What electric current is called direct. Constant electric current. main points

4.1. Characteristics of electric current. The condition for the existence of conduction current.

Electricity- ordered movement of charged particles. Electric current arising in conducting media as a result of the ordered movement of free charges under the action of electric field created in these environments is called conduction current. In metals, current carriers are free electrons, in electrolytes - negative and positive ions, in semiconductors - electrons and holes, in gases - ions and electrons.

The direction of the electric current is the direction of the ordered movement of positive electric charges. But in reality, in metal conductors, the current is carried out by the ordered movement of electrons, which move in the direction opposite to the direction of the current.

current strength called scalar physical quantity, equal to the charge ratio dq, transferred through the considered surface in a small period of time, to the value of this interval: .

Electric current is called permanent, if the current strength and its direction do not change with time. For direct current.

In accordance with the classical electronic theory, the current strength , Where e- electron charge, - concentration of free electrons in the conductor, - speed of the directed movement of electrons, S- cross-sectional area of ​​the conductor. The unit of current strength in SI is ampere: 1 A \u003d 1 C / s - the current strength at which in 1 s a charge of 1 C passes through the conductor section.

The direction of the electric current at various points of the surface under consideration and the distribution of the current strength over this surface are determined by the current density.

Current density vector is directed opposite to the direction of movement of electrons - current carriers in metals and is numerically equal to the ratio of the current strength through a small surface element, normal to the direction of movement of charged particles, to the value dS area of ​​this element: .

Current through an arbitrary surface S:, where is the projection of the vector j to the direction of the normal.

for a homogeneous conductor.

Electric current occurs under the influence of an electric field. In this case, the equilibrium (electrostatic) distribution of charges in the conductor is disturbed, and its surface and volume cease to be equipotential. Inside the conductor appears electric field, and the tangential component of the electric field strength at the surface of the conductor . The electric current in the conductor continues until all points of the conductor become equipotential. In order for the current to be constant in time, it is necessary that for the same time intervals through a unit surface flow same charge, i.e. the strength of the electric field at all points of the conductor through which this current flows remained unchanged. Therefore, charges should not accumulate or decrease anywhere in a conductor carrying direct current. Otherwise, the electric field of these charges would change. The specified condition means that the DC circuit must be closed, and the current strength must be the same in all cross sections of the circuit.

To maintain current, source electrical energy - a device in which any type of energy is converted into electric current energy.

If an electric field is created in the conductor and no measures are taken to maintain it, then the field inside the conductor will disappear very quickly and the current will stop. To maintain the current, it is necessary to carry out the circulation of charges, in which they would move along a closed path. The circulation of the electrostatic field vector is equal to zero, therefore, along with areas in which positive charges move along the lines of force of the electric field, there must be areas where the transfer of charges occurs against the forces of the electric field. The movement of charges in these areas is possible with the help of forces of non-electric origin, i.e. outside forces.

4.2. Electromotive force. Voltage. Potential difference.

External forces to maintain the current can be characterized by the work they do on the charges. The value equal to the work of external forces, referred to a unit of positive charge, is called electromotive force(EMF). EMF acting in a closed circuit can be defined as the circulation of the field strength vector of external forces.

EMF is expressed in volts.

voltage(or voltage drop) in the circuit section 1-2 called a physical quantity numerically equal to the work done by the resulting field of electrostatic and external forces when moving along the chain from the point 1 exactly 2 unit positive charge: .

In the absence of external forces, the voltage U matches the potential difference.

4.2. Direct current laws.

In 1826, the German scientist G. Ohm experimentally established the law according to which the strength of the current flowing through a homogeneous metal conductor is proportional to the voltage drop across the conductor: (Ohm's law in integral form). Homogeneous is called a conductor in which external forces do not act.

Value R called electrical resistance conductor, it depends on the properties of the conductor and its geometric dimensions: , where - resistivity, i.e. resistance of a conductor with a length of 1m 2 with a cross-sectional area of ​​​​1m 2, - the length of the conductor, S- cross-sectional area of ​​the conductor. The resistance of the conductor is, as it were, a measure of the resistance of the conductor to the establishment of an electric current in it. The unit of resistance is 1 ohm. A conductor has a resistance of 1 ohm if, with a potential difference of 1 V, the current in it is 1 A.

Generalized Ohm's law for a circuit section with EMF: the product of the electrical resistance of a circuit section and the current in it is equal to the sum of the fall electrical potential in this section and the EMF of all sources of electrical energy included in the section under consideration: .

The generalized Ohm's law for a section of a circuit expresses the law of conservation and transformation of energy in relation to a section of an electric current circuit.

Ohm's Law in differential form: The conduction current density is proportional to the intensity E electric field in the conductor and coincides with it in direction, i.e. . The proportionality factor is called specific electrical conductivity of the medium, and the value - the electrical resistivity of the medium.

Resistivity versus temperature is expressed by the formula , where - resistivity at , - thermal coefficient of resistance, depending on the properties of the conductor, - temperature in degrees Celsius.

Many metals and alloys at temperatures below 25K completely lose their resistance - they become superconductors. Superconductivity is a quantum phenomenon. When current flows in a superconductor, there is no energy loss. A very strong magnetic field destroys the superconducting state.

Temperature dependence:

Consistent Such a connection of conductors is called when the end of one conductor is connected to the beginning of another. The current flowing through the series-connected conductors is the same. The total resistance of the circuit is equal to the sum of the resistances of all individual conductors included in the circuit:.

Parallel such a connection of conductors is called when one end of all conductors is connected into one node, the other ends into another . At parallel connection the voltage in all conductors is the same, equal to the potential difference in the connection nodes:. The conductivity (i.e., the reciprocal of the resistance) of all parallel conductors is equal to the sum of the conductivities of all individual conductors: .

Ohm's law for a complete circuit: complete closed circuit consists of external resistance R and a current source with an EMF equal to , and internal resistance . The current strength in a complete circuit is directly proportional to the EMF of the current source and inversely proportional to the impedance of the circuit: .

2.1. Constant electricity.
Current strength. current density

An electric current is a directed movement of electric charges. If the substance contains free charge carriers - electrons, ions, capable of moving over considerable distances, then in the presence of an electric field they acquire a directed movement, which is superimposed on their thermal chaotic movement. As a result, free charge carriers drift in a certain direction.

The quantitative characteristic of the electric current is the magnitude of the charge transferred through the surface under consideration per unit time. It is called current strength. If a charge D is transferred across the surface in time q, then the current is equal to:

The unit of current strength in the SI system of units is Ampere (A), . A current that does not change with time is called a constant current.

Both positive and negative carriers can participate in the formation of current; the electric field moves them in opposite directions. The direction of the current is usually determined by the direction of movement of positive carriers. In fact, the current in most cases is created by the movement of electrons, which, being negatively charged, move in the direction opposite to that taken for the direction of the current. If positive and negative carriers move simultaneously in an electric field, then full current is defined as the sum of the currents formed by the carriers of each sign.

To quantify the electric current, another value is also used, which is called the current density. The current density is the quantity equal to the charge passing per unit time through a unit area perpendicular to the direction of movement of charges. The current density is a vector quantity.

Rice. 3.1

Denote by n the concentration of current carriers, that is, their number per unit volume. Let us draw an infinitely small area D in a current-carrying conductor S, perpendicular to the velocity of charged particles . Let us construct on it an infinitely short straight cylinder with height , as shown in Fig. 3.1. All particles enclosed inside this cylinder will pass through the area in time, transferring an electric charge through it in the direction of speed:

Thus, an electric charge is transferred through a unit area per unit time. Let us introduce a vector coinciding in direction with the velocity vector . The resulting vector will be the electric current density. Since there is a volumetric charge density, the current density will be equal to . If current carriers are both positive and negative charges, then the current density is determined by the formula:

,

where and - bulk densities positive and negative charges, and are the velocities of their ordered motion.

The vector field can be depicted using streamlines, which are constructed in the same way as the lines of the intensity vector, that is, the current density vector at each point of the conductor is directed tangentially to the current line.

Electromotive force

If an electric field is created in the conductor and this field is not maintained, then the movement of current carriers will cause the field inside the conductor to disappear, and the current will stop. In order to maintain the current in the circuit for a sufficiently long time, it is necessary to carry out the movement of charges along a closed path, that is, to make the DC lines closed. Therefore, in a closed circuit there must be sections where charge carriers will move against the forces of the electrostatic field, that is, from points with a lower potential to points with a higher potential. This is possible only in the presence of non-electric forces, called extraneous forces. External forces are forces of any nature, except for the Coulomb ones.

A physical quantity equal to the work of external forces when moving a unit charge in a given section of the circuit is called the electromotive force (EMF) acting in this section:

The electromotive force is the most important energy characteristic of the source. Electromotive force is measured, like potential, in volts.

In any real electrical circuit you can always select a section that serves to maintain the current (current source), and consider the rest as a "load". External forces necessarily act in the current source, therefore, in the general case, it is characterized by an electromotive force and resistance r, which is called the internal resistance of the source. External forces can also act in the load, but in the simplest cases they are absent, and the load is characterized only by resistance.

The resulting force acting on the charge at each point of the circuit is equal to the sum of the electric and third-party forces:

The work done by this force on the charge in some section of the circuit 1-2 will be equal to:

where is the potential difference between the ends of section 1-2, is the electromotive force acting on this section.

The value numerically equal to the work performed by electric and external forces when moving a single positive charge is called voltage drop or simply voltage in a given section of the circuit. Hence, .

The section of the chain on which external forces do not act is called homogeneous. The area where external forces act on current carriers is called inhomogeneous. For a homogeneous section of the circuit, that is, the voltage coincides with the potential difference at the ends of the circuit section.

Ohm's law

Ohm experimentally established the law according to which the strength of the current flowing through a homogeneous metal conductor is proportional to the voltage drop across the conductor:

where is the length of the conductor, is the cross-sectional area, is a coefficient that depends on the properties of the material, called the electrical resistivity. Resistivity is numerically equal to the resistance of a unit length of a conductor having a cross-sectional area equal to unity.

Rice. 3.2

In an isotropic conductor, the ordered movement of current carriers occurs in the direction of the electric field strength vector. Therefore, the directions of the vectors and coincide. Let's find the connection between and at the same point of the conductor. To do this, we mentally select in the vicinity of a certain point an elementary cylindrical volume with generators parallel to the vectors and (Fig. 3.2). A current flows through the cross section of the cylinder. Since the field inside the selected volume can be considered uniform, the voltage applied to the cylinder is equal to , where is the field strength at a given location. The resistance of the cylinder, according to (3.2), is . Substituting these values ​​into formula (3.1), we arrive at the relation:

,

Taking advantage of the fact that the vectors and have the same direction, we can write

Let us rewrite (3.4) in the form

.

Rice. 3.3

This formula expresses Ohm's law for an inhomogeneous section of a chain.

Consider the simplest closed circuit containing a current source and a load with resistance R(Fig. 3.3). We neglect the resistance of the lead wires. Putting , we obtain the expression of Ohm's law for a closed circuit:

An ideal voltmeter, connected to the terminals of a working current source, shows voltage, as follows from Ohm's law for a homogeneous section of the circuit - in this case, for the load resistance. Substituting the current strength from this expression into Ohm's law for a closed circuit, we get:

It can be seen from this that the voltage U at the terminals of a working source is always less than its EMF. It is the closer to , the greater the load resistance R. In the limit at , the voltage at the terminals of an open source is equal to its EMF. In the opposite case, when R=0, which corresponds to a short circuit of the current source, U=0, and the short circuit current is maximum: .

Ohm's law allows you to calculate any complex chain. A branched circuit is characterized by the strength of the currents flowing through its sections, the resistance of the sections and the EMF included in these sections. The current strength and EMF are algebraic quantities, that is, they are considered positive if the electromotive force contributes to the movement of positive charges in the chosen direction, and the current flows in this direction, and negative in the opposite case. However, the direct calculation of branched chains can be difficult. This calculation is greatly simplified by using the rules proposed by Kirchhoff.

Kirchhoff rules

G. Kirchhoff (1824–1887) studied Ohm's law in detail and developed general method calculation of direct currents in electrical circuits, including those containing several sources of EMF. This method is based on two rules called Kirchhoff's laws. Kirchhoff's first rule applies to nodes, that is, points where at least three conductors converge. Since we are considering the case of constant currents, at any point in the circuit, including at any node, the available charge must remain constant, so the sum of the currents flowing to the node must be equal to the sum of the outflowing ones. If we agree to consider the currents approaching the node as positive, and the outgoing currents as negative, then we can say that the algebraic sum of the strengths of the currents in the node is equal to zero:

You can get the same ratio if you agree, bypassing the circuit in a certain direction, for example, clockwise, consider positive those currents whose direction coincides with the direction of the bypass and negative - those whose direction is opposite to the direction of the bypass. We will also consider positive those EMFs that increase the potential in the direction of bypassing the circuit and negative - those that lower the potential in the direction of bypassing.

This reasoning can be applied to any closed loop, so Kirchhoff's second rule in general view can be written as follows:

,

Where n is the number of sections in the circuit, and m is the number of EMF sources. Kirchhoff's second rule expresses the obvious circumstance that when we go around the circuit completely, we return to the starting point with the same potential.

Thus, in any closed circuit, arbitrarily chosen in a branched circuit of conductors, the algebraic sum of the products of the strengths of the currents flowing through the resistances of the corresponding sections of the circuit is equal to the algebraic sum of the EMF encountered in this circuit.

Electricity

When charged particles move in a conductor, an electric charge is transferred from one place to another. However, if charged particles perform random thermal motion, as, for example, free electrons in a metal, then charge transfer does not occur. An electric charge moves through the cross section of the conductor only if, along with random movement, electrons participate in ordered movement. In this case, we say that an electric current is established in the conductor.
electric shock called the ordered (directed) movement of charged particles. An electric current arises from the ordered movement of free electrons or ions.
The total charge transferred through any section of the conductor is zero, since charges of different signs move with the same average speed.
Electric current has a certain direction. The direction of movement of positively charged particles is taken as the direction of the current.. If the current is formed by the movement of negatively charged particles, then the direction of the current is considered opposite to the direction of movement of the particles.
We do not directly see the motion of particles in a conductor. The presence of an electric current is indicated by the following actions or phenomena that accompany it:
1. the conductor through which the current flows is heated,
2. electric current can change the chemical composition of the conductor,
3. current has a force effect on neighboring currents and magnetized bodies.
If an electric current is established in the circuit, this means that an electric charge is constantly transferred through the cross section of the conductor. The charge transferred per unit of time serves as the main quantitative characteristic of the current, called current strength. If through the cross section of the conductor in time Δt charge is transferred ∆q, then the current is equal to:

The current strength is equal to the ratio of the charge Δq transferred through the cross section of the conductor during the time interval Δt to this time interval. If the current strength does not change with time, then the current is called constant.
The current strength is a scalar quantity. It can be both positive and negative. The sign of the current strength depends on which of the directions along the conductor is taken as positive. Current strength I > 0 if the direction of the current coincides with the conditionally chosen positive direction along the conductor. Otherwise I< 0.
The strength of the current depends on:
1. charge carried by each particle (q 0);
2. concentration of particles (n);
3. velocity of the directed motion of particles (v);
4. cross-sectional area of ​​the conductor (S).

In the International System of Units current strength is expressed in amperes (A). Measure the current with ammeters.
Conditions for the emergence and existence of direct electric current:
1. the presence of free charged particles;
2. Forces must act on charged particles to ensure their orderly movement over a finite period of time.
In order for a direct conduction current to exist in the conductor, it is necessary to perform following conditions:
a) the electric field strength in the conductor must be non-zero and must not change over time;
b) the DC conduction circuit must be closed;
c) on free electric charges, in addition to Coulomb forces, non-electrostatic forces, called external forces, must act. Third-party forces can be created by current sources (galvanic cells, batteries, electrical generators and etc.).

Ohm's law for a circuit section

The strength of the current in the conductor is directly proportional to the applied voltage and inversely proportional to the resistance of the conductor:

Conductor resistance R- a value that characterizes the resistance of the conductor to the establishment of an electric current in it. Resistance is measured in ohms (Ohm). If, at a voltage of 1 V, a current of 1 A is established in the conductor, then the resistance of such a conductor is 1 ohm.
The resistance of a conductor is directly proportional to its length l and inversely proportional to its cross-sectional area S:

where the coefficient of proportionality ρ is called resistivity. Resistivity depends on the type of substance and on temperature (with increasing temperature, the resistivity of most metals increases), numerically it is equal to the resistance of a conductor of unit length with a unit cross-sectional area.

Electromotive force

A physical quantity equal to the ratio of the work of an external field in moving a charge to the value of this charge is called electromotive force:

The electromotive force is expressed in volts.
third party is called a field of non-electrostatic origin, the work of which in any closed circuit is not equal to zero. Such a field, along with the Coulomb field, is created in current sources: batteries, galvanic cells, generators, etc. It is the external field that compensates for energy losses in the electrical circuit.

Ohm's law for a complete circuit

The source resistance is often called the internal resistance r as opposed to the external resistance R of the circuit. In a generator, r is the resistance of the windings, and in galvanic cell- resistance of the electrolyte solution and electrodes.
Ohm's law for a closed circuit relates the current strength in the circuit, the EMF and the impedance R+r of the circuit.

The product of current and resistance of a section of a circuit is often referred to as the voltage drop across that section. Thus, the EMF is equal to the sum of the voltage drops in the internal and external sections of a closed circuit.
Ohm's law for a closed circuit is written in the form

The current strength in a complete circuit is equal to the ratio of the EMF of the circuit to its total resistance.
The strength of the current depends on three quantities; EMF, resistances R and r of the external and internal sections of the circuit. The total EMF of the circuit is equal to the algebraic sum of the EMF of individual elements.

Series and parallel connection of conductors

Serial connection of conductors. At serial connection the electrical circuit has no branches. All conductors are included in the circuit one after another.

current strength	voltage	resistance	relationship between voltage and resistance

Parallel connection of conductors

current strength	voltage	resistance	relationship between current and resistance

Parallel connection is the most common way to connect different consumers. In this case, the failure of one device does not affect the operation of the others, while in a series connection, the failure of one device opens the circuit.

Kirchhoff rules

1. At each branching point of the wires, the algebraic sum of the current strengths is zero. The currents going to the branch point and the currents outgoing from it should be considered as values ​​of different signs.

2.In any closed circuit of the circuit, the algebraic sum of the products of the current strengths in individual sections and their resistance is equal to the algebraic sum of the EMF of the sources in this circuit.

1. Directions of currents are chosen arbitrarily. If after calculations I>0, then the direction is chosen correctly, if I<0, то направление противоположно.
2. An arbitrary closed loop is traversed in one direction. If this direction coincides with the direction of the arrow, then IR>0, if it is opposite, then IR<0. Если при обходе контура источник тока проходит от "-" к "+", то его ξ>0.
3. All EMF and all R must be included in the system of equations.

Work and current power

Coulomb and third-party electric forces do work A when moving charges along an electric circuit. If the electric current is constant, and the conductors forming the circuit are stationary, then the energy W, which is irreversibly converted in time t in the volume of the conductor, is equal to the perfect work:
W \u003d A \u003d IUΔt,

Where I is the current strength, U is the voltage drop in the conductor.
Current work in a circuit section is equal to the product of the current strength, voltage and time during which the work was done.
Irreversible energy transformations in a conductor with current are due to the interaction of conduction electrons with nodes crystal lattice metal. As a result of the collision of electrons with positive ions located at the lattice sites, the electrons transfer energy to the ions. This energy is used to heat the conductor.
Electric current poweris equal to the ratio of the current work for the time to this time interval:

Where A is the work that is done by the current in time - the current strength, U is the voltage drop in this section of the circuit. The unit of electric current power is watt, [P] =.

Quantity of heat, which stands out in the conductor over time:

The last formula expresses Joule-Lenz law: the amount of heat that is released by the current in the conductor is directly proportional to the strength of the current, the time of its passage through the conductor and the voltage drop across it.

Electric current in semiconductors

Semiconductors in terms of electrical conductivity, they occupy an intermediate position between metals and dielectrics. Current in semiconductors is an ordered movement of electrons and holes that occurs under the influence of an electric field. The resistance of semiconductors decreases sharply with increasing temperature, in contrast to metals.
Own conductivity semiconductors is usually small. In the presence of impurities in semiconductors, along with intrinsic conductivity, an additional impurity.
If an element is used as an impurity, the valence of which is one less than the valency of the given semiconductor ( acceptor impurity), then for the formation of normal pair-electron bonds with neighboring atoms, the impurity atom lacks one electron: as a result, hole. Such semiconductors are called p-type semiconductors(the main charge carriers in them are holes, the minor ones are electrons). If the valency of the impurity is one more than that of the semiconductor ( donor impurity), then one of the electrons in the impurity atom, not participating in chemical bond, easily leaves the atom and becomes free. It turns out a semiconductor n-type(major carriers are electrons, minor carriers are holes).
The contact area of ​​semiconductors of two types is called p-n-junction. When such a contact is formed, electrons begin to diffuse from the n-type semiconductor into the p-type semiconductor, and holes begin to diffuse towards them. As a result, the n-region is positively charged, and the p-region is negatively charged, and an electric field appears, which stops the diffusion of electrons and holes. If you include a semiconductor with a p-n junction in an electrical circuit by attaching the p-region to the positive pole, and the n-region to the negative (direct connection), the transition resistance will be negligible. At reverse inclusionр-n - the transition practically does not pass current. This property is used in semiconductor diodes.
Semiconductor diodes are used in electronic engineering for rectifying electric current along with vacuum two-electrode lamps. Moreover, in the production of consumer electronics, lamps are practically no longer used, since semiconductor diodes have a number of advantages.
For example, for the operation of a two-electrode lamp, a special source of energy is needed to heat the cathode filament (otherwise, thermionic emission will not occur, and charge carriers - thermoelectrons - will not appear in the lamp). Semiconductor diodes do not require such a power source, and when used in sufficiently large and complex circuits, significant energy savings are obtained. In addition, for the same rectified current, semiconductor diodes are much smaller than vacuum tubes.

Electric current in electrolytes

Experiments show that liquids can be dielectrics, semiconductors or conductors. The most well-known dielectric liquid is water. It is easy to verify that water is a dielectric if you lower two electrodes into a jar of water by connecting them to a current source. In such a circuit, there will be practically no current.
The situation will be quite different if the water is replaced by some conductive solution. Such solutions with electrical conductivity are called electrolytes. When an electric field is created in electrolytes, a current arises in them, as a result of which positive ions begin to move towards the cathode, and negative ions (and electrons) towards the anode.
Ionic conductivity in such electrolytes, which are solutions of acids, alkalis and salts, is explained by electrolytic dissociation. Dissociation- this is the disintegration of molecules into ions under the influence of the electric field of polar solvent molecules. Oppositely charged ions in a collision can recombine into neutral molecules - recombine. In the absence of an electric field, a dynamic equilibrium is established in the solution, when the processes of dissociation and recombination balance each other.
When current passes through the electrolyte, the process of electrolysis is observed - the release of substances that make up the electrolyte on the electrodes.

Electric current in gases

Gases, unlike metals and electrolytes, consist of electrically neutral atoms and molecules and in normal conditions do not contain free current carriers (electrons and ions). Gases under normal conditions are dielectrics. Carriers of electric current in gases can arise only when gas ionization- detachment from their atoms or molecules of electrons. In this case, atoms (molecules) of gases turn into positive ions. negative ions in gases can arise if atoms (molecules) attach electrons to themselves.
Electric current in gases is called gas discharge. To carry out a gas discharge, an electric or magnetic field must be applied to a tube containing ionized gas (discharge tube).

Plasma.

A substance containing a mixture of neutral atoms, free electrons and positive ions is called plasma. Plasma resulting from relatively low-current electrical discharges (for example, in tubes “ daylight”) is characterized by very low concentrations of charged particles compared to neutral ones ( ). Usually it is called low-temperature, since the temperature of atoms and ions is close to room temperature. The average energy of much lighter electrons turns out to be much higher. That. low-temperature plasma is essentially a non-equilibrium, open medium. As noted, self-organization processes are possible in such media. Fine famous example is the generation of highly ordered coherent radiation in the plasma of gas lasers.
The plasma can also be in thermodynamic equilibrium. For its existence it is necessary heat(at which the energy of thermal motion is comparable to the ionization energy). Such temperatures exist on the surface of the Sun, can occur during very powerful electrical discharges (lightning), during nuclear explosions. Such a plasma is called hot.

Joule-Lenz law

In an electric circuit, when a current passes, a series of energy transformations occurs. In outer section In the chain, the work of moving the charge is done by the forces of a stationary electric field and the energy of this field is converted into other forms: mechanical, thermal, chemical, into the energy of electromagnetic radiation. Hence, full work current in the outer section of the circuit

A 0=Wmeh+Ahim+wizl+Q.

If, on the section of the circuit, under the action of an electric field, no mechanical work and chemical transformations do not occur, then the work of an electric current leads only to heating the conductor.

In this case, the amount of heat released is equal to the work done by the current.

Quantity of heat Q, emitted by the current I during t in the section of the circuit with resistance R, equals Q=I 2Rt.

This formula expresses Joule-Lenz law installed empirically in the 19th century two scientists (English - J. Joule and Russian E. X. Lenz).

When an electric current passes through a conductor, the amount of heat released in the conductor is directly proportional to the square of the current, the resistance of the conductor, and the time it takes for the current to pass..

The action of many electric heaters is based on the Joule Lenz law. These are irons, electric stoves, electric kettles, boilers, soldering irons, electric fireplaces, etc.

The main part of any electric heater is a heating element (a conductor with high resistivity is wound on a plate of heat-resistant material: mica, ceramics).

The above formula of the Joule-Lenz law is convenient to apply when resistors are connected in series, since the current strength in all sections of the series-connected circuit is the same. If two resistors are connected in series R 1 and R 2 , then Q 1=I 2R 1t, Q 2=I 2R 2t, where Q 1Q 2=R 1R 2 , i.e. the amount of heat generated by the current in sections of a series-connected circuit is proportional to the resistances of these sections.

According to Ohm's law, for a homogeneous section of the DC circuit I=UR. Then Q=U 2Rt .

This formula is convenient to use when connecting resistors in parallel, since the voltage on each branch of such a circuit is the same. If two resistors are connected in parallel R 1 and R 2 , then Q 1=U 2R 1t , Q 2=U 2R 2t, where

Q 1Q 2=R 2R 1,

those. the amount of heat generated by the current in the branches of a parallel-connected circuit is inversely proportional to the resistances of the resistors included in these branches.

Topic 4. Direct electric current

Study questions:

1. Laws of direct electric current.

2. A simple electrical circuit.

Introduction

Electrostatics studies the interaction of electrified bodies (charges) that are not

moving relative to each other. But in nature, and especially in electrical engineering,

phenomena are most often associated with moving charges, that is, electrical

ski currents. The study of electric current as a phenomenon and the discovery of ways to create (generate) it was the factor that ensured the development of the electric power industry, electronics, electrochemistry, and thereby contributed to the development of many modern technologies.

Modern methods of obtaining and transmitting electrical energy are based on several laws discovered in the 19th century. Phenomena and processes associated with electric current are studied in the section of the doctrine of electricity, which is called electrodynamics. To date, the application of these laws has led to the creation of several technical sciences, in their complexity significantly exceeding electrodynamics.

This lecture discusses the main regularities of the simple form current - direct electric current, as well as its laws for current in metal conductors and a simple system of conductors, which is called an electrical circuit.

1 . Laws of direct electric current

1.1 Electricity. Conduction current

1. The phenomenon of electric current is found in simple experience. If two oppositely charged bodies (for example, capacitor plates) are connected with a metal wire (Fig. 1.1.1), then a short-term increase in the temperature of the wire can be detected, up to its melting with a sufficient capacitor charge. The reason is that the charged bodies had different potentials and a common electric field, and when they were connected by a wire, the field did the work and

moving charges along a wire from one body to another. The moved (“flowed”) charges compensated each other, the potential difference of the plates decreased to zero, and the process of moving charges stopped. This movement of charges is an electric current. In the considered case, the current was short-term. In practice, both short-term and long-term currents are used.

Definition . An electric current is called the ordered movement of electric charges - micro- and macroscopic electrified bodies.

known three varieties electric current:

1) macroscopic currents in nature, due to the movement of thunderclouds in the atmosphere or magma flows internally

ri globe, lightning electrical discharges; 2) conduction currents in matter; charge carriers are electrons and io-

3) currents in vacuum, that is, in regions of space in which matter is absent or has a very low concentration (for example, electron currents in cathode ray tubes, elementary particles in cosmic rays and accelerators).

Electric currents are detected by their effect on external bodies. These influences are:

1) thermal - currents heat the bodies through which they pass;

2) mechanical - currents deflect a magnetic needle or other currents;

3) chemical - currents provide the process of electrolysis in solutions of substances (electrolytes);

4) biological - currents initiate muscle contraction and affect the vital functions of biological objects.

2. Of greatest practical importance are conduction currents.

Definition . Conduction current is an electric current in bodies.

For the existence of a conduction current, it is necessary to have (1) a potential difference between the points of the body and (2) free carriers of electric charge in the bodies.

The bodies in which the existence of a conduction current is possible are called electrical conductors . They must be in solid or liquid state. Conductors include metals and electrolytes - salt solutions. In metals, free carriers of electric charge are electrons, and in electrolytes

– ions (cations and anions).

In the absence of an external electric field, charge carriers inside the conductors also move, but this movement is thermal, that is, chaotic. The microcurrents existing in the conductors compensate each other. An external electric field imparts to all charges directional motion component, which is superimposed on the chaotic.

Definition . The speed of the ordered movement of charge carriers in a conductor with electric current is called the drift velocity of charge carriers

v DR.

Definition . Lines along which there is an ordered movement of charge carriers in a conductor are called streamlines.

The drift velocity vectors are directed tangentially to the corresponding streamlines.

Rule: the direction of the drift velocity of positive charge carriers (q0 0 .

By an electrostatic field, positive charges move from points with a greater potential in absolute value to points with a lower potential.

In metal conductors, the direction of current is opposite to the true direction of movement of electrons - real charge carriers.

3. The main quantitative quantities used to describe the electric current are current strength and current density.

We select some point N inside the conductor and draw the drift velocity vector v DR and the corresponding streamline through it (Fig. 1.1.2). Then we construct an elementary (infinitely small) area dS, which passes through t. Nperpendi-

cularly to the vector v DR : dS v DR .

In the presence of current in the conductor, a charge dq passes through the area dS in time dt. It's obvious that

d qd td q= Id t.

Definition. Current strength in the vicinity of a given point N conductor is called

a scalar physical quantity equal to the electric charge passing through the elementary area d S per unit of time:

I = dq/dt.

If the concentration of charge carriers in the conductor is n, and each carrier has a charge q 0,

then it is easy to show that dq =q 0 n v DS dS dt . Then Fig. 1.1.2 current density and current strength at point N of the conductor

are described by expressions:

j =q 0 n v DR ,j =q 0 n v DR ;

I = jd S = q0 nv DR d S.

The basic unit for measuring current strength is "ampere": \u003d 1A, and current density - "ampere divided by square meter": \u003d 1A / m 2.

The estimate shows that at a current I = 1A in a copper conductor, for which the volume concentration of valence electrons is n 1028 m–3, their drift velocity is v DR 10–2 m/s. This speed is much less than the average speed of the chaotic motion of valence electrons in the volume of the conductor (v СР 106 m/s).

4. In practice, metal conductors are very widely used. constant normal cross section:S=idem. For them, the streamlines are parallel, and the vector

ry current density at all points of any normal section in the same mo-

The time points are the same, that is, they are parallel, directed in one direction and equal in absolute value: j S , j = = const. The current strength in conductors of constant cross section is the sum of the current strengths through all n elementary areas dS i, into which any normal section S can be divided:

5. Definition. An electric current is called constant if the current

does not change over time.

From the definition of the current strength, it follows that at a constant current through a given section S of the conductor for equal periods of time t passes the same amount

charge q :

IPOST =const d q = Id t q= Id t= IPOST d t = IPOST t IPOST = q/ t.

For two conductors of different cross-sections S 1 and S 2 at the same current strength (I 1 \u003d I 2), the current density modules, inversely proportional to the cross-sectional areas of the conductors (j \u003d I / S) are related according to the following expression:

j1 / j2 = S2 / S1 .

1.2 Ohm's law for current in a conductor

1. An electric current in a conductor exists when there is a potential difference in the electric field (electrostatic voltage) at the ends of the conductor. Experimentally, the relationship between current strength and voltage was established by the German physicist G. Ohm

Ohm's law for current in a conductor: the current strength in a homogeneous conductor is directly proportional to the electrostatic voltage at its ends -

The coefficient of proportionality (Greek "lambda") is called electrical conductivity(electrical conductivity) conductor.

But usually, instead of electrical conductivity, the inversely proportional

its value - electrical resistance of the conductor R 1/ .

In this case, Ohm's law for the conductor has the form:

I = U/R.

The basic unit of measurement of electrical resistance is "ohm": [ R ] \u003d 1 V / A \u003d 1 Ohm - this is the resistance of the conductor, in which, at a potential difference of 1V, a direct current 1A flows.

2. It has been experimentally established that the electrical resistance depends (1) on chemical composition conductors, (2) their shape and size, and (3) their temperature.

Resistance of a homogeneous conductor of constant cross section directly proportional to its length and inversely proportional to its area normal cross section:

R = l/S.

The coefficient of proportionality in this expression is physical characteristic the substance that makes up the conductor is called specific electrical

the chemical resistance of the substance of which the conductor is composed.

The unit of resistivity is "ohm times

meter ": \u003d 1 Ohm m. Silver has the lowest resistivity

(= 1.6 10–8 ohm m) and copper (= 1.7 10–8 ohm m).

3. The dependence of the conductor resistance on temperature is due to the temperature dependence of the resistivity. At temperatures not too different from normal, this dependence in the first approximation has the following form:

0 (1 +t) =0 T ,R =R 0 (1 +t) =R 0 T ;

here and 0 ,R and R 0 – resistivity and conductor resistance at temperatures, respectively, t and 0C (T and 273.15K). The coefficient of proportionality (1/273)K -1 is almost the same for all metal conductors:

(1/273) K -1 - and is called the temperature coefficient of resistance.

The increase in electrical resistance with increasing temperature is the main feature, according to which, from all conductive substances, group of conductors. Other groups of substances are characterized by a decrease in resistance with increasing temperature; they make up semiconductor groups go-

electricians.

4. In electrical and radio circuits, it is often necessary to have certain specific values ​​\u200b\u200bof the resistance of conductors. They are installed by selecting standardized conductors called resistors. Resistors are combined into systems. Calculation of the resistance of the resistor system (equivalent to

system resistance) is based on dependencies, which are subject to

tivleniya two simple systems- parallel and serial chain-

zistors.

Scheme parallel chain resistors with resistances R 1, R 2, R 3, .., R n is shown in Fig. 1.2.1a: first, one of the two terminals of each resistor are connected and form the first node A, and then the second conclusions are connected in the second node B. At the node

ly A and B voltage U is applied, the same for all resistors:

U 1 \u003d U 2 \u003d U 3 \u003d ... \u003d U n \u003d U.

A current of force I flows to node A from the positive pole of the source. Here it is divided into currents I 1, I 2, I 3,.., I n, which will connect at node B into a current of the same initial strength I. That is, the current strength I is equal to the sum of the current strengths in all resistors:

On the other hand, according to Ohm's law, I \u003d U / R PAR, where R PAR is the equivalent resistance of a parallel chain of resistors. Equating the right parts of the last expressions

zhenii, we obtain a formula for calculating RPAR : the value inversely proportional to the equivalent resistance of a parallel string of resistors is equal to the sum of the values ​​inversely proportional to their resistances:

5. Scheme serial chain resistors with resistances R 1, R 2, R 3, .., R n is shown in Fig. 1.2.1b: the resistors are connected with their terminals like train cars.

If voltage is applied to the free terminals of the extreme resistors R 1 and R n, then

la current will be the same in all resistors:

I 1 \u003d I 2 \u003d I 3 \u003d ... \u003d I n \u003d I,

and the voltage across each of the resistors, according to Ohm's law, depends on its own resistance:

Ui = Ii Ri = IRi .

Obviously, the voltage U at the ends of the chain is equal to the sum of the voltages across each resistor:

On the other hand, U = IR LAST , where R LAST is the equivalent resistance of the considered circuit. Equating the right parts of the last expressions, we obtain that the equivalent

The tape resistance of a series chain of resistors is equal to the sum of their resistances:

R LAST= R i . i 0

Using the ratios R PAR and R LATCH obtained, it is possible to calculate the resistance of any system of resistors, gradually highlighting serial and / or parallel chains in it.

1.3 Joule-Lenz law for current in a conductor

1. The electric current in the conductor exists due to the work done by the electrostatic field to transfer a positive charge along the conductor:

AR \u003d q (1 - 2) \u003d q U.

At direct current q \u003d I t. Then, considering Ohm's law for current in a conductor, we can express the work of the electrostatic field in terms of the current parameters:

AR \u003d I2 R t \u003d (U2 / R) t \u003d IU t

2. J.P. Joule and, independently of him, the Russian physicist E.Kh. Lenz (1804-1865) in

1841-42 experimentally established: if current is passed through a stationary

metal conductor, then the only observed effect is the heating of the conductor, that is, the release of heat Q into the surrounding space.

In this case, by virtue of the law of conservation and transformation of energy

QR = AR = I2 R t.

This equality is a quantitative expression of the Joule-Lenz law for a conductor: amount of heat released in any conductor when pro-

when a direct current is passed through it, it is equal to the product of the square of the current strength and the electrical resistance of the conductor and the time the current is passed.

Using Ohm's law allows you to modify the expression of Joule-Lenz's law:

QR = I2 R t = (U2 / R) t = IU t.

It is clear that if a current-carrying conductor moves under the action of magnetic field(electric motor) or chemical processes (electrolysis) take place in it, then the work of the current will exceed the amount of heat released.

The intensity of heat release is characterized by the power of the current - physical

with a value equal to the work of the current per unit of time:

N A / t \u003d I 2 R \u003d U2 / R \u003d IU.

3. The release of heat is explained by the fact that charge carriers interact with the crystal lattice of the conductor and transfer to it the energy of their ordered motion.

The thermal effect of the current has found wide application in technology, which began with the invention in 1873. Russian engineer A.N. Lodygin (1847-1923) light bulb incandescent. The action of electric muffle furnaces, equipment for electric arc and resistance welding of metals, household electric heaters, and much more is based on this phenomenon.

2. Simple electrical circuit

2.1 Direct current source. Electromotive force of current source

1. If only the force of the electrostatic field acts on the charge carriers in the conductor (resistor) (as in the experiment illustrated in Fig. 1.1.1), then the carriers move from points of the conductor with a higher potential to points with a lower potential. This leads to equalization of potentials at all points of the conductor and, accordingly, to the disappearance of the current.

Main practical use have continuous currents, including direct currents. For existence direct current devices are needed that are able to create and maintain at the ends of the conductor constant potential difference. Ta-

which devices are called direct current sources.In current sources, pro-

comes a continuous spatial separation of positive and negative charges at the poles of the source , which provides a potential difference across them.

to the poles of the current source (Fig.2.1.1).

It is important that, unlike the current in the conductor, inside source current (as

positive charges) is directed from negative pole is positive

nomu . This direction is called the natural direction of the current in the source.

It physically correctly reflects the essence of the processes in the current source and corresponds to the rule that determines the direction of the current in the resistor connected to the poles of the source.

The role of the current source is similar to the role of a pump, which is necessary for pumping liquid through pipes. hydraulic system. Formally speaking, the current source "pumps" positive charges from its negative pole to the positive one.

2. External forces do the work A STOP on the separation and movement of electric charges inside the source and the creation of an electric field between its poles.

Definition . The electromotive force (EMF) of a current source is a physical quantity equal to the work of external forces performed in the source in the production of a unit of positive charge:

E A STOR / q + .

The similarity of the definitions of the EMF of the current source and the potential of the electric field explains that the main unit of measurement of the EMF is also "volt":

[ E ] \u003d 1 J / C \u003d 1 V.

3. The basis of all current sources are electrically conductive substances. Therefore, the sources have an electrical resistance, which is called internal resistance and is denoted by the letter r. Internal resistance manifests itself in heating the source in operating mode, that is, when a resistor is connected to a current source. The amount of heat released in current sources obeys the Joule-Lenz law:

Qr = I2 r t.

Internal resistance increases with temperature.

2.2 Section of the electrical circuit. Simple closed circuit

1. For creating electric currents resistors and current sources must be used together.

Definition . Simple electrical circuits are called systems, state-

from resistors, current sources and keys (switches) connected in series.

Definition . Section of a simple chain A part of a simple electrical circuit is called, containing one or another number of resistors and / or current sources.

Definition . Homogeneous section of a simple chain is called the area containing

pulling only resistors.

An example of a homogeneous section of a circuit is a series chain of resistors (Fig. 1.2.1b). The phenomenon of direct current in a homogeneous section of the circuit, consisting of resistors, is described by the Ohm and Joule-Lenz laws for the current in the conductor.

2. Definition. Inhomogeneous section of the chain called a section containing series-connected resistors and current sources.

Definition . The sum of the resistances of resistors R and internal resistances r i of current sources in an inhomogeneous section of a simple circuit is called total resistance

by the formation of an inhomogeneous section of the chain.

kov current in the area.

Definition . Electric voltage on the inhomogeneous section of the circuit A-

B is the value equal to the algebraic sum of the external electrical voltage and EMF (summation taking into account the signs) of the current sources included in the section:

U AB (A -B) + E AB \u003d U + E AB;

here E AB \u003d E 1 + E 2 + ... is the algebraic sum (summation taking into account the signs) of the EMF of the current sources in the section.

Comment. It can be seen that for a homogeneous section of the circuit, the voltage is identically equal to electrostatic voltage between current entry and exit points:

(U AB) ONE (A - B) ONE = U.

EMF E i in the expression for E AB are algebraic quantities: value of E i

is taken with a "+" sign if the direction of the current IAB in the circuit section coincides with the natural direction of movement of positive charges in the i-th source (in Fig. 2.2.1 E 1 0); if the direction of the current IAB is opposite to the natural direction of movement of positive charges in the source, then the value of E i is taken from

sign "-" (in Fig.2.2.1E 2 0). Thus,

E AB \u003d E 1E 2 ... .

3. If the conductors of an inhomogeneous section chains A-B are motionless, then according to the law of conservation and transformation of energy, the work of the electrostatic and external forces acting in the area is equal to the heat released in the resistor and current sources:

A AB \u003d Q AB.

Consider a circuit section containing only one current source with internal resistance r (in this case, E AB \u003d E 1 ). It's obvious that

A AB \u003d A R + A r + A STOR,

where (A R + A r) \u003d q + (A -B) - work electrostatic forces when moving a positive charge q + .

From the definition of EMF it follows that A STOR \u003d q + E AB. Then

A AB \u003d q + (A - B) + q + E AB \u003d q + (A - B) + E AB \u003d q + U AB.

On the other hand, the amount of heat Q AB \u003d Q R + Q r and according to the Joule-Lenz law

and the definition of electric current (I t \u003d q + )

QAB = I2 R t+ I2 r t= I(R+ r)(I t) = I(R+ r) q+ .

Equating the right parts of the last expressions for A AB and Q AB gives the expression

generalized Ohm's law for an inhomogeneous chain section:

the current strength in an inhomogeneous section of an electrical circuit is directly proportional to electrical voltage at the ends of the section and is inversely proportional to the total resistance of the section -

I \u003d (A -B) + E AB / (R + r) \u003d U AB / (R + r).

Hence it follows that

U AB \u003d I (R + r) \u003d IR + Ir U R + U r,

where U R IR and U r Ir are the electrostatic voltages across the resistor and the internal

chain section resistance. That is the electrical voltage at the ends of the inhomogeneous section of the circuit is equal to the sum of the electrostatic voltages across the resistor and the internal resistance of the current source:

U R + U r \u003d ( A - B) + E AB.

Comment. For a homogeneous section of the circuit (E AB \u003d 0, r \u003d 0, U r \u003d 0) with equivalent resistance R, the generalized Ohm's law turns into Ohm's law for the current in the conductor:

U=UR=IR.

Comment. The generalized Ohm's law holds not only for direct current (U = const), but also for any change in current over time. In this case, the chain segment may contain other electrical elements: (1) capacitors with voltage U C \u003d q / C on their plates and (2) solenoids that create electromagnetic induction EMF E i \u003d -LdI / dt. Then the quantities U C and E i must be taken into account, respectively, in the left and right parts of the equation of the generalized Ohm's law:

U R + U r + U C \u003d ( A - B) + E AB + E i].

It is important to remember that the letter A denotes the end of the circuit section from where the current (q 0) flows into the section.

4. The generalized Ohm's law indicates a method for measuring the EMF of a current source. If there is no current in the inhomogeneous section (I = 0), then it follows from it that

E AB \u003d - (A -B) \u003d (B -A),

that is, the EMF acting in an inhomogeneous circuit is equal to the electrostatic potential difference at the ends of the circuit in the mode when they are not closed through other sections.

This measurement is realized by connecting the poles of the source to the terminals of the voltmeter.

2.3 Simple closed circuit

1. Definition. Simple closed circuit a chain is called, which is obtained by connecting (closing) the key K to the ends of a section of a simple chain (Fig. 2.3.1).

The resistance R in a simple closed circuit is called external resistance

eat.

Using Ohm's law for the current in the conductor, you can determine what fraction of the EMF E is the voltage U R on the external resistance R:

I \u003d U R / R U R \u003d I R \u003d E R / (R + r) \u003d E / (1 + (r / R )) \u003d E (1 - (r / R )), with r R.

It can be seen that the greater the external resistance of the circuit, the closer the value of U R to the value of E .

If the external resistance of the circuit is much less than the internal

(R r ), then the chain will go current short circuit :

I KOR \u003d E / r.

The short circuit mode is extremely dangerous for current sources. Their internal resistance has values ​​close to 1Ω (r 1Ω). Therefore, short-circuit currents, even at low EMF, can reach tens of amperes. The Joule heat released in this case, proportional to the square of the current strength (Q I 2 ), can disable the source.

2. Electric current in metals. Experimental proof of the nature of electric charge carriers in metals. Fundamentals of the classical electronic theory of conduction in metals.

The idea of ​​the electronic nature of charge carriers in metals, which was laid down in the theory of Drude and Lorentz, is based on a number of classical experimental proofs.

The first of these experiments is the experience of Rikke (1901), in which during the year el. the current was passed through three metal cylinders (Cu, Al, Cu) of the same radius connected in series with carefully polished ends. Despite the fact that the total charge that passed through the cylinders reached a huge value (about 3.5 * C), no changes were found in the mass of the outermost metals. This was proof of the assumption that particles of extremely small mass are involved in the charge transfer.

Despite the small mass of charge carriers, they have the property of inertia, which was used in the experiments of Mandelstam and Papaleksi, and then in the experiments of Stuart and Tolman, who spun the coil with a very large number of turns to a huge speed (of the order of 300 m/s), and then abruptly braked it. As a result of the displacement of charges due to inertia, it created a current pulse, and knowing the dimensions and resistance of the conductor and the magnitude of the current recorded in the experiment, it was possible to calculate the ratio of the charge to the mass of the particle, which turned out to be very close to the value that is obtained for an electron (1.7 * C /kg).

Fundamentals of the classical electronic theory of conduction in metals

The existence of free electrons in metals is explained by the fact that during the formation of a crystal lattice of a metal (as a result of the approach of isolated atoms), valence electrons, relatively weakly bound to atomic nuclei, break away from metal atoms, become “free” and can move through the volume. positive metal ions are located at the nodes of the crystal lattice, and free electrons move randomly between them, forming a kind of electron gas, the mean free path of electrons is about m (the distance between the lattice nodes). Conduction electrons collide with lattice ions, transferring energy to them, in as a result, a thermodynamic equilibrium is established between the electron gas and the lattice.According to the Drude-Lorentz theory, electrons have the same energy of thermal motion as molecules of an ideal monatomic gas and at room temperatures the thermal velocity of electrons will be orders of magnitude / s, all electrons are considered as independent and to explain macroscopic phenomena (for example, current) it is enough to know the behavior of one electron in order to determine the behavior of all electrons. Therefore, such a theory is called the "single-electron approximation" and, despite its simplification, it gives some satisfactory results.

The thermal chaotic motion of electrons cannot lead to the appearance of a current. When an electric field is applied to a metal conductor, all electrons acquire a directed motion, the velocity of which can be estimated from the current density; even at very high densities (of the order of 10 -10 A / m), the speed of ordered motion is about m / s. Therefore, in calculations, the resulting velocity of the electron (thermal + ordered) can be replaced by the velocity of thermal motion.

The question arises, how to explain the fact of the instantaneous transmission of electrical signals over long distances? The fact is that the electrical signal is not carried by those electrons that are at the beginning transmission lines, and the electric field, which has a speed of about 3 * m / s, involving in motion almost instantly all the electrons along the chain. Therefore, an electric current occurs almost instantly with the closing of the circuit