Assembly of complex electrical circuits presentation. Presentation "Electrical circuits

Slide 1

An electrical circuit is a collection of devices and objects that form a path of electric current. A separate device that is part of an electrical circuit and performs a specific function in it is called an element of the electrical circuit. An electrical circuit consists of a source of electrical energy, consumers and connecting wires connecting the source of electrical energy to the consumer.

Slide 2

Types of circuits

The electrical circuit diagram is graphic image electrical circuit containing symbols of its elements, showing the connections of these elements. Types of diagrams: structural (block diagram); functional; principled; installation, etc. Functional, compared to structural, reveals in more detail the functions of individual elements and devices.

Slide 3


The schematic diagram shows the complete composition of the elements and indicates all the connections between them. This diagram gives a detailed understanding of the principles of operation of the product (installation). Installation diagrams are drawings that show the actual location of components both inside and outside the object shown in the diagram.

Slide 4

Symbols for electrical appliances

• Slide 5

  The simplest electrical circuit

  Basic elements electrical circuits: Resistance Inductance Capacitance Voltage source Current source. The main elements of the simplest electrical circuit: 1 - source of electrical energy; 2 - electrical energy receivers; 3 - connecting wires  1 2 3

  Slide 6

  E.M.S source

  This is an idealized power source, the voltage at the terminals of which is constant (independent of the magnitude of the current I) and equal to the E.M.F. E, and the internal resistance is zero. I =0 c 0 E U

  Slide 7

  Current source

  It is an idealized power source that produces a current I=Ik, independent of the resistance of the load to which it is connected, and the E.M.F. its Eit and internal resistance Rit are equal to infinity. I =900 Ik=Eit/Rit 0 U

  Slide 8

  Auxiliary elements

  These include: controls (switches, switches, contactors); protection (fuses, relays, etc.); regulation (rheostats, current and voltage stabilizers, transformers); control (ammeters, voltmeters, etc.)

  Slide 9

  Kirchhoff's first law

  In the branches forming a node in an electrical circuit, the algebraic sum of the currents is equal to zero. The sum of currents directed to a node in an electrical circuit is equal to the sum of currents directed from this node. I1 + I 2 + I 3 +... + I n = 0 This law follows from the principle of current continuity. If we assume that currents of one direction predominate in a node, then a charge of the same sign should accumulate, and the potential of the nodal point should continuously change, which is not observed in real circuits.

  Slide 10

  Kirchhoff's second law

  We go around the contour in an arbitrary direction, for example clockwise. If the directions of the E.M.F. and currents coincide with the direction of bypassing the circuit, then the E.M.F. (E) and voltage drops (U=I*R) are taken with a plus sign, if they do not coincide - with a minus sign: E 1 -E 2 +E 3 =U1+U2+U3+U4 E3 R1 R2 R3 R4 E1 E2 I2 I3 I4 I1 In any closed circuit, the algebraic sum of electromotive forces is equal to the algebraic sum of voltage drops ∑E= ∑I*R

  Slide 11
  

  Under the chains DC mean circuits in which the current does not change its direction, i.e. the polarity of EMF sources in which is constant.

  Areas of application for DC systems (stationary batteries) Energy (power plants, substations, power supply systems) Telecommunications systems Mobile communications Uninterruptible power supply installations Backup power for emergency lighting systems Energy storage systems in solar panels Power systems that meet increased safety requirements (for example, public and medical institutions) Computer centers Automation systems for production and technological processes Power supplies for sea-based facilities

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Municipal budgetary educational institution "Kordonskaya secondary school"

Electrical circuits

WITH: technology teacher

Kudinov A. A.

Cordon 2018

The simplest electrical circuit may contain only three elements:

source, load and connecting wires.

Electric circuit -

a set of devices, elements designed for the flow of electric current, electromagnetic processes in which can be described using the concepts of current and voltage.

When assembling electrical circuits, the electrician is guided by

electrical circuit diagram .

Schematic diagram, electrical circuit diagram - a graphic image (model) used to convey, using conventional graphic and alphanumeric symbols (pictograms), connections between the elements of an electrical device.

A schematic diagram, unlike a printed circuit board layout, does not show the relative (physical) arrangement of elements, but only indicates which pins of real elements (for example, microcircuits) are connected to which.

Let's look at some graphic symbols on circuit diagrams

Galvanic

element

Galvanic battery

elements

Intersection

wires

Compound

wires

node

Button

switch

Resistor

(resistance)

Fuse

Electric lamp

incandescent

Electric

call

Coil

wire

Coil

with iron core

Capacitor

constant capacity

Learning new educational material

Capacitor

variable capacity

Learning new educational material

Capacitor

electrolytic

Ammeter

Voltmeter

Electrical circuit diagrams are graphic documents.

Symbols and rules for the execution of electrical circuits are determined by the state standard, which all engineers and technicians are required to comply with.

The connection lines between the circuit elements are drawn parallel or mutually perpendicular, observing

closed circuit condition, inclined lines do not apply.

Let's draw in a notebook a table from the textbook (p. 49), which shows the symbols of some elements of the electrical circuit.

Wiring diagrams - these are drawings showing the actual location of components both inside and outside the object shown on the diagram. Designed primarily to enable the production of an object. Takes into account the location of circuit components and electrical connections (electrical wires and cables). Only general requirements for the preparation of design documentation apply.

What is an electrical circuit?

- What is a schematic diagram?

- What is a wiring diagram?

What can be classified as elements of an electrical circuit?

- depict schematic diagram electrical wiring of a house or apartment.

Homework assignment

- study paragraph 9 of the textbook;

- answer questions 1-2 on page 50 of the textbook.

Express in one sentence, choosing the beginning of the phrase:

Today I found out...

It was interesting...

It was difficult...

I completed tasks...

I realized that...

Now I can...

I purchased...

I learned (learned)…

I did it...

I was able (was able)…

I will try…

I was surprised...

1 DC electrical circuits 1.1 Elements of DC electrical circuits Electrical diagrams- These are drawings that show how electrical devices are connected in a circuit. An electrical circuit is a set of devices designed for the transmission, distribution and mutual conversion of energy. The main elements of an electrical circuit are sources and receivers of electrical energy, which are connected to each other by conductors. In sources of electrical energy, chemical, mechanical, thermal energy or other types of energy are converted into electrical energy. In electrical energy receivers, electrical energy is converted into thermal, light, mechanical and others. Electrical circuits in which energy production, transmission and transformation occur at constant currents and voltages are called direct current circuits.

An electrical circuit consists of individual devices or elements, which, according to their purpose, can be divided into 3 groups. The first group consists of elements intended for generating electricity (power supplies). The second group is elements that convert electricity into other types of energy (mechanical, thermal, light, chemical, etc.). The third group includes elements designed to transmit electricity from a power source to an electrical receiver (wires, devices that ensure the level and quality of voltage, etc.).

1.2 Energy sources EMF sources An EMF source is characterized by an EMF value equal to the voltage (potential difference) at the terminals in the absence of current through the source. EMF is defined as the work of external forces inherent in the source to move a single positive charge inside the source from a terminal with a lower potential to a terminal with a higher potential. Figure Designation of EMF source and galvanic element in circuits

DC circuit power sources are galvanic cells, electric batteries, electromechanical generators, thermoelectric generators, photocells, etc. All power sources have internal resistance, the value of which is small compared to the resistance of other elements of the electrical circuit. DC power receivers are electric motors that convert electrical energy into mechanical energy, heating and lighting devices, etc. All power receivers are characterized by electrical parameters, among which are the most basic voltage and power. For normal operation of the electrical receiver, it is necessary to maintain the rated voltage at its terminals. For DC receivers it is 27, 110, 220, 440 V, as well as 6, 12, 24, 36 V.

The terminal voltage of a real source depends on the current through the source. If this dependence can be neglected, then such a source is called ideal. On the design diagrams it is necessary to indicate the directions of voltages and currents (selected arbitrarily). Figure Scheme with a real EMF source

For real sources, let's write Ohm's law for a complete circuit: U= I ·R n (1.1) where I - current [A], E - emf [B], R - resistance [Ohm]. It follows: U=E-I×R BH (1.2) The voltage U at the terminals of a real source is less than the EMF by the amount of the voltage drop across the internal resistance. An ideal source has R in =0. The maximum current occurs in the mode short circuit at R n =0, in this case output voltage U also tends to zero.

1.2.2 Current source The current source is characterized by current I with short-circuited terminals (in the absence of voltage). If the current does not depend on voltage, such a source is called ideal. Figure Image of a current source in circuits

The current I of a real energy source depends on the voltage U at its terminals. From Ohm's law for a complete circuit: (1.3) where is the conductivity [Sm]. Figure Circuit with a real current source In this circuit, the element g in parallel connected to an ideal source J is called internal conductivity. An ideal current source has g in = 0 (that is, R in =).

1.2.3 Electric power Characterizes the energy generated by the source per unit time. For a real voltage source: P=E × I [W] (1.4) For a real current source: [W] (1.5) Load resistance Rn characterizes the consumption of electrical energy, that is, its conversion into other types at a power determined by the formula: [W] (1.6)

1.3 Generalized Ohm's law for a section of a circuit with EMF - direction from a point with a high potential to a point with a lower potential; - direction of current. Figure Unbranched circuit with EMF sources

(1.7) where: - total resistance of the circuit section; - voltage between the terminals of the section under consideration; - algebraic sum of the EMF acting in a given area. If the EMF coincides in direction with the current, then a sign is placed, if it does not coincide -. Conclusion: the current of a section of a circuit with EMF sources is equal to the algebraic sum of its voltage and EMF, divided by the resistance of the section.

1.4 The simplest transformations in electrical circuits Series connection of resistances The current flowing in the circuit is the same at any point. Figure Equivalent resistance when resistors are connected in series

1.4.2 Parallel connection of resistances Figure Parallel connection of resistances

For the equivalent resistance, we write the formula: (1.11) The equivalent resistance of a circuit consisting of parallel components is always less than the smaller resistance of the circuit. Therefore, with a parallel connection, the equivalent conductance of the circuit is equal to the sum of the conductances of the individual branches.

1.4.3 Replacing a current source with an EMF source Figure Replacing a current source with an EMF source The power balance is different in these circuits because different current flows through the resistance R. The result of solving a problem must always be reduced to the original diagram. For a circuit with a current source, the following relationship is valid: J - I total - I R =0 (1.12)

1.5 Connection measuring instruments to electrical circuits Before making measurements in electrical circuits, you need to decide on the following questions, based on the answer to which, a measuring device is selected: - direct or alternating current is present in this electrical circuit. If variable, then which one (signal shape, frequency); - what order of currents and voltages are there in this circuit; -what measurement error will satisfy us.

1.5.1 Voltage measurement To measure the voltage drop on any section of the circuit, connect a voltmeter in parallel to it, taking into account the polarity. The voltmeter has some internal resistance R v, therefore, during operation, part of the current from the electrical circuit will flow through the voltmeter, thereby changing the mode of the electrical circuit when the voltmeter is connected. This means that the measurement result will contain an error. Figure Measuring the voltage drop across R 2 with a voltmeter

Voltage on R 2, a circuit consisting of a source and series-connected resistances R 1 and R 2 without a voltmeter: (1.13) where R ext is the internal resistance of the source. Voltage on R 2, a circuit consisting of a source and series-connected resistances R 1 and R 2 with a voltmeter: (1.14) If, then In order for the voltmeter not to affect the circuit under study, they try to make the internal resistance of the voltmeter as large as possible.

1.5.2 Measuring currents To measure the amount of current flowing through a certain element of the circuit, an ammeter is connected in series with it in the open branch, taking into account the polarity. Since the ammeter has some resistance R A, its inclusion in an electrical circuit changes its mode, and the measurement result contains an error. Figure Measuring current with an ammeter

Current strength in a circuit consisting of a source and series-connected resistances R 1 and R 2 without an ammeter: (1.15) where R ext is the internal resistance of the source. Current strength in a circuit consisting of a source and series-connected resistances R1 and R2 with an ammeter: (1.16) Where R ext is the internal resistance of the source; R A - ammeter resistance. To reduce errors, they try to make the resistance of ammeters as small as possible.

1.5.3 Measuring Power To measure the power consumed by any circuit element, it is necessary for the meter to measure the voltage drop across it and the current through it and multiply these values. Wattmeters have four input terminals - two for current and two for voltage. Figure: Circuit diagram for connecting a wattmeter to measure the power consumed by R 2.

1.5.4 Bridge circuits Bridge circuits are used to measure resistance. ac, cb, ad, bd - bridge arms. ab, cd - diagonals of the bridge. Drawing of Wheatstone Bridge

To measure resistance with a balanced bridge, an unknown resistance is included in one of its arms. By adjusting any of the other arms, using known resistances, the balance of the bridge is achieved (i.e. when the voltmeter shows zero). After this, unknown resistance is found. For powering the bridge, the value of EMF E is not significant. It is important that there is no noticeable heating of the resistances, and that the sensitivity of the voltmeter is sufficient. The resistance of the measuring device also does not matter, because in a balanced state, the potential difference between points c and d is zero, therefore, no current flows through the voltmeter. Unbalanced bridges are also used, in which the arms are not adjusted, and the value of the unknown resistance is calculated according to the readings of a measuring device with a specially calibrated scale. When measuring with an unbalanced bridge, it is necessary to stabilize the EMF E. (1.45)

1.5.5 Compensation measurement method The EMF value is measured using potentiometers. The potentiometer is designed in such a way that when measuring the EMF value E x, there is no input current. Figure Potentiometer

Before work, the device is calibrated: to do this, turn the switch to position. Using R I, the operating current in the circuit is adjusted so that the voltage drop across the resistance R is equal to the value of the EMF of a normal NE element. In this case, the voltmeter should show zero. To measure the EMF E X, the switch is moved to position, using the calibrated slider slider R p, the voltmeter shows zero, and the readings of the device are read.

1. The concept of “Electrical circuit” 2. The main elements of an electrical circuit 3. What is commonly called “DC circuits”? 4.How is the “EMF source” characterized? 5.What does the voltage at the terminals of a real source depend on? 6.How is the “current source” characterized? 7. From Ohm's law for a complete circuit. 8.Calculation determination of conductivity. 9.What characterizes “Electric power”? 10. Generalized Ohm's law for a section of a circuit with an EMF. 11.Series connection of resistances. 12.Parallel connection of resistances. 13.Replacement of a current source with an EMF source, characteristics. 14.Connecting measuring instruments to electrical circuits. 15.Measurement of voltages, technique. 16.Measurement of currents, methodology. 17. Power measurement, methodology. 18.Bridge circuits 19.Compensation method of measurement CHECK QUESTIONS Notes, additions The section of an electrical circuit along which the same current flows is called a branch. The junction of the branches of an electrical circuit is called a node. On electrical diagrams, a node is indicated by a dot. Any closed path passing through several branches is called an electrical circuit. The simplest electrical circuit has a single circuit; complex electrical circuits have several circuits. Matched mode between the power supply and the external circuit occurs when the resistance of the external circuit is equal to the internal resistance. In this case, the current in the circuit is 2 times less than the short circuit current. The most common and simplest types of connections in an electrical circuit are series and parallel connections.

The elements of an electrical circuit are various electrical devices that can operate in different modes. The operating modes of both individual elements and the entire electrical circuit are characterized by current and voltage values. Since current and voltage can generally take on any values, there can be an infinite number of modes. Idle mode is a mode in which there is no current in the circuit. This situation can occur when the circuit breaks. The nominal mode occurs when the power source or any other circuit element operates at the values ​​of current, voltage and power specified in the passport of this electrical device. These values ​​correspond to the most optimal operating conditions of the device in terms of efficiency, reliability, durability, etc. Short circuit mode is a mode when the receiver resistance is zero, which corresponds to the connection of the positive and negative terminals of the power source with zero resistance. The short circuit current can reach large values, many times higher than the rated current. Therefore, short circuit mode is an emergency for most electrical installations.

References Main 1. Fundamentals of circuit theory. G. V. Zeveke, P. A. Ionkin, A. V. Netushil, S. V. Strakhov. M.: Energoatomizdat, 1989, 528 p. 2.Theoretical foundations of electrical engineering. Volume 1. L. R. Neiman, K. S. Dimirchyan L.: Energoizdat, 1981, 536 p. 3.Theoretical foundations of electrical engineering. Volume 2. L. R. Neiman, K. S. Dimirchyan L.: Energoizdat, 1981, 416 p. 4.Theoretical foundations of electrical engineering. Electrical circuits. L. A. Bessonov M.: Higher. school, 1996, 638 p. Additional 1. Fundamentals of the theory of electrical circuits. Tatur T. A. Higher school, 1980, 271 p. Collection of problems and exercises on the theoretical foundations of electrical engineering. /Ed. P. A. Ionkina. M.: Energoizdat, 1982, 768c Guide to laboratory work on the theory of linear circuits of direct and sinusoidal current. /Ed. V. D. Eskova - Tomsk: TPU, 1996, 32 pp. Guide to laboratory work on steady-state modes of nonlinear circuits and transient processes in linear circuits. /Ed. V. D. Eskova - Tomsk: TPU, 1997, 32 p.

Class: 8

Presentation for the lesson

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Lesson type: lesson of learning new material and primary consolidation.

Target: study the components of an electrical circuit, symbols used in diagrams.

Tasks:

• Educational– provide perception, comprehension and primary consolidation components electrical circuit, their purpose and symbols.
• Educational– contribute to instilling compliance with safety rules when assembling a chain, and interest in physics.
• Developmental- contribute to the development of the ability to assemble electrical circuits, depict electrical circuit diagrams.

Lesson plan.

1. Organizational moment (1 min.)
2. Updating knowledge. (8 min.)
3. Learning new material. (12 min)
4. Consolidation of knowledge. (15 min.)
5. Stage of primary knowledge testing. (5 min.)
6. Homework. (1 min.)
7. Lesson summary. (1 min.)
8. Reflection. (2 min.)

Equipment: galvanic element, light bulb, key, connecting wires, plates with symbols of EC elements, control table, computer, multimedia projector.

Lesson progress

1. Org. Moment (explain group work)

Electricity all around
The factory and house are full of them.
Life is radically easier!
It's amazing
For our benefit,
Farewell to your Majesty
It's called electricity!

2. Updating knowledge.

Each group is asked to choose a sheet with the question:

• What is electric current?
• What conditions are necessary for the existence of electric current?
• Why is electric current needed?
• Direction of electric current?

(To prepare students for the State Examination, it is necessary to include in various stages of the lesson and homework a variety of tasks that will contribute to the development of methodological knowledge and skills - a task with a choice of answers, the level of proficiency in experimental skills, the ability to solve a qualitative problem, as well as tasks on working with text of physical content.)

When repeating the material, students are offered the following task: (slide 2)

3 . Using the letters on the lines, write the names of the current sources:

Slide 3

4. Studying new material.

Lesson topic:"Electric circuit."

Open your notebooks and write down the topic of the lesson. A set of devices through which electric current flows is called electrical circuit. Circuits can be simple (as in the demonstration) or complex (electrical wiring), but in all of them the component parts can be identified. Devices that use electrical energy are called consumers. This is the first component of the chain. Give examples of consumers... in the classroom... at home... on the table... (for L.R. light bulb). The second component of the circuit is the current source (for l.r. - a galvanic element). The current source is connected to the circuit last using connecting wires - this is the third component of the circuit. There is another important part of the electrical circuit. In Paris in 1881, at the electrical exhibition, everyone was delighted with this invention. This is a switch. Its role is to close and open the electrical circuit. In technology, different types of closing and breaking devices are used. For there to be current in the circuit, it must be closed, i.e. consist of conductors of electricity. If the wire breaks at any point, the current in the circuit will stop. This is what the switches operate on. Name the closing devices in the classroom (switch, knife switch, buttons, for l.r. - key) slide 4.

Please note: the circuit is assembled with the switch open; The switch is made of electrical conductors, and you need to touch the insulating handle.

So, what are the components of an electrical circuit? Write in your notebook:

• consumer
• current source
• connecting wires
• closing device

On your desk is a page from G.N.’s textbook. Stepanova, the peculiarity of the textbook is that in each paragraph there is keyword, in the first, for example, “Electric circuit”, we will place it in the center. In the rest, the constituent blocks are chains. In the margins is what is included in the blocks and how it is indicated on the diagram. On the table for each group there is a netbook, on the desktop there is a file with the word cluster. Open it and create a cluster using the tutorial.

Electrical circuits can be complex. The TV is out of order, and you need information about what the electrical circuit consists of, and the information is contained in electrical diagrams. Electrical diagrams are drawings that show how to connect elements of an electrical circuit.

Guys, you have to do practical work.

What safety rules will you follow?

Practical work.

Target: assemble an electrical circuit from the devices that everyone has on their tables so that the light bulb lights up.

A simple circuit is assembled in groups (current source, lamp, key, connecting wires)

Getting the job done. Drawing up a diagram. The teacher checks.

5. Stage of initial knowledge testing.

Individual tasks: arrange the condition. designations by “place”, connecting with an arrow by convention. designation with the name of the device.

Let's check using control table:

Errors				> 4
Grade

Lecture No. 1

Lecture No. 1
Topic: “Basic
theory concepts
electrical
chains"

Study questions

1. Introduction.
2. The concept of an electrical circuit.
3. Basic electrical quantities:
electric current, voltage,
EMF, power and energy.
4. Idealized passives
elements. Real equivalent circuits
elements of electrical circuits.
5. Idealized active elements.
Equivalent circuits for real sources.

Literature

1. Popov V.P. Circuit Theory Basics:
Textbook for universities special.
"Radio Engineering". - M.: Higher School,
2007, p. 6-36.
2. Kasatkin A.S., Nemtsov M.V.
Electrical Engineering: Textbook for
non-electrical students
specialties of universities. – M.: Higher
school, 2003, p. 4-15.

Content and subject of the discipline
"Theory of Electric Circuits"
The content of the discipline consists of tasks
analysis and synthesis of linear and nonlinear
electrical circuits, studying how to
qualitative and quantitative side
established and transient processes,
flowing in various electronic
instruments and devices.
The subject of circuit theory is the development of engineering
methods for studying processes in electrical engineering and
radio-electronic devices based on replacing these
devices with simplified models, the processes in which
are described in terms of currents and voltages.

Electrical circuit composition

GOST R52002-2003
"Electrical engineering.
Terms and
definitions
basic concepts"
Electric
chain
Electric circuit –
This
totality
devices
And
objects,
forming
path
For
electrical
current,
electromagnetic
processes in which they can
be described using
concepts
about
electromotive
strength,
electrical
current
And
electrical voltage.
Sources
electrical
energy
Receivers
electrical
energy
Auxiliary
elements

Serial connection
conductors
Schematic diagram
Wiring diagram

Parallel connection
conductors
Schematic diagram
Wiring diagram

Basic assumptions and
principles of circuit theory
Circuit theory assumes:
Each element of the chain is fully characterized
relationship between current and voltage on
its clamps, while the processes taking place
inside elements are not considered.
Based on the theory of electrical circuits
lies the principle of modeling. IN
in accordance with this principle, real
circuit elements are replaced by their simplified ones
models built from idealized
elements.

Idealized bipolar elements

IDE
Ideal
resistor
Perfect
inductive coil
Ideal
capacitor
Ideal
source
voltage
Ideal
source
current

The concept of electric current

Electric conduction current is a directional phenomenon
free carrier movements electric charge V
substance or in emptiness, quantitatively characterized
scalar quantity equal to the time derivative of
electric charge carried by free
charge carriers through the surface under consideration.
q dq
i(t)lim
t 0 t
dt
q q
i(t) I const
t t
Direct electric current is something that does not change over time.
unidirectional movement of charged particles (charges).
Conditional positive direction of current in calculations
electrical circuits can be selected completely
arbitrarily.

Electrical quantities and units
their measurements
The instantaneous current value is
rate of charge change in
time:
q dq
i lim
.
t 0 t
dt
Andre-Marie
Ampere 1775 - 1836
The SI unit of current is
ampere (A).
Electrical engineering and electronics
Slide 4
Dovgun V.P.

Current strength. Units of current. Ammeter.
The charge flowing through a given cross-section of a conductor in
unit of time, characterizes electric current.
The current in the circuit is measured with a special device - an ammeter.
Connection diagram: the ammeter is connected to the electrical
circuit in series with the element in which it measures
electric current.
Ammeter - electrical appliance to measure current.
Ammeter
Ammeter
laboratory technical
Ammeter
demonstration
AMPER Andre Marie
(22.I 1775 - 10.VI 1836)
French physicist
mathematician and chemist
Conditional
designation on
diagrams

Concept of voltage

1
A
A E dl FE dl
qA
q
A
B
Edl
B
IN
u A B E dl
A
Electrical voltage between points A and B of an electrical circuit
(or the potential difference between points A and B) is work
made by electric field forces to move
unit positive charge along an arbitrary path from
point A to point B of the field and equal to the linear integral
electric field strength.

Concept of voltage

w dw
u lim
q 0 q
dq
Voltage between points A and B of the electrical
circuit can be defined as the limit
electric field energy ratio w,
spent on transferring positive
charge q from point A to point B to this charge at
Voltage unit
in the SI system - volt (V).
q 0

Luigi Galvani (1737-1798)

Luigi Galvani's experiment with frog legs

Alessandro Volta(1745-1827)

Galvanic (or chemical) cell
Alessandro Volta

The concept of EMF

Electromotive force –
scalar quantity,
numerically equal to work
outside forces
spent on
movement of a single
positive charge
inside the source from
clamping with less
terminal potential with
great potential.
Regardless of the nature of external forces, EMF source
numerically equal to the voltage between the source terminals
energy in the absence of current in it, i.e. in idle mode
progress.

Electrical voltage. Units
voltage. Voltmeter
Voltmeter –
electric
device for
measurements
voltage.
.
Connection diagram:
the voltmeter is turned on
electrical circuit
parallel to that
element on which it
measures voltage.
Symbol on
diagrams
VOLTA Alessandro (1745-1827) Italian
physicist and physiologist
Technical voltmeter
Voltmeter
laboratory
Laboratory voltmeter

Concept of power and energy

w dw
u lim
q 0 q
dq
dw udq uidt
Energy,
spent on
moving
charge:
dw dq dw
pui
dq dt dt
q
w udq
0
t
uidt

Concept of power and energy

Instantaneous power
chain section:
dw
p
ui.
dt
t
w(t)
pdt
Power
measured in
watts (W)
James Watt
1736 – 1819
Energy
measured in
joules (J)
W w(t 2) w(t1)
t2
pdt
t1
James Joule
1818 – 1889

Experimental determination of power
electric current
P U I
1W 1V A

An electrical circuit can be a consumer and
source of energy
If the signs match
voltage and current power
positive. This
corresponds to consumption
energy section of the circuit.
If the signs do not match
voltage and current power
negative. It means,
that the chain section is
source of energy.
pui 0
pui 0

Resistive element
Resistive element –
idealized element
which only happens
irreversible transformation
electromagnetic energy in
heat and other types of energy.

Conventional graphic designation and current-voltage characteristic of a resistive element

Resistive element
Current-voltage characteristics of nonlinear
resistive elements
Incandescent lamp
Semiconductor diode

Resistive element
If the current-voltage characteristic is straight, passing
through
start
coordinates
That
The resistor is called linear.
Ohm's Law:
u R Ri R
i R Gu R
R – resistance
Georg Simon Ohm
1789 – 1854
u Ri
The unit of resistance is Ohm.

Resistive element
Ohm's Law:
i Gu
Conductivity:
G 1
Werner von Siemens
1816-1892
R
Conductivity unit – Siemens
(Cm).
Electrical engineering and electronics
Slide 14
Dovgun V.P.

Electrical resistance. Units
resistance. Ohm's law for a section of a circuit.
An ohmmeter is an electrical device for measuring the resistance of a conductor.
Definition: resistance is a measure of the counteraction of a conductor
establishing an electric current in it.
Designation: R.
Unit: 1 ohm.
Defining formula:
U
R
I
Ohm Georg Simon
(1787-1854)
German physicist
- specific resistance of the substance,
l is the length of the conductor, S is the area of ​​the transverse
conductor cross sections.
Connection diagram:
ohmmeter turns on
similar to an ammeter
together with a current source
and a variable resistor,
necessary for
setting the scale zero.
Conditional
designation on
diagrams
Laboratory ohmmeter

Electrical heating of conductors
electric shock Joule-Lenz law.
U I R
A IUt I IRt I Rt
2
PR u R iR Ri R2 GuR2
t
t
t
WR (t) PR dt R i dt G u R2 dt 0
2
R
JOLE JAMES
PRESCOTT
(1818–1889), English
physicist
Lenz Emilius
Khristianovich
(1804-1865),
Russian
physicist
U
I
R
U
U 2t
A
Ut
R
R

Work of electric current
!
A Pt
1 J 1 W s
1Wh 3600 J
1kWh 1000Wh 3600000 J

Inductive element

Li
Weber-amp
characteristic
N
F
k 1
To
NF

d
e
dt
Michael Faraday (1791-1867)

Law of Electromagnetic Induction
Michael Faraday (opened 1831)
d
e
dt
diL
u L e L
dt
1
iL
L
t
u
L
dt
diL
PL u L iL LiL
dt
This law establishes the relationship between magnetic and
electrical phenomena.
Formulation: EMF of electromagnetic induction, in
contour is numerically equal and opposite in
sign of the rate of change of magnetic flux
through the surface bounded by this contour.

Capacitive element

q=CUс
duC
iC C
dt
iC
dq
dq duC
dt
duC
dt
uC
1
C
t
i
C
dt
duC
PC uC iC uC
dt

Equivalent circuits of real elements of an electrical circuit

CONCLUSIONS: 1.The higher the required accuracy, the greater the number
factors are taken into account, and the more complex the scheme will be
replacement of each element.
2. In order to reduce the complexity of calculations, they strive to use
simplified equivalent circuits containing minimal
allowed number of elements.
3. Equivalent circuits of the same element may have different
type depending on the frequency range under consideration.

Ideal voltage source (source
voltage, emf source) is
idealized active element, voltage
at the terminals of which does not depend on the current through these
clamps.
u=e(t)
2
2
p
1
R
u
1
R
e
(t)
i u / Rн (1 / Rн)e(t)
n
n
The ideal voltage source can be
viewed as a source of energy, internal
whose resistance is zero.

Ideal current source (current source) -
it is an idealized active element,
whose current does not depend on the voltage on
his clamps.
i=j(t)
u Rнi Rн j (t) p Rнi 2 Rн j 2 (t)
An ideal current source can be considered as a source
energy with infinitesimal internal conductivity
(infinitely large internal resistance).

Equivalent circuits for real sources

External characteristics of real sources

U E RinI
E
J
R in n
I J Gв nU
G in n
1
R in n
J
E
G in n
R in n
1
G in n

Thank you for your attention!!!

Basic Concepts of Circuit Topology

The chain node is
independent if
attached to him though
there would be one new branch, no
matching earlier
considered
nodes.
The circuit circuit is
independent if he
contains at least one
new branch, not
included in earlier
considered
contours.

Component equations of idealized elements

uL L
diL
dt
uR = RiR
iR = GuR
iR
t
iL
1
u L dt
L
uR
R
uR
i
G
u = e(t)
i = j(t)
duC
iC C
dt
uC
1
C
t
i
C
dt
u = E – Ri i
i=J–Giu

Mathematical modeling of electrical circuit branches based on component equations

u1 R1i1 L1
u 2 R2i2 ;
di3
u3 L3
;
dt
1
u 4 R3i4
C
di1
e;
dt
t
i
4
dt.

Kirchhoff's first law

Kirchhoff's first law is the law
balance of currents in a branched circuit,
is formulated for the nodes of an electrical circuit.
It reads: the algebraic sum of the currents in
any node of the electrical circuit in any
moment of time is equal to zero, i.e.
m
i
k 1
k
(t)0
I1 – I2 – I3 +J = 0.

Kirchhoff's second law

Kirchhoff's second law is the law
stress balance in closed areas
circuits, formulated for circuits
electrical circuit.
It reads: algebraic
sum
voltage in any closed
circuit at any time
equal to zero:
n
u
k 1
k
(t)0

Kirchhoff's second law

Second formulation of the second
Kirchhoff's law: algebraic
the amount of emf in any closed circuit
circuit circuit at any time
time is equal to algebraic
the sum of the voltage drops on
elements of this circuit:
m
e
k 1
k
n
(t) u k (t)
k 1

Example 1.

uR1 uba uJ uR 2 u12 uR3 ucd uR 4 0
e1 e4 R1i1 u J u12 R2i2 R3i3 R4i4

Example 2.

1
di
Ri idt L
e(t)
C
dt

Main problems of circuit theory

x(t) x1 (t), x2 (t),..., xn (t)
S (t) s1 (t), s2 (t),..., sm (t)
Circuit analysis problems are problems in which
known to external influence x(t),
circuit configurations and parameters are determined
chain reaction S(t).
Synthesis problems are problems that require
determine the structure and parameters of the circuit by
given chain reaction S(t) to some
external influence x(t).