is connected to the "+" of the current source.
Task 2.
The internal resistance of a current source can be calculated using Ohm's law:
1. Prepare a multimeter to measure DC current until 10(20) A .
2. Make an electrical circuit from a series-connected current source, a resistor (one of the set) and an ammeter.
3. Measure the current in the circuit.
4. Calculate and record the internal resistance of the source.
5. Take similar measurements for another element.
Task 3. Calculation of the DC electric circuit
1. Assemble the electrical circuit according to the scheme proposed by the teacher (schemes 1-7).
2. Draw a diagram in the work report and indicate the values of the selected resistors.
3. Using Kirchhoff's rules, calculate the currents in all branches of the circuit. Calculate the voltage drops across each resistor.
4. Using a multimeter, measure the current in a place accessible for measurement. Measure the voltage drop across each resistor.
5. In the output, compare the measured and calculated values and indicate the reasons for possible discrepancies.
Task 4. Connection of current sources in batteries
1. Current sources can be connected to batteries in two main ways: in parallel and in series. If the sources are connected in series, then their emf. and the internal resistances add up:
With a parallel connection of identical current sources, the total emf. battery is equal to emf. one source, and the internal resistance of the battery is n times less than the internal resistance of one current source:
(10)
Assemble the circuits according to schemes 8, 9, in which both connection schemes are implemented. Calculate and measure the current in the circuit at these connections. In the output, compare the calculated and measured values.
Lab Report #3
Studying the application of Ohm's law to the calculation of DC circuits
performed by a student of the school "Search"
…………………………………………………………………………………
“…….”………….. 200….
Exercise 1 . Definition of emf current sources
First current source e 1 = ……… AT
Second current source e 2 = ……… AT
Task 2 . Measurement of the internal resistance of current sources
First current source
R = ……… Ohm, I = ……… A, r 1 = ……… Ohm
Second current source
R = ……… Ohm, I = ……… A, r 2 = ……… Ohm
Table 1
Conclusion: ……………………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………………………… ……………………………………………………
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, for a better understanding of the processes, this law must be known. Ohm's laws are divided into two categories:
- for a separate section of the electrical circuit;
- for a complete closed circuit.
In both cases, 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 is considered with a minimum number of elements, EMF and active resistive load. Connecting wires can be added to the kit. A 12V car battery is ideal for power supply, it is considered as an EMF source 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 heat. Only a few percent are spent on the emission of a stream of light. When calculating such circuits, Ohm's law for a closed circuit is used.
The 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 - current source, denoted as E. measured in volts
it was noticed that the current strength is directly proportional to the EMF and inversely proportional to the sum of the resistances that are closed in series in the circuit. Algebraically, we formulate this as follows:
The considered example of a closed circuit circuit is with one power supply and one external load resistance element in the form of a filament lamp. When calculating complex circuits with several circuits and many load elements, Ohm's law is applied for the entire circuit and other rules. In particular, you need to know Kirhoff's laws, understand what two-terminal networks, quadripoles, outlet nodes and individual branches are. This requires a detailed consideration in a separate article; earlier this course TERC (the theory of electrical and radio circuits) was taught at institutes for at least two years. Therefore, we restrict ourselves to a 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 real design, then the internal resistance in the design of a 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 the diagrams.
Internal resistance is created at the molecular level. The conductive materials of a battery or other generator power source with a rectifier are not 100% conductive. There are always elements with particles of a dielectric or metals of other conductivity, this creates current and voltage losses in the battery. On accumulators and batteries, the influence of the resistance of structural elements on the magnitude of the voltage and current at the output is most clearly displayed. The ability of the source to deliver the maximum current determines the purity of the composition of the conductive elements and the 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 is connected to it, capable of consuming a power of 21 W, in this mode the lamp coil heats up to the maximum allowable glow. The formulation of the current passing through it is written as:
I \u003d P\U \u003d 21 W / 12V \u003d 1.75 A.
In this case, the lamp spiral burns at half heat, we will find out the reason for this phenomenon. For total load resistance calculations (R + r) apply Ohm's laws for individual sections of circuits and the principles of proportionality:
(R + r) \u003d 12\ 1.75 \u003d 6.85 ohms.
The question arises how to extract the value of r from the sum of resistances. An option is allowed - to measure the resistance of the lamp spiral with a multimeter, subtract it from the total and get the value of r - EMF. This method will not be accurate - when the spiral is heated, the resistance changes its value significantly. It is obvious that the lamp does not consume the power declared in its characteristics. It is clear that the voltage and current for heating the coil are small. To find out the reason, let's measure the voltage drop on the battery with the load connected, for example, it will be 8 volts. Assume that the coil resistance is calculated using the principles of proportionality:
U / I \u003d 12V / 1.75A \u003d 6.85 Ohms.
When the voltage drops, the resistance of the lamp remains constant, in this case:
- I \u003d U / R \u003d 8V / 6.85 Ohm \u003d 1.16 A at the required 1.75A;
- Current loss \u003d (1.75 -1.16) \u003d 0.59A;
- Voltage = 12V - 8V = 4V.
The power consumption will be P = UxI = 8V x 1.16A = 9.28 W instead of the prescribed 21 W. 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 values of voltage and current:
r \u003d 4V / 0.59A \u003d 6.7 ohms.
It turns out that the internal resistance of the power source “devours” half of the energy allocated to itself, and this, of course, is not normal.
This happens in old spent 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 ohms.
Knowing Ohm's law for a closed circuit, using the postulates of proportionality, you can easily calculate the necessary parameters for electrical circuits to determine faulty elements or design new circuits for various purposes.
Video
Ohm's law for a complete circuit is an empirical (obtained from experiment) law that establishes the relationship between current strength, electromotive force (EMF), and external and internal resistance in a circuit.
When conducting real 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 obliges to use Ohm's law for a complete circuit.
We 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 the total resistance is understood as the sum of external and internal resistances.
Rice. 2. Scheme of Ohm's law for a complete circuit.
- R – external resistance [Ohm];
- r is the resistance of the EMF source (internal) [Ohm];
- I - current strength [A];
- ε – EMF of the current source [V].
Let's consider some problems on this topic. Ohm's law tasks for the complete circuit are usually given to students in grade 10 so that they can better understand the specified topic.
I. Determine the current strength in a circuit with a light bulb, a resistance of 2.4 ohms and a current source whose EMF is 10 V and an internal resistance of 0.1 ohms.
By definition of Ohm's law for a complete circuit, the current strength is:
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.
We write Ohm's law for a complete circuit and express the internal resistance from it:
III. Once a schoolboy asked a physics teacher: “Why is the battery running low?” How to correctly answer this question?
We already know that a real source has its own resistance, which is due either to 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 can decrease either due to a decrease in EMF or due to an increase in internal resistance. The EMF value of the battery is almost constant. Therefore, the current in the circuit is reduced by increasing the internal resistance. So, the "battery" sits down, as its internal resistance increases.
Topic: "Studying Ohm's law for a chain section"
Objective: to establish experimentally the dependence of current strength on voltage and resistance.
Equipment: laboratory ammeter, laboratory voltmeter, power supply, a set of three resistors with resistances of 1 ohm, 2 ohm, 4 ohm, rheostat, current closing switch, connecting wires.
Working process.
Brief theoretical information
Electricity -orderly motion of charged particles
The 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 in a time interval t, to this time interval:
In the International System of Units SI, current is measured in amperes [BUT].
Instrument for measuring current strength Ammeter. Included in the chain successively
Voltage- this is a physical quantity that characterizes the action of an electric field on charged particles, numerically equal to the work of an electric field in moving a charge from a point with a potentialφ 1 to the point of potentialφ 2
U 12 \u003d φ 1 - φ 2
U- voltage
A – current work
q – electric charge
Voltage unit - Volt [V]
Voltage measuring instrument - Voltmeter. It is connected to the circuit in parallel to that section of the circuit on which the potential difference is measured.
On the diagrams of electrical circuits, the ammeter is indicated.
The value characterizing the opposition to the electric current in the conductor, which is due to the internal structure of the conductor and the chaotic movement of its particles, is calledthe electrical 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 is the cross-sectional area of the conductor
l – conductor length
ρ – specific resistance of the conductor
In SI, the unit of electrical resistance of conductors is ohm[Ohm].
Graphic dependency current strength I from voltage U - volt-ampere characteristics
Ohm's law for a homogeneous section of the 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 George Ohm.
Practical part
1. To perform the work, assemble an electrical circuit from a current source, an ammeter, a rheostat, a 2 ohm wire resistor and a key. Connect a voltmeter in parallel with the wire resistor (see diagram).
2. Experience 1.
Table 1. Section resistance 2 ohm
3.
4. Experience 2.
Table 2.
5.
6. Answer security questions.
test questions
1. What is electric current?
2. Define the current strength. How is it designated? What is the formula?
3. What is the unit of current measurement?
4. What instrument measures the current strength? How is it connected to the electrical circuit?
5. Define voltage. How is it designated? What is the formula?
6. What is the unit of voltage measurement?
7. What device measures voltage? How is it connected to the electrical circuit?
8. Define resistance. How is it designated? What is the formula?
9. What is the unit of measure for resistance?
10. Formulate Ohm's law for the chain section.
Measurement option.
Experience 1. Study of the dependence of current strength on voltage in a given section of the circuit. Turn on the current. Using a rheostat, bring the voltage at the terminals of the wire resistor to 1 V, then to 2 V and up to 3 V. Each time, measure the current and record the results in Table. one.
Table 1. Section resistance 2 ohm
Plot a graph of current versus voltage based on the experimental data. Make a conclusion.
Experience 2. Investigation of the dependence of the current strength on the resistance of a circuit section at a constant voltage at its ends. Include in the circuit in the same way a wire resistor, first with a resistance of 1 ohm, then 2 ohms and 4 ohms. Using a rheostat, set the same voltage at the ends of the section each time, for example, 2 V. Measure the current strength, write the results in Table 2.
Table 2.Constant voltage on the plot 2 V
Based on the experimental data, plot the dependence of the current strength on the resistance. Make a conclusion.
Presentation: "Laboratory work: "Studying Ohm's law for a chain section" .
(edocs)fizpr/lr7f.pptx,800,600(/edocs)
Laboratory work №10. "The study of Ohm's law for a complete circuit - 3 ways." The purpose of the work: to study Ohm's law for a complete circuit. Tasks of the work: determination of EMF and internal resistance of a DC source by 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: direct current source, ammeter, voltmeter, connecting wires, key, rheostat. Theory and method of work performance: Ohm's law I Rr for a complete circuit I Rr . 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 the DC source on the magnitude of the current strength (voltage characteristic) has the form (see Fig. 1): fig. 1 Analysis of the current-voltage characteristic of a DC 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 I r I I 2 r . Therefore, the graphic dependence P f I is a parabola, the branches of which are directed downwards (see Fig. 2). rice. 2 Analysis of the graphic dependence P f I (see Fig. 3): fig. 3 1) for point B: P=0, then 0 I I 2 r 0 I r I r I k.z. , i.e. 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 t.A I I k.z. , and the ordinate corresponds to the maximum power value; 2 2r Rr and I 2r , then after the transformations we get R=r – the condition under which the power released in the external circuit with a direct current source takes the maximum value; 2 r 4) maximum power value P I 2 R . 4r 2r 2 Operation: 1. Connect the 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 DC 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 scheme shown in Figure 5: fig. 5 3. Conduct a series of 5-10 experiments, with smooth movement of the rheostat slider, enter the measurement results in the table: Current Voltage I U A B 4. Based on the experimental data obtained, construct the current-voltage characteristic of the DC source. 5. Determine the possible value of the EMF of the DC source and the short circuit current. 6. Apply the method of graphical processing of experimental data and calculations to calculate the internal resistance of a DC source. 7. Present the results of calculations in the form: EMF of the DC source: (avg±avg) V; Internal resistance of DC source: r=(rav±rav) Ohm. 8. Build a graphical dependence U f I in Microsoft Excel, using the chart wizard with the addition of a trend line and an indication of the straight line equation. Based on the main parameters of the equation, determine the possible value of the EMF of a direct current source, short circuit current and internal resistance. 9. On the numerical axes, indicate the range of values of EMF, internal resistance of a direct current source and short-circuit current, obtained by various methods of determination. 10. Investigate the power released in the external circuit from the magnitude of the electric current. To do this, fill in the table and build a graphical dependence P f I : Current strength Power I P A W 11. According to the graph, determine the maximum power value, short circuit current, internal resistance of the current source and EMF. 12. It is possible to build a graphical dependence P f I in Microsoft Excel, using the diagram wizard with the addition of a polynomial trend line with a degree of 2, the intersection of the curve with the OY (P) axis at the origin and indicating the equation on the diagram. Based on 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 on the work.
