Elements of the circuit diagram. Electrical circuit and its components
Real electrical circuit - a set of devices designed for transmission, distribution and transformation of energy. Contains sources of electrical energy, receivers of electrical energy, measuring instruments, switching equipment, connecting lines and wires. Electrical circuitis a set of connected in a certain way, consumers (or respectively active and passive elements) and converters of electrical energy. The chain is called passiveif it consists only of passive elements, and activeif it also contains active elements.A source of electrical energyis called an element of an electrical circuit that converts non-electrical energy into electrical energy. Consumer of electrical energyis called an element of an electrical circuit that converts electrical energy into non-electrical energy. Electric energy converteris called a device that changes the amount and form of electrical energy.
A magnet that moves near an electrical circuit, such as a coil, generates an electrical current in that circuit that circulates in the opposite direction to the displacement of the magnet. It is this phenomenon that allows the production of generators and electric motors.
In a power plant generator, these are electromagnets that rotate inside the coil and generate alternating current inside a coil connected to an external circuit. When the coil is connected to an external circuit, a current is generated which, like electromotive force, will vary depending on the sinusoidal function as shown in the figure. This current is called sinusoidal alternating current. Alternating current is a variable that changes over time according to sinusoidal variation, which is a function of amplitude and frequency and phase, which depends on the beginning of time.
In order to perform the calculation, it is necessary for each electrical device to present it equivalent circuit... The equivalent circuit of an electric circuit consists of a set of idealized elements (resistor, capacitor, inductor).
Voltage :
The relationship between current and voltage on a circuit element is called current-voltage characteristic (VAC)element, which is usually depicted graphically.
It is characterized by a period, which is the time interval between two successive peaks, and a frequency, which is the number of periods per unit of time. Frequency is a constant across the entire length of the network because all generators rotate at the same speed. There are two main frequency values \u200b\u200bin the world.
In electrical systems, sinusoidal alternating current is the most common form of generation, transport, and use of electrical energy. There is, however, another form of current and voltage at which electric Energy can be produced, transported and used: direct current. Its main characteristic, like voltage, is that its amplitude is constant over time.
As a consumer in the theory of electrical circuits direct current there is a resistor characterized by resistance (R), for which Ohm's law is valid:
Idealized current sourceIs a circuit element, the current of which does not depend on voltage and is a given constant value.
With a real current source, the generated current decreases with increasing voltage. Any real current source can be converted to an idealized one as follows:
Receiver-level application
There are two types of devices at this level. Appliances operating on alternating current directly under mains voltage: lighting, heating and all receivers containing motors. Also in industry, all devices that operate with motors or require high power are supplied with alternating current. Electronic receivers do not work in alternating current, but only in direct current low voltage... They operate on AC power from an AC outlet using a special device called an AC adapter that switches AC power from the AC outlet to DC. In most electronic devices, the adapter is built into the device that is powered by the power supply. The superposition of two currents of a different nature, such as direct current and alternating current, may be surprising, because it includes conversion devices for using one from the other.
Combining these two formulas, we get:
For a counter current source
The combined form of the generalized Ohm's law for branches containing a current source:
Where the upper mark corresponds to the diagram in which U J and J co-directed.
Electrical circuit structure.
Branchan electrical circuit is called a section, the elements of which are connected in series one after another and are flowed around by the same current.
In fact, this existence is historical. The first use of electricity was in urban lighting, developed in New York by Thomas Edison and in Grenoble by Aristide Berges. They were in direct current produced by the Gramme load cells (article 026). The increasing demand for power to power installations has led to an increase in current intensity, which required an increase in the diameter of the conductors and, therefore, their weight and price, which led to a blockage situation.
It was then that we saw the emergence of alternating current generated by generators with a rotating field in connection with the discovery of a transformer by Lucien Gaoulard and Josiah Willard Gibbs, which allowed the voltage to be changed according to needs. It was then possible to produce at low or medium voltage, and then, for transportation, raise the voltage to limit losses and cross-section of conductors, and finally use it to lower the voltage to adapt it to the characteristics of the receiving device.
Knotan electrical circuit is the junction of several branches. A node connects at least three branches and is a branch point.
Branches are considered connected consistently,if they are flown around by the same current. Branches are considered connected parallel,if they are attached to the same pair of nodes.
Nikola Tesla proposed this type of current. For commercial reasons, Thomas Edison rejected that he killed animals in a public square to demonstrate the dangers of high tension. However, it was alternating current, which for economic and practical reasons prevailed and became a versatile means of production, transportation, and in most cases using electricity.
Today, however, electricians are rediscovering direct current thanks to the evolution of technology that allows high-voltage direct current installations, which gives him a new interest in long-distance transport or in underground or underwater connections. The material consists of chemical elements... The smallest element is the atom.
Outlinean electrical circuit is called a set of successive branches. The nodes at which these branches connect are branch points. When traversing closedthe contour start and end points are the same.
A chain in which there are no branches is called single-circuit,if there are branches - multi-circuit.A multi-circuit chain is characterized by the number of independent circuits. The set of independent contours is determined by the fact that each of the subsequent contours, starting from the elementary one, differs in at least one new branch. The number of independent contours can be determined by the Euler formula:
The atom itself is made up of electrons, protons, and neutrons, which serve as the glue between the protons. The atomic nucleus is shown in blue. Electrons are very small particles, negatively charged, that revolve around the core, like satellites around the Earth.
On the other hand, protons are positively charged. Electrons are easily detached from an atom and can be loaded onto another atom. When an overloaded surface of electrons is brought into contact with a surface that is discharged in electrons, it causes sparks and cracks: electricity.
Some substances are attracted to light objects after friction. You can rub a balloon on a sweater and then imagine it over the head of someone with short hair. When you take off your acrylic sweater, electrons come off and, for example, are applied to your hair. Then you hear wheezing. If you are in the dark, you may see small sparks such as lightning.
When parallel connection, the role of equivalent conductivity (or the conductivity of an equivalent consumer) is played by the sum of the conductivities of all consumers (Fig. 1.12.).
9-10) Equivalent transformation "Star - triangle"
In knots a, b, c both the triangle and the star in fig. 1.14. connect to the rest of the circuit. The transformation of a triangle into a star should be such that for the same values the potentials of the points of the same name of the triangle and the star, the currents flowing to these points were the same, then all external circuit Will not "notice" the replacement.
In thunderclouds, strong air currents cause friction between water or ice particles. These clouds form positive and negative layers. Lightning then occurs inside clouds or between a cloud and the ground. An average thunderstorm produces electricity from a small nuclear power plant.
You can move and control the direction of moving electrons. A constant stream of electrons is called electric shock... The element that organizes the movement of electrons is called a generator. Conductive materials are composed of atoms that have at least one mobile electron that can freely circulate from one atom to another.
Let us express U ab of the triangle through the parameters of consumers and the currents flowing to these nodes. Let's write Kirchhoff equations for the contour and nodes a and b.
Replace currents in the first equation I 3 and I 2 to the corresponding expressions:
Now we get an expression for the same voltage when connecting consumers with a star:
Thus , the resistance of the star beam is equal to the product of the resistances of the adjacent sides of the triangle divided by the sum of the resistances of the three sides of the triangle.
Electric current is a constant stream of electrons, which moves in a circuit always in one direction, and the number of electrons in circulation is measured in watts. In "power plants" several very powerful magnets rotate in several coils, which have thousands of revolutions, the flow of electrons becomes significant.
All circuits contain a power source, a conductor in which a current can flow, and one or more resistors. Why start an Equipment course with electronics concepts? It will also be necessary to know the characteristics of the various components, which, even when they are very complex, are produced from a small number of basic components: resistors, capacitors, coils, semiconductors, that's all! But this is also the minimum base.
The inverse transformation formulas can be derived independently, or as a consequence of the relations through the conductivity:
Or through resistance:
11) Power balance.
According to the Joule-Lenz law, all electrical energy imparted to a conductor as a result of the work of forces electric field, turns into heat energy:
Finally, we will need to use a multimeter to take measurements such as voltage or checking a pin or cable. Some concepts about the units used by electricians won't be too big. Electric charge is a property of some elementary particles... In ancient times, the Greeks observed the appearance of these charges by rubbing amber on fabric. Amber loaded in this way can attract light objects. This force of attraction is comparable to the attraction of masses if there are two types of electric charges, and it is observed that these electrostatic forces are attracted and repelled.
According to the generalized Ohm's law.
Hence follows the law of conservation of energy, according to which the algebraic sum of the powers supplied to all branches of the branched electric circuit is equal to zero:
There is another form of recording the power balance:
On the left side, the powers of the energy sources are summed up, and on the right side - the powers converted into heat in consumers. Capacities that give off energy are taken with a "+" sign, and those working in the mode of consumers - with a "-" sign.
It would be Benjamin Franklin, in particular his experiments on lightning, who, after studying electrical charges, arbitrarily decided to name some positive and other negative ones, which allowed him to state his behavior: accusations of opposite signs attract those who have the same signs reflect themselves.
We've all seen and redone the experience of rubbing a plastic object against a cloth to electrify it and attract small pieces of paper. This experience is only possible when using insulating materials. Electrical loads can build up locally and dissipate in the conductor.
12) Calculation of unbranched electrical circuits
The basis for calculating single-circuit (unbranched) electrical circuits containing sources of both types and consumers is the Ohm and Kirchhoff laws considered earlier.
If there is no chain current sources, and consumer parameters ( R)and voltage sources ( E) are given, then the task is usually to determine the loop current. The positive direction of the desired current is chosen arbitrarily and an equation is drawn up:
Phenomenon static electricity located at the beginning of lightning, it is also a source of electrical discharges when we take out the clothes dryer and discharges that sometimes surprise us when we get out of the car. Electricity static can also occur when feet are attached to carpets in dry weather conditions. This phenomenon can be dangerous for electronic components and technicians, before touching electronic cards, be sure to carry these loads too important for some sensitive components.
Static electricity is used in some devices, mainly for us, copiers and laser printers. Displacement of free electrons in a conductor. To be accurate enough, we must talk about electric charges... Usually these are electrons in a metal conductor, but sometimes they are ions, i.e. electrically charged atoms. This occurs in the case of electrical discharges in an ionized gas or ions in an electrolyte.
If in the circuit, except for the consumer ( R) and EMF sources ( E), there is a current source ( J), then the problem is usually reduced to determining the voltage at the current source U J because loop current I coincides with the specified source current J. Positive polarity U J is chosen arbitrarily, but it is preferable to put a "+" sign at the arrowhead (this polarity corresponds to the formula:). True polarity U J coincides with the selected one if during the calculation U J is expressed as a positive number, and is opposite to the chosen one if U J. Desired voltage drop across the current source U J in the absence of EMF sources is determined by the formula.
Free electrons are electrons that easily remove their original atoms. Free electrons are found in conductive materials, mainly metals. Insulators are made up of atoms that do not easily pass through their electrons. The flow of current is practically impossible, there is no perfect conductor, and conversely, insulators are also not perfect.
Consider starting the simplest electrical circuit: a simple cycle. On the left, the electrical generator acts as a pump that will circulate the "electrical fluid" provided the loop is not interrupted by the breaker. It is interesting to draw an analogy between the current in an electrical circuit and the circulation of fluid in a hydraulic circuit. This comparison allows you to better imagine what voltage and current are.
13) Proportional value method.
In the branch farthest from the source ( R 6) are set by some current or voltage value. For convenience of calculations, this is usually 1A or 1B. Then, moving to the beginning of the circuit, the currents and voltages of all branches are determined in turn up to the branch containing the source. This determines what voltage U input and current I in x ... must have a source in order to induce in all branches the currents and voltages of the calculated values. If EMF ( E) or driving current ( J) do not coincide with these values, then it is necessary to proportionally change the calculated values \u200b\u200bof the currents and voltages of the branches by multiplying them by the ratio or.
However, the comparison between a hydraulic circuit and an electrical circuit has some limitations. Water moves to unoccupied spaces, such as empty pipes or open air leaving a tap. Electricity, on the other hand, must move in a closed loop of conductive materials.
The voltage is similar to the pressure difference between the two points in the hydraulic circuit that cause the fluid to circulate, from the point where the pressure is highest to the very low pressure... The voltage or potential difference is expressed in volts.
I 3 can be determined by Kirchhoff's I law:
U 24 is determined according to Kirchhoff's II law:
14) The method of equivalent transformations. Formula of currents in parallel branches.
A branched circuit with a single source is usually simplified by converting to an unbranched one.
Further calculation:.
Current I 3 determined by Kirchhoff's law:
When making calculations it is convenient to use formula for currents in two parallel passive branches... Let's deduce it on the example of a circuit. Ohm's law voltage is determined by the formula
15) The method of Kirchhoff equations.
Designate the currents of the branches and arbitrarily choose their positive direction.
Freely select pivot node and population p \u003d m - n +1 independent circuits.
For all nodes, except for the reference one, draw up equations according to Kirchhoff's I law. There should be such equations ( n -1).
For each selected contour, draw up equations according to Kirchhoff's II law. There should be such equations p.
System m Kirchhoff equations with m unknown currents are solved together and the numerical values \u200b\u200bof the currents are determined.
If necessary, calculate the branch voltages or the potential difference of the nodes using the generalized Ohm's law.
Check the correctness of the calculation using the power balance.
16) Loop Current Method
Loop currents are taken as the sought ones. The number of unknowns in this method is equal to the number of equations that would have to be drawn up for the scheme according to Kirchhoff's II law, i.e. ... Based on Kirchhoff's II Law
From the found loop currents using the I Kirchhoff's law, the currents of the branches are determined.
Thus, the method for calculating a DC circuit using the loop current method is as follows:
Randomly select a population p independent circuits, apply on the circuit the positive direction of the circuit currents flowing in the selected circuits.
Determine own, general resistances and contour EMF and substitute them into a system of equations of the form.
Intrinsic loop resistance (R ii ) is the arithmetic sum of the resistances of all consumers located in ith contour.
Contour EMFrepresent an algebraic sum EMF sourcesincluded in the contour. With the “+” sign, this sum includes the EMF of sources acting in accordance with the bypass of the circuit, with the “-” sign, the EMF of sources acting in opposite directions.
Solve the resulting system of equations for loop currents using Cramer's method.
Determine the currents of the branches through the loop currents according to the I Kirchhoff's law.
Check the correctness of the calculations using the power balance.
17) Method of nodal potentials.
In the event that p-1 - number of nodes, p - the number of independent loops), this method is more economical than the loop current method. Derived from the first Kirchhoff's law and the generalized Ohm's law (through potentials).
The intrinsic conductivity of the node (G ii )
is the arithmetic sum of the admittances of all branches connected in ith node.
Designate all branch currents and their positive direction.
Freely select a reference node (?
n )
and number all the others ( n-1)-e nodes.
Determine the intrinsic and total conductivity of the nodes, as well as the nodal currents, i.e. calculate the coefficients in the system of equations.
The total conductivity of the i-th and j-th nodes (G ij \u003d G ji ) is the sum of the admittances of the branches connected simultaneously to i-oh and j-th nodes.
The conductances of the branches with current sources are assumed to be zero and are not included in the intrinsic and general conductances!
Nodal current (J ii ) consists of two algebraic sums: the first contains the currents of the current sources contained in the branches connected in i -ohm node; the second is the product of the EMF of voltage sources by the conductivity of the corresponding branches connected in i -ohm node. With a "+" sign, this amount includes E and J sources, action
Classification of electrical circuits and their elementsin
Electric circuitcall a set of devices and objects intended for the distribution, mutual transformation and transmission of electrical and other types of energy and (or) information... The circuit performs its purpose when there is an electric current in it. Electromagnetic processes in a circuit and its parameters can be described using integral concepts known from the course of physics: current, voltage (potential difference), charge, magnetic flux, electromotive force, resistance, inductance, mutual inductance and capacitance.
It should be noted that it is in field theory that the definition of integral concepts (such as current and voltage) characterizing an electrical circuit is given. Calculation of circuit parameters (resistances, inductances, capacitances) in the general case is also possible only with the help of concepts used in field theory.
An electrical circuit consists of individual parts (objects) that perform specific functions and are called circuit elements.
The main elements of the circuit are sources and receivers of electrical energy ( signals).
Energy sources (signals ) , such as electromechanical or electronic generators, batteries, galvanic cells, temperature sensors, etc., are designed to convert various types of energy into electrical energy.
Energy receivers (signals ) serve to convert electrical energy into other types of energy. These include electric motors, heaters, electric lamps, cathode ray tubes, dynamic speakers, and more.
In addition to the main elements, the circuit contains various auxiliary elements that connect sources to receivers (connecting wires, transmission lines), suppress or amplify certain signal components (filters, amplifiers), change the voltage and current level in other parts of the circuit (transformers), improve or change the characteristics and parameters of the sections of the chain and its elements (correcting devices, phase links), etc.
By purpose, there are circuits for the transmission and conversion of electrical energy (circuits used in the electric power industry) and circuits for the transmission and conversion of information (circuits in communication technology, radio circuits, circuits of automation and telemechanics devices, etc.).
Chains can be classified according to the type of elements they are made of, for example resistive circuits - circuits consisting of resistors and energy sources, electronic circuits - circuits containing vacuum tubes and transistors, etc.
Each element of the chain can be allocated a certain number clamps (poles, leads),with the help of which it connects with other elements.
Distinguish between two-pole and multi-pole(three-pole, four-pole, etc.) circuit elements. Two-pole elements have two terminals; these include energy sources (with the exception of polyphase and controlled sources), resistors, capacitors, inductive coils.
The most common three-pole elements are vacuum tubes (vacuum triodes) and transistors (semiconductor triodes). four
Examples of four-pole elements are transformers (two-winding), bias inductive coils (bias chokes), integrated operational amplifiers.
Circuit elements with more than four clamps are also used (for example, multi-winding transformers, various micromodules - solid-state electronic components, multi-electrode vacuum tubes).
Distinguish active and passive circuit elements... Energy sources belong to active elements. Often, active elements are also called vacuum tubes, transistors, operational amplifiers, which are capable of amplifying electrical signals. Passive elements are those in which energy dissipates and (or) accumulates (resistors, inductive coils, capacitors, transformers).
If an element of a circuit is characterized by linear algebraic or differential equations (with the previously mentioned idealization), then it is called linear... The coefficients connecting voltages and currents and their derivatives represent the parameters of the element. Linear element parameterscan be constant (stationary element) or can change depending on time according to some law (non-stationary, parametric element).
If an element of a circuit is described by nonlinear algebraic or differential equations, then it is called nonlinear. Nonlinear features can also be parametric.
In many cases, the parameters of an element are considered as lumped (an element with lumped parameters); the voltages and currents at the terminals of the element are not functions of the spatial coordinates that determine the geometric dimensions of the element. Element parameters can also be distributed (element with distributed parameters); such an element is characterized by equations in which voltages and currents depend on spatial coordinates. As examples of elements with distributed parameterscan be called energy and information transmission lines, multilayer film resistive-capacitive microstructures.
Elements of an electrical circuit may or may not satisfy the principle of reciprocity. Simplified, the principle of reciprocity is as follows: the reaction of the circuit in section 1 from the disturbance in section 2 is equal to the reaction in section 2 from the same disturbance in section 1. The mathematical formulation of this principle and its illustrations are given below. In accordance with this, mutual and non-reciprocal elements are distinguished. Examples of reciprocal elements are resistors, inductive coils, capacitors, transformers; non-reciprocal elements include vacuum tubes, transistors, etc.
If a circuit contains one or more parametric elements, then it is called parametric (non-stationary).
Similarly, if a circuit contains one or more non-linear elements, then it is called non-linear. For a nonlinear circuit, the superposition principle is generally not applicable.
You can also talk about active and passivechains. A circuit is considered active if, in relation to some terminals, it is a source of energy. This chain contains active elements. Otherwise, the circuit is called passive.