In different environments, the carriers of electric current are different charged particles.
The electric field in the medium is necessary to create directed movement of free charges. As is known, for a charge q in an electric field of strength E force acts F= q* E, which causes free charges to move in the direction electric field. A sign of the existence of an electric field in a conductor is the presence of a non-zero potential difference between any two points of the conductor,
However, electrical forces cannot maintain an electric current for a long time. The directed movement of electric charges after some time leads to equalization of potentials at the ends of the conductor and, consequently, to the disappearance of the electric field in it.
To maintain current at electrical circuit forces other than Coulomb forces must act on charges non-electric nature (external forces).
A device that creates external forces, maintains a potential difference in a circuit and converts different kinds energy in electrical energy, is called a current source.
For the existence of electric current in a closed circuit, it is necessary to include a current source in it.
Main characteristics:
1. Current strength - I, unit of measurement - 1 A (Ampere).
Current strength is a quantity equal to the charge flowing through cross section conductor per unit of time.
Formula (1) is valid for direct current, in which the current strength and its direction do not change over time. If the current strength and its direction change over time, then such a current is called variables.
For AC:
I = lim Dq/Dt , (*)
Dt - 0
those. I = q", where q" is the time derivative of the charge.
2. Current density - j, unit of measurement - 1 A/m 2.
Current density is a value equal to the strength of the current flowing through a unit cross-section of a conductor:
3. Electromotive force of the current source - emf. (e), unit of measurement is 1 V (Volt). E.m.f.- physical quantity, equal to the work done by external forces when moving a single positive charge along an electrical circuit:
e = A st. /q.(3)
4. Conductor resistance - R, unit of measurement - 1 Ohm.
Under the influence of an electric field in a vacuum, free charges would move accelerated. In matter they move uniformly on average, because part of the energy is given to particles of matter during collisions.
The theory states that the energy of the ordered movement of charges is dissipated by distortions of the crystal lattice. Based on the nature of electrical resistance, it follows that
l - conductor length,
S - cross-sectional area,
r is a proportionality coefficient called the resistivity of the material.
This formula is well confirmed by experience.
The interaction of conductor particles with charges moving in a current depends on the chaotic movement of the particles, i.e. on the temperature of the conductor. It is known that
r = r 0 (1 + a t) , (5)
R = R 0 (1 + a t) . (6).
Coefficient a is called the temperature coefficient of resistance:
a = (R - R 0)/R 0 *t.
For chemically pure metals a > 0 and equals 1/273 K -1. For alloys, temperature coefficients are less important. The r(t) dependence for metals is linear:
In 1911 the phenomenon was discovered superconductivity, which consists in the fact that at a temperature close to absolute zero, the resistance of some metals drops abruptly to zero.
For some substances (for example, electrolytes and semiconductors), the resistivity decreases with increasing temperature, which is explained by an increase in the concentration of free charges.
The reciprocal of resistivity is called electrical conductivity s
5. Voltage - U, unit of measurement - 1 V.
Voltage is a physical quantity equal to the work done by external and electrical forces when moving a single positive charge.
U = (A st. + A el.)/q .(8)
Since A st. /q = e, and A el. /q = f 1 -f 2, then
U = e + (f 1 - f 2) .(9)
2. LAWS OF DC CURRENT:
Electricity. Current strength. Ohm's law for a section of a circuit. Conductor resistance. Serial and parallel connection of conductors. Electromotive force. Ohm's law for a complete circuit. Work and current power.
Any movement of electric charges is called electric shock. Electrons can move freely in metals, ions can move freely in conducting solutions, and both electrons and ions can exist in a mobile state in gases.
Conventionally, the direction of current is considered to be the direction of movement of positive particles, therefore in metals this direction is opposite to the direction of movement of electrons.
Current Density- the amount of charge passing per unit time through a unit surface perpendicular to the current lines. This value is denoted j and is calculated as follows:
Here n is the concentration of charged particles, e is the charge of each particle, v is their speed.
Current strength i- the amount of charge passing per unit time through the full cross-section of the conductor. If during the time dt a charge dq passed through the full cross-section of the conductor, then
Otherwise, the current strength is found by integrating the current density over the entire surface of any section of the conductor. The unit of current measurement is Ampere. If the state of the conductor (its temperature, etc.) is stable, then there is an unambiguous relationship between the voltage applied to its ends and the current that arises. It is called Ohm's law and is written like this:
R- electrical resistance conductor, depending on the type of substance and its geometric dimensions. A conductor has a unit resistance in which a current of 1 A occurs at a voltage of 1 V. This unit of resistance is called Ohm.
Ohm's law in differential form:
where j is the current density, E is the field strength, s is the conductivity. In this entry, Ohm's law contains quantities that characterize the state of the field at the same point.
Distinguish serial and parallel conductor connections.
In a series connection, the current flowing through all sections of the circuit is the same, and the voltage at the ends of the circuit is added as the algebraic sum of the voltages in all sections.
When the conductors are connected in parallel, the voltage remains constant, and the current is the sum of the currents flowing through all branches. In this case, the reciprocal values of the resistance are added:
To obtain direct current, charges in an electrical circuit must be subject to forces other than the forces of the electrostatic field; they are called outside forces.
If we consider complete electrical circuit, it is necessary to include in it the action of these third-party forces and internal resistance current source r. In this case Ohm's law for a complete circuit will take the form:
E is the electromotive force (EMF) of the source. It is measured in the same units as voltage. The quantity (R+r) is sometimes called circuit impedance.
Let's formulate Kirkhoff's rules:
First rule: the algebraic sum of the current strengths in sections of the circuit converging at one branch point is equal to zero.
Second rule: for any closed circuit, the sum of all voltage drops is equal to the sum of all emfs in this circuit.
The current power is calculated using the formula
P=UI=I 2 R=U 2 /R.
Joule-Lenz law. Work of electric current (thermal effect of current) A=Q=UIt=I 2 Rt=U 2 t/R.
Electronic conductivity of metals. Superconductivity. Electric current in solutions and melts of electrolytes. Law of electrolysis. Electric current in gases. Independent and non-independent categories. The concept of plasma. Current in a vacuum. Electronic emission. Diode. Cathode-ray tube.
Electric current in metals is movement electrons, metal ions do not take part in the transfer of electric charge. In other words, metals have electrons that can move around the metal. They got the name conduction electrons. The positive charges in a metal are ions that form a crystal lattice. In the absence of an external field, electrons in the metal move chaotically, undergoing collisions with lattice ions. Under the influence of an external electric field, electrons begin an ordered movement, superimposed on their previous chaotic fluctuations. In the process of ordered movement, electrons still collide with ions of the crystal lattice. This is what causes electrical resistance.
In the classical electronic theory of metals, it is assumed that the movement of electrons obeys the laws of classical mechanics. The interaction of electrons with each other is neglected, the interaction of electrons with ions is reduced only to collisions. We can say that conduction electrons are considered as an electron gas, similar to an ideal atomic gas in molecular physics. Since the average kinetic energy per one degree of freedom for such a gas is equal to kT/2, and a free electron has three degrees of freedom, then
mv 2 t /2=3kT/2,
where v 2 t is the average value of the square of the velocity of thermal motion.
Each electron is acted upon by a force equal to eE, as a result of which it acquires acceleration eE/m. The speed at the end of the free run is equal to
where t is the average time between collisions.
Since the electron moves uniformly accelerated, its average speed is equal to half the maximum:
The average time between collisions is the ratio of the mean free path to the average speed:
Since usually the speed of ordered motion is much less than the thermal speed, the speed of ordered motion was neglected.
Finally, we have
v c =eEL/(2mv t).
The proportionality coefficient between v c and E is called electron mobility.
Using the classical electronic theory of gases, many patterns can be explained - Ohm's law, the Joule-Lenz law and other phenomena, but this theory cannot explain, for example, the phenomena superconductivity:
At a certain temperature, the resistivity for some substances abruptly decreases to almost zero. This resistance is so small that once the electric current is excited in the superconductor, it exists for a long time without a current source. Despite the abrupt change in resistance, other characteristics of the superconductor (thermal conductivity, heat capacity, etc.) do not change or change little.
A more accurate method to explain such phenomena in metals is the approach using quantum statistics.
Related information.
Electricity. Ohm's law
If insulated conductor place in electric field then to free charges q a force will act in the conductor. As a result, a short-term movement of free charges occurs in the conductor. This process will end when the own electric field of the charges arising on the surface of the conductor completely compensates for the external field. The resulting electrostatic field inside the conductor will be zero (see § 1.5).
However, in conductors, under certain conditions, continuous ordered movement of free electric charge carriers can occur. This movement is called electric shock . The direction of the electric current is taken to be the direction of movement of positive free charges. For an electric current to exist in a conductor, an electric field must be created in it.
A quantitative measure of electric current is current strength I – scalar physical quantity equal to the charge ratio Δ q, transferred through the cross section of the conductor (Fig. 1.8.1) during the time interval Δ t, to this time interval:
IN International system SI units of current are measured in amperes (A). The current unit of 1 A is established by the magnetic interaction of two parallel conductors with current (see § 1.16).
Direct electric current can only be created in closed circuit , in which free charge carriers circulate along closed trajectories. The electric field at different points of such a circuit is constant over time. Consequently, the electric field in a direct current circuit has the character of a frozen electrostatic field. But when an electric charge moves in an electrostatic field along a closed path, the work done by electric forces is zero (see § 1.4). Therefore, for the existence of direct current, it is necessary to have a device in the electrical circuit that is capable of creating and maintaining potential differences in sections of the circuit due to the work of forces non-electrostatic origin. Such devices are called DC sources . Forces of non-electrostatic origin acting on free charge carriers from current sources are called outside forces .
The nature of external forces may vary. IN galvanic cells or batteries they arise as a result of electrochemical processes; in direct current generators, external forces arise when conductors move in a magnetic field. The current source in the electrical circuit plays the same role as the pump, which is necessary to pump fluid in a closed hydraulic system. Under the influence of external forces, electric charges move inside the current source against electrostatic field forces, due to which a constant electric current can be maintained in a closed circuit.
When electric charges move along a direct current circuit, external forces acting inside the current sources perform work.
Physical quantity equal to the work ratio A st external forces when moving a charge q from the negative pole of the current source to the positive pole to the magnitude of this charge is called electromotive force of the source(EMF):
 |
Thus, the EMF is determined by the work done by external forces when moving a single positive charge. Electromotive force, like potential difference, is measured in volts (V).
When a single positive charge moves along a closed direct current circuit, the work done by external forces is equal to the sum of the emf acting in this circuit, and the work done by the electrostatic field is zero.
A DC circuit can be divided into separate sections. Those areas where no external forces act (i.e. areas that do not contain current sources) are called homogeneous . Areas containing current sources are called heterogeneous .
When a single positive charge moves along a certain section of the circuit, work is performed by both electrostatic (Coulomb) and external forces. The work of electrostatic forces is equal to the potential difference Δφ 12 = φ 1 – φ 2 between the initial (1) and final (2) points of the inhomogeneous section. The work of external forces is equal, by definition, to the electromotive force 12 acting in a given area. Therefore the total work is equal to
The German physicist G. Ohm in 1826 experimentally established that the current strength I, flowing along a homogeneous metal conductor (i.e., a conductor in which no external forces act), is proportional to the voltage U at the ends of the conductor:
|
Where R= const.
Size R usually called electrical resistance . A conductor with electrical resistance is called resistor . This ratio expresses Ohm's law for a homogeneous section of a chain: The current in a conductor is directly proportional to the applied voltage and inversely proportional to the resistance of the conductor.
The SI unit of electrical resistance of conductors is ohm (Ohm). A resistance of 1 ohm has a section of the circuit in which a current of 1 A occurs at a voltage of 1 V.
Conductors that obey Ohm's law are called linear . Graphical dependence of current strength I from voltage U(such graphs are called volt-ampere characteristics , abbreviated as CVC) is depicted by a straight line passing through the origin of coordinates. It should be noted that there are many materials and devices that do not obey Ohm's law, for example, a semiconductor diode or a gas-discharge lamp. Even with metal conductors, at sufficiently high currents, a deviation from Ohm’s linear law is observed, since the electrical resistance of metal conductors increases with increasing temperature.
For a section of a circuit containing an emf, Ohm's law is written in the following form:
According to Ohm's law
Adding both equalities, we get:
| I (R + r) = Δφ CD + Δφ ab + . |
But Δφ CD = Δφ ba = – Δφ ab. That's why
| |
This formula will express Ohm's law for a complete circuit : the current strength in a complete circuit is equal to the electromotive force of the source divided by the sum of the resistances of the homogeneous and inhomogeneous sections of the circuit.
Resistance r heterogeneous area in Fig. 1.8.2 can be thought of as internal resistance of the current source . In this case, the area ( ab) in Fig. 1.8.2 is the internal portion of the source. If points a And b short with a conductor whose resistance is small compared to the internal resistance of the source ( R << r), then the chain will flow short circuit current
| |
Short circuit current - the maximum current that can be obtained from a given source with electromotive force and internal resistance r. For sources with low internal resistance, the short circuit current can be very large and cause destruction of the electrical circuit or source. For example, lead-acid batteries used in automobiles can have short-circuit currents of several hundred amperes. Short circuits in lighting networks powered from substations (thousands of amperes) are especially dangerous. To avoid the destructive effects of such large currents, fuses or special circuit breakers are included in the circuit.
In some cases, to prevent dangerous values of short circuit current, some external resistance is connected in series to the source. Then resistance r is equal to the sum of the internal resistance of the source and the external resistance, and during a short circuit the current strength will not be excessively large.
If the external circuit is open, then Δφ ba = – Δφ ab= , i.e. the potential difference at the poles of an open battery is equal to its emf.
If the external load resistance R turned on and current is flowing through the battery I, the potential difference at its poles becomes equal
| Δφ ba = – Ir. |
In Fig. 1.8.3 shows a schematic representation of a direct current source with an equal emf and internal resistance r in three modes: “idling”, load operation and short circuit mode (short circuit). The electric field strength inside the battery and the forces acting on the positive charges are indicated: – electric force and – external force. In short circuit mode, the electric field inside the battery disappears.
To measure voltages and currents in DC electrical circuits, special instruments are used - voltmeters And ammeters.
Voltmeter designed to measure the potential difference applied to its terminals. He connects parallel the section of the circuit where the potential difference is measured. Any voltmeter has some internal resistance R B. In order for the voltmeter not to introduce a noticeable redistribution of currents when connected to the circuit being measured, its internal resistance must be large compared to the resistance of the section of the circuit to which it is connected. For the circuit shown in Fig. 1.8.4, this condition is written as:
| R B >> R 1 . |
This condition means that the current I B = Δφ CD / R B flowing through the voltmeter is much less than the current I = Δφ CD / R 1, which flows through the tested section of the circuit.
Since there are no external forces acting inside the voltmeter, the potential difference at its terminals coincides, by definition, with the voltage. Therefore, we can say that a voltmeter measures voltage.
Ammeter designed to measure current in a circuit. The ammeter is connected in series to an open circuit so that the entire measured current passes through it. The ammeter also has some internal resistance R A. Unlike a voltmeter, the internal resistance of an ammeter must be quite small compared to the total resistance of the entire circuit. For the circuit in Fig. 1.8.4 The resistance of the ammeter must satisfy the condition
Conditions for the existence of direct electric current.
For the existence of a constant electric current, the presence of free charged particles and the presence of a current source are necessary. in which any type of energy is converted into the energy of an electric field.
Current source- a device in which any type of energy is converted into the energy of an electric field. In a current source, external forces act on charged particles in a closed circuit. The reasons for the emergence of external forces in various sources current are different. For example, in batteries and galvanic cells, external forces arise due to the flow of chemical reactions, in power plant generators they arise when a conductor moves in a magnetic field, in photocells - when light acts on electrons in metals and semiconductors.
Electromotive force of the current sourceis the ratio of the work of external forces to the amount of positive charge transferred from the negative pole of the current source to the positive one.
Basic concepts.
Current strength- a scalar physical quantity equal to the ratio of the charge passing through the conductor to the time during which this charge passed.
Where I - current strength,q - amount of charge (amount of electricity),t - charge transit time.
Current Density- vector physical quantity equal to the ratio of the current strength to the cross-sectional area of the conductor.
Where j -current density, S - cross-sectional area of the conductor.
The direction of the current density vector coincides with the direction of motion of positively charged particles.
Voltage - a scalar physical quantity equal to the ratio of the total work of Coulomb and external forces when moving a positive charge in an area to the value of this charge.
WhereA - complete work of external and Coulomb forces,q - electric charge.
Electrical resistance- a physical quantity characterizing the electrical properties of a section of a circuit.
Where ρ - specific resistance of the conductor,l - length of the conductor section,S - cross-sectional area of the conductor.
Conductivitycalled the reciprocal of resistance
WhereG - conductivity.
For the existence of a constant electric current, the presence of free charged particles and the presence of a current source are necessary. in which any type of energy is converted into the energy of an electric field.
Current source - a device in which any type of energy is converted into the energy of an electric field. In a current source, external forces act on charged particles in a closed circuit. The reasons for the occurrence of external forces in different current sources are different. For example, in batteries and galvanic cells, external forces arise due to the occurrence of chemical reactions, in power plant generators they arise when a conductor moves in a magnetic field, in photocells - when light acts on electrons in metals and semiconductors.
Electromotive force of the current source is the ratio of the work of external forces to the amount of positive charge transferred from the negative pole of the current source to the positive one.
Basic concepts.
Current strength - a scalar physical quantity equal to the ratio of the charge passing through the conductor to the time during which this charge passed.
Where I - current strength, q - amount of charge (amount of electricity), t - charge transit time.
Current Density - vector physical quantity equal to the ratio of the current strength to the cross-sectional area of the conductor.
Where j -current density, S - cross-sectional area of the conductor.
The direction of the current density vector coincides with the direction of motion of positively charged particles.
Voltage - a scalar physical quantity equal to the ratio of the total work of Coulomb and external forces when moving a positive charge in an area to the value of this charge.
Where A - full work of external and Coulomb forces, q - electric charge.
Electrical resistance - a physical quantity characterizing the electrical properties of a circuit section.
Where ρ - specific resistance of the conductor, l - length of the conductor section, S - cross-sectional area of the conductor.
Conductivity called the reciprocal of resistance
Where G - conductivity.
Ohm's laws.
Ohm's law for a homogeneous section of a chain.
The current strength in a homogeneous section of the circuit is directly proportional to the voltage at a constant resistance of the section and inversely proportional to the resistance of the section at a constant voltage.
Where U - tension in the area, R - resistance of the area.
Ohm's law for an arbitrary section of a circuit containing a direct current source.
Where φ 1 - φ 2 + ε = U voltage at a given section of the circuit,R - electrical resistance of a given section of the circuit.
Ohm's law for a complete circuit.
The current strength in a complete circuit is equal to the ratio of the electromotive force of the source to the sum of the resistances of the external and internal sections of the circuit.
Where R - electrical resistance of the external section of the circuit, r - electrical resistance of the internal section of the circuit.
Short circuit.
From Ohm's law for a complete circuit it follows that the current strength in a circuit with a given current source depends only on the resistance of the external circuit R.
If a conductor with resistance is connected to the poles of a current source R<< r, then only the EMF of the current source and its resistance will determine the value of the current in the circuit. This current value will be the limit for a given current source and is called short circuit current.
Electromotive force. Any current source is characterized by electromotive force, or, in short, EMF. So, on a round flashlight battery it says: 1.5 V. What does this mean? Connect two metal balls carrying charges of opposite signs with a conductor. Under the influence of the electric field of these charges, an electric current arises in the conductor ( Fig.15.7). But this current will be very short-lived. The charges quickly neutralize each other, the potentials of the balls will become the same, and the electric field will disappear.
Outside forces. In order for the current to be constant, it is necessary to maintain a constant voltage between the balls. For this you need a device ( current source), which would move charges from one ball to another in the direction opposite to the direction of the forces acting on these charges from the electric field of the balls. In such a device, in addition to electrical forces, charges must be acted upon by forces of non-electrostatic origin ( Fig.15.8). The electric field of charged particles alone ( Coulomb field) is unable to maintain constant current in the circuit.
Any forces acting on electrically charged particles, with the exception of forces of electrostatic origin (i.e., Coulomb forces), are called by outside forces. The conclusion about the need for external forces to maintain a constant current in the circuit will become even more obvious if we turn to the law of conservation of energy. The electrostatic field is potential. The work done by this field when charged particles move in it along a closed electrical circuit is zero. The passage of current through the conductors is accompanied by the release of energy - the conductor heats up. Therefore, there must be some source of energy in the circuit supplying it to the circuit. In addition to Coulomb forces, third-party, non-potential forces must act in it. The work of these forces along a closed loop must be different from zero. It is in the process of doing work by these forces that charged particles acquire energy inside the current source and then give it to the conductors of the electrical circuit. Third-party forces set in motion charged particles inside all current sources: in generators at power plants, in galvanic cells, batteries, etc. When a circuit is closed, an electric field is created in all conductors of the circuit. Inside the current source, charges move under the influence of external forces against Coulomb forces(electrons from a positively charged electrode to a negative one), and in an external circuit they are driven by an electric field (see. Fig.15.8). The nature of external forces. The nature of external forces can be varied. In power plant generators, extraneous forces are forces acting from a magnetic field on electrons in a moving conductor. In a galvanic cell, such as a Volta cell, chemical forces operate. The Volta cell consists of zinc and copper electrodes placed in a sulfuric acid solution. Chemical forces cause the zinc to dissolve in the acid. Positively charged zinc ions pass into the solution, and the zinc electrode itself becomes negatively charged. (Copper dissolves very little in sulfuric acid.) A potential difference appears between the zinc and copper electrodes, which determines the current in a closed electrical circuit. Electromotive force. The action of external forces is characterized by an important physical quantity called electromotive force(abbreviated EMF). The electromotive force of a current source is equal to the ratio of the work done by external forces when moving a charge along a closed circuit to the magnitude of this charge:
Electromotive force, like voltage, is expressed in volts. We can also talk about electromotive force in any part of the circuit. This is the specific work of external forces (work to move a single charge) not throughout the entire circuit, but only in a given area. Electromotive force of a galvanic cell is a quantity numerically equal to the work of external forces when moving a single positive charge inside an element from one pole to another. The work of external forces cannot be expressed through a potential difference, since external forces are non-potential and their work depends on the shape of the trajectory of the charges. So, for example, the work of external forces when moving a charge between the terminals of a current source outside the source itself is zero. Now you know what EMF is. If the battery says 1.5 V, this means that external forces (chemical in this case) do 1.5 J of work when moving a charge of 1 C from one pole of the battery to the other. Direct current cannot exist in a closed circuit if no external forces act in it, i.e. there is no EMF.
PARALLEL AND SERIES CONNECTION OF CONDUCTORS
Let us include two incandescent lamps in the electrical circuit as loads (current consumers), each of which has a certain resistance, and each of which can be replaced with a conductor with the same resistance.
SERIAL CONNECTION
Calculation of electrical circuit parameters with series connection of resistances:
1. the current strength in all series-connected sections of the circuit is the same 
2. the voltage in a circuit consisting of several sections connected in series is equal to the sum of the voltages in each section 
3. the resistance of a circuit consisting of several sections connected in series is equal to the sum of the resistances of each section 
4. the work of an electric current in a circuit consisting of sections connected in series is equal to the sum of the work in individual sections
A = A1 + A2 5. The power of the electric current in a circuit consisting of sections connected in series is equal to the sum of the powers in the individual sections
PARALLEL CONNECTION
Calculation of electrical circuit parameters with parallel connection of resistances:
1. the current strength in an unbranched section of the circuit is equal to the sum of the current strengths in all parallel-connected sections
3. When connecting resistances in parallel, the reciprocal values of the resistance are added:
(R - conductor resistance, 1/R - electrical conductivity of the conductor)
If only two resistances are connected in parallel in a circuit, then O:
(with a parallel connection, the total resistance of the circuit is less than the smaller of the included resistances)
4. The work of an electric current in a circuit consisting of parallel-connected sections is equal to the sum of the work in individual sections: A=A1+A2 5. The power of the electric current in a circuit consisting of parallel-connected sections is equal to the sum of the powers in the individual sections: P=P1+P2
For two resistances: i.e. The greater the resistance, the less current it contains.
The Joule-Lenz law is a physical law that allows us to determine the thermal effect of current in a circuit, according to this law: 
, where I is the current in the circuit, R is the resistance, t is time. This formula was calculated by creating a circuit: a galvanic cell (battery), a resistor and an ammeter. The resistor was dipped into a liquid into which a thermometer was inserted and the temperature was measured. This is how they derived their law and etched themselves into history forever, but even without their experiments it was possible to derive the same law:
U=A/q A=U*q=U*I*t=I^2*R*t but even despite this, honor and praise to these people.
Joule Lenz's law determines the amount of heat released in a section of an electrical circuit that has finite resistance when current passes through it. A prerequisite is the fact that there should be no chemical transformations in this section of the chain.
WORK OF ELECTRIC CURRENT
The work done by an electric current shows how much work was done by the electric field when moving charges along a conductor.
Knowing two formulas: I = q/t ..... and..... U = A/q, we can derive a formula for calculating the work of electric current: 
The work of an electric current is equal to the product of the current strength and the voltage and the time the current flows in the circuit.
The SI unit for measuring the work of electric current is [A] = 1 J = 1A. B. c
LEARN IT, IT WILL BE USEFUL! When calculating the work of electric current, an off-system multiple unit of work of electric current is often used: 1 kWh (kilowatt-hour).
1 kWh = ..........W.s = 3,600,000 J
In each apartment, to account for consumed electricity, special electricity meters are installed, which show the work of electric current performed over a certain period of time when various household electrical appliances are turned on. These meters show the work of electric current (electricity consumption) in “kWh”.
You need to learn how to calculate the cost of consumed electricity! We carefully understand the solution to the problem on page 122 of the textbook (paragraph 52)!
ELECTRIC POWER
The power of an electric current shows the work done by the current per unit time and is equal to the ratio of the work done to the time during which this work was done.
(power in mechanics is usually denoted by the letter N, in electrical engineering - the letter R) because A = IUt, then the power of the electric current is equal to:
or 
Unit of electric current power in the SI system:
[P] = 1 W (watt) = 1 A. B
Kirchhoff's laws – rules that show how currents and voltages relate in electrical circuits. These rules were formulated by Gustav Kirchhoff in 1845. In the literature they are often called Kirchhoff's laws, but this is not true, since they are not laws of nature, but were derived from Maxwell's third equation with a constant magnetic field. But still, the first name is more familiar to them, so we will call them, as is customary in the literature, Kirchhoff’s laws.
Kirchhoff's first law – the sum of currents converging at a node is equal to zero.
Let's figure it out. A node is a point connecting branches. A branch is a section of a chain between nodes. The figure shows that current i enters the node, and currents i 1 and i 2 exit the node. We compose an expression for the first Kirchhoff law, taking into account that the currents entering the node have a plus sign, and the currents emanating from the node have a minus sign i-i 1 -i 2 =0. Current i seems to spread into two smaller currents and is equal to the sum of currents i 1 and i 2 i=i 1 +i 2 . But if, for example, current i 2 entered the node, then current I would be defined as i=i 1 -i 2. It is important to consider signs when composing an equation.
Kirchhoff's first law is a consequence of the law of conservation of electricity: the charge arriving at a node over a certain period of time is equal to the charge leaving the node over the same time interval, i.e. The electric charge in the node does not accumulate and does not disappear.
Kirchhoff's second law – the algebraic sum of the emf acting in a closed circuit is equal to the algebraic sum of the voltage drops in this circuit.
Voltage is expressed as the product of current and resistance (according to Ohm's law).
This law also has its own rules for application. First, you need to set the direction of traversal of the contour with an arrow. Then sum up the EMF and voltage accordingly, taking it with a plus sign if the value coincides with the direction of the bypass and minus if it does not coincide. Let's create an equation according to Kirchhoff's second law for our scheme. We look at our arrow, E 2 and E 3 coincide with it in direction, which means a plus sign, and E 1 is directed in the opposite direction, which means a minus sign. Now we look at the voltages, the current I 1 coincides in the direction of the arrow, and the currents I 2 and I 3 are directed in the opposite direction. Hence:
-E 1 +E 2 +E 3 =I 1 R 1 -I 2 R 2 -I 3 R 3
Based on Kirchhoff's laws, methods for analyzing alternating sinusoidal current circuits have been compiled. The loop current method is a method based on the application of Kirchhoff’s second law and the nodal potential method based on the application of Kirchhoff’s first law.
For the emergence and existence of a constant electric current in a substance, it is necessary, firstly, the presence of free charged particles. If positive and negative charges are bonded to each other in atoms or molecules, their movement will not produce an electric current.
But the presence of free charges is not yet sufficient for the generation of current. To create and maintain the ordered movement of charged particles, it is necessary, secondly, to act on them in a certain direction. If this force ceases to act, then the ordered movement of charged particles will cease due to the resistance provided to their movement by ions of the crystal lattice of metals or neutral molecules of electrolytes.
Charged particles, as we know, are affected by an electric field with a force. Usually, it is the electric field inside the conductor that serves as the cause that causes and maintains the ordered movement of charged particles. Only in the static case, when the charges are at rest, the electric field inside the conductor is zero.
If there is an electric field inside the conductor, then between the ends of the conductor, in accordance with formula (8.28), there is a potential difference. When this potential difference does not change over time, a constant current is established in the conductor. Along the conductor, the potential decreases from a maximum value at one end of the conductor to a minimum value at the other. This decrease in potential can be detected by simple experiment.
As a guide, take a not very dry wooden stick and hang it horizontally. (Such a stick, although poorly, still conducts current.) Let the voltage source be an electrostatic machine. To record the potential of different sections of the conductor relative to the ground, you can
use pieces of metal foil attached to a stick. We connect one pole of the machine to the ground, and the second to one end of the conductor (stick). The chain will not be closed. When we rotate the handle of the machine, we will find that all the leaves are deflected at the same angle (Fig. 146). This means that the potential of all points of the conductor relative to the ground is the same. This is how it should be if the charges on the conductor are in balance. If the other end of the stick is now grounded, then when the machine handle is rotated, the picture will change. (Since the ground is a conductor, grounding the conductor makes the circuit closed.) At the grounded end, the leaves will not diverge at all: the potential of this end of the conductor is almost equal to the potential of the ground (the potential drop in a metal wire is small). The maximum angle of divergence of the leaves will be at the end of the conductor connected to the machine (Fig. 147). A decrease in the angle of divergence of the leaves as they move away from the machine indicates a drop in potential along the conductor.
Outside forces. Electromotive force and voltage.
External forces are those forces that differ in nature from the forces of the electrostatic field.
These forces can be caused by chemical processes, diffusion of current carriers in an inhomogeneous medium, electric (but not electrostatic) fields generated by time-varying magnetic fields, etc.
EMF is a physical quantity equal to the work done by external forces when moving a single positive charge along an electrical circuit:
ε = А st./q Unit of measurement - 1 V (Volt)
Voltage is a physical quantity equal to the work done by external and electrical forces when moving a single positive charge.
U = (A st. + A el.)/q Unit of measurement - 1 V.
Electrical circuit. Homogeneous and heterogeneous section of the chain.
Homogeneous and heterogeneous sections of the chain
A homogeneous section of the circuit is a section of the circuit on which no external forces act (no source of current)
An inhomogeneous section of a circuit is a section of a circuit where there is a current source.
Electrical circuit
Electrical circuit. External and internal section of the circuit, voltage drop.
Electrical circuit- a set of devices, elements intended for the flow of electric current, electromagnetic processes.
The electrical circuit can be divided into two sections: external and internal.
The external section, or, as they say, the external circuit, consists of one or more electrical energy receivers, connecting wires and various auxiliary devices included in this circuit.
The internal section, or internal circuit, is the source itself.
Voltage drop- a gradual decrease in voltage along a conductor through which an electric current flows, due to the fact that the conductor has active resistance.
Conductor resistance
Resistance is a value proportional to the length of the conductor l and inversely proportional to its cross-sectional area S
The greater the resistance of a conductor, the worse it conducts electric current, and, conversely, the lower the resistance of the conductor, the easier it is for electric current to pass through this conductor.
Specific electrical resistance of the conductor ρ [Ohm*m] ρ=RS/l R = ρ*l/S
Ohm's law for a section of a circuit and for a closed circuit
Ohm's law for a section of an electrical circuit - the current strength in a section of an electrical circuit is directly proportional to the voltage and inversely proportional to the resistance of the section.
Ohm's law for a complete electrical circuit - the current strength in an electrical circuit is directly proportional to the emf of the source and inversely proportional to the total resistance of the circuit (the sum of external and internal resistances)
I = ε / (R + r). where R is the resistance of the external section of the circuit,
r - internal resistance.
Series connection of energy consumers
In a series connection, the conductors are connected in series, that is, one after another, with I=const, U=U 1 +U 2 +U 3 +…+U n and R=R 1 +R 2 +R 3 +…+R n
Parallel connection of current sources.
Work of electric current
The work of electric current A is equal to the product of the value of the moved charge Q and the voltage U
A=Q*U [A]=J, [U]=B, [Q]=Cl, [t]=c.
Because I=Q/t, => Q=I*t, means A=I*U*t
According to Ohm's law for a section of the chain I=U/R, U=I*R
A=I*U*T => A=U 2 *t/R(convenient for parallel connections) => A=I 2 *R*t(convenient for serial connections)
The nature of light.
Nature of light - wave
17th century Christiaan Huygens: 1) diffraction - bending of light around obstacles 2) interference - addition of waves.
19th century- Maxwell's theory (the speed of light is a special case of electromagnetic waves) - electromagnetic theory the speed of propagation of electromagnetic waves in a vacuum is 3*10 8 m/s equal to the speed of light in a vacuum. 299 thousand km/s
17th century O. Roemer using the astronomical method obtained the speed of light approximately 214.3 km/s
19th century. Physical speed of light is approximately 313 thousand km/s
Nature of light - quantum.
approximately 500 BC Pythagoras: light is a stream of particles.
17th century Isaac Newton adhered to the same theory. Carpuscula (from Latin) – particle.
Newton's carpuscular theory: 1) rectilinear propagation of light 2) law of reflection 3) formation of shadows from objects
19 in Heinrich Hertz discovered the phenomenon of the photoelectric effect.
20th century. The light has dual nature - has a particle-wave dualism: during propagation - like a wave, and during emission and absorption - like a stream of particles.
relationship between lambda wavelength and nu frequency
lambda = s/nu s - speed of light in vacuum [m/s] lambda [m] nu [Hz]
Laws of reflection
1. The incident ray, the reflecting ray and the perpendicular to the interface between the two media, reconstructed at the point of incidence of the ray, lie in the same plane.
2The angle of reflection γ is equal to the angle of incidence α: γ = α
Specular reflection - if the roughness is less than lambda and diffuse roughness is comparable to lambda
Diffuse reflection of light. Specular reflection of light.
Laws of light refraction.
The law of light refraction: the incident and refracted rays, as well as the perpendicular to the interface between two media, restored at the point of incidence of the ray, lie in the same plane. The ratio of the sine of the angle of incidence α to the sine of the angle of refraction γ is a constant value for two given media:
The constant value n is called the relative refractive index of the second medium relative to the first. The refractive index of a medium relative to vacuum is called the absolute refractive index.
The relative refractive index of two media is equal to the ratio of their absolute refractive indices:
The physical meaning of the refractive index is the ratio of the speed of propagation of waves in the first medium υ 1 to the speed of their propagation in the second medium υ 2:
Nature of light from 26.
Wave interference– this is the phenomenon of superposition of coherent waves; characteristic of waves of any nature (mechanical, electromagnetic, etc.)
Coherent waves are waves emitted by sources that have the same frequency and constant phase difference.
When coherent waves are superimposed at any point in space, the amplitude of the oscillations (displacement) of this point will depend on the difference in distances from the sources to the point in question. This distance difference is called the stroke difference.
When superposing coherent waves, two limiting cases are possible:
Maximum condition:
Where 
The wave path difference is equal to an integer number of wavelengths (in other words, an even number of half-wavelengths).
In this case, the waves at the point under consideration arrive with the same phases and reinforce each other - the amplitude of oscillations of this point is maximum and equal to double the amplitude.
Minimum condition:
, Where
The wave path difference is equal to an odd number of half-wave lengths.
The waves arrive at the point in question in antiphase and cancel each other out.
The amplitude of oscillations of a given point is zero.
As a result of the superposition of coherent waves (wave interference), an interference pattern is formed.
With wave interference, the amplitude of the oscillations of each point does not change over time and remains constant.
When incoherent waves are superimposed, there is no interference pattern, because the amplitude of oscillations of each point changes over time.
Interference of light
1802 English physicist Thomas Young conducted an experiment in which the interference of light was observed.
Thomas Young's experience
Two beams of light were formed from one source through slit A (through slits B and C), then the light beams fell on screen E. Since the beams from slits B and C were coherent, an interference pattern could be observed on the screen: alternating light and dark stripes .
Light stripes – the waves reinforced each other (the maximum condition was met).
Dark stripes – the waves were added in antiphase and canceled each other out (minimum condition).
If Young’s experiment used a source of monochromatic light (one wavelength), then only light and dark stripes of a given color were observed on the screen.
If the source produced white light (i.e., complex in its composition), then rainbow stripes were observed on the screen in the area of light stripes. The iridescence was explained by the fact that the conditions of maximums and minimums depend on the wavelengths.
Interference in thin films
The phenomenon of interference can be observed, for example:
Rainbow stains on the surface of a liquid during an oil spill, kerosene, or in soap bubbles;
The thickness of the film must be greater than the wavelength of light.
During his experiment, Young was able to measure the wavelength of light for the first time.
As a result of the experiment, Jung proved that light has wave properties.
Application of interference:
- interferometers – devices for measuring the wavelength of light
- coating of optics (in optical instruments, when light passes through the lens, light loss is up to 50%) - all glass parts are covered with a thin film with a refractive index slightly lower than that of glass; interference maxima and minima are redistributed and light losses are reduced.
Nature of light from 26.
DIFFRACTION OF LIGHT
Diffraction- this is a phenomenon inherent in wave processes for any kind of waves.
Diffraction of light- this is the deviation of light rays from rectilinear propagation when passing through narrow slits, small holes or when going around small obstacles.
The phenomenon of light diffraction proves that light has wave properties.
To observe diffraction you can:
Pass the light from the source through a very small hole or place the screen at a large distance from the hole. Then a complex pattern of light and dark concentric rings is observed on the screen.
- or direct the light onto a thin wire, then light and dark stripes will be observed on the screen, and in the case of white light, a rainbow stripe.
Diffraction grating
This is an optical instrument for measuring the wavelength of light.
A diffraction grating is a collection of a large number of very narrow slits separated by opaque spaces.
If a monochromatic wave falls on the grating. then the slits (secondary sources) create coherent waves. A collecting lens is placed behind the grille, followed by a screen. As a result of the interference of light from various grating slits, a system of maxima and minima is observed on the screen.
The path difference between the waves from the edges of adjacent slits is equal to the length of the segment AC. If this segment contains an integer number of wavelengths, then the waves from all slits will reinforce each other. When using white light, all maxima (except the central one) have a rainbow color.
So, the maximum condition is:
where k is the order (or number) of the diffraction spectrum
The more lines are applied to the grating, the further the diffraction spectra are from each other and the smaller the width of each line on the screen, so the maxima are visible as separate lines, i.e. the resolving power of the grating increases.
The more lines there are per unit length of the grating, the greater the accuracy of wavelength measurement.
POLARIZATION OF LIGHT
Wave polarization
The property of transverse waves is polarization.
A polarized wave is a transverse wave in which all particles oscillate in the same plane.
Polarization of light
The experiment with tourmaline is proof of the transverse nature of light waves.
A tourmaline crystal is a transparent, green mineral with an axis of symmetry.
In a beam of light from a conventional source, there are fluctuations in the vectors of electric field strength E and magnetic induction B in all possible directions perpendicular to the direction of propagation of the light wave. Such a wave is called a natural wave.
When light passes through a tourmaline crystal, it becomes polarized.
In polarized light, oscillations of the intensity vector E occur only in one plane, which coincides with the symmetry axis of the crystal.
The polarization of light after passing through tourmaline is detected if a second tourmaline crystal (analyzer) is placed behind the first crystal (polarizer).
If the axes of two crystals are identically directed, the light beam will pass through both and will only be slightly weakened due to partial absorption of light by the crystals.
Scheme of operation of the polarizer and the analyzer behind it:
If the second crystal begins to rotate, i.e. shift the position of the symmetry axis of the second crystal relative to the first, then the beam will gradually go out and go out completely when the position of the symmetry axes of both crystals becomes mutually perpendicular.
Application of polarized light:
Continuously adjustable lighting using two Polaroids
- for extinguishing glare when photographing (glare is extinguished by placing a Polaroid between the light source and the reflective surface)
To eliminate glare from the headlights of oncoming cars.
Polaroid, polarizing filter, one of the main types of optical linear polarizers; is a thin polarizing film, sealed to protect against mechanical damage and the action of moisture between two transparent plates (films).
DISPERSION
A ray of white light passing through a triangular prism is not only deflected, but also decomposed into component colored rays.
This phenomenon was discovered by Isaac Newton through a series of experiments.
Newton's experiments
Experience in decomposing white light into a spectrum:
or 
Newton directed a beam of sunlight through a small hole onto a glass prism.
When hitting the prism, the beam was refracted and on the opposite wall gave an elongated image with a rainbow alternation of colors - a spectrum.
Experience in the synthesis (production) of white light:
Newton first directed Sunbeam to the prism. Then, having collected the colored rays emerging from the prism using a collecting lens, Newton received a white image of a hole on a white wall instead of a colored stripe.
Newton's conclusions:
The prism does not change the light, but only decomposes it into components
- light rays that differ in color differ in the degree of refraction; Violet rays are refracted most strongly, red ones less strongly
Red light, which is less refracted, has the highest speed, and violet light has the least speed, which is why the prism decomposes the light.
The dependence of the refractive index of light on its color is called dispersion.
Remember the phrase, the initial letters of the words give the sequence of colors in the spectrum:
"Every Hunter Wants to Know Where the Pheasant Sits."
White light spectrum:
Conclusions:
The prism decomposes the light
- white light is complex (composite)
- violet rays are refracted more strongly than red ones.
The color of a light beam is determined by its vibration frequency.
When moving from one medium to another, the speed of light and wavelength change, but the frequency that determines the color remains constant.
The boundaries of the ranges of white light and its components are usually characterized by their wavelengths in vacuum.
White light is a collection of waves with lengths from 380 to 760 nm.
Where can you observe the phenomenon of dispersion?
When light passes through a prism
- refraction of light in water droplets, for example, on grass or in the atmosphere when a rainbow is formed
- around the lanterns in the fog.
How to explain the color of any object?
White paper reflects all rays of different colors falling on it
- a red object reflects only red rays, and absorbs rays of other colors
-
The eye perceives rays of a certain wavelength reflected from an object and thus perceives the color of the object.
Spectral analysis is a set of methods for qualitative and quantitative determination of the composition of an object, based on the study of the spectra of interaction of matter with radiation, including spectra electromagnetic radiation, acoustic waves, distribution of masses and energies of elementary particles, etc.
Electric current and conditions of its existence.
Electric current is the ordered, directed movement of free charges in a conductor.
D.C– this is electric current, the characteristics of which do not change over time.
Conditions for the existence of electric current
For the occurrence and maintenance of current in any environment, two conditions must be met:
-presence of free electric charges in the environment
-creation of an electric field in the environment.
In different environments, the carriers of electric current are different charged particles.
Current strength I is a scalar quantity characterizing the charge Q passing through the cross section of the conductor per unit time. Q=q*N I=Q/t
Current is measured in amperes and charge in coulombs. I=[A], Q=[Cl]
Current density – j vector quantity j V q, shows the current strength per unit S section.
j=I/S section Sectional area S section. measured in square meters