Biographies Characteristics Analysis

Definition of electric current. What is electric current? Nature of electricity

". Today I want to touch on such a topic as electric current. What is it? Let's try to remember the school curriculum.

Electric current is the ordered movement of charged particles in a conductor.

If you remember, in order for charged particles to move, (an electric current arises) you need to create an electric field. To create an electric field, you can carry out such elementary experiments as rubbing a plastic handle on wool and for some time it will attract light objects. Bodies capable of attracting objects after rubbing are called electrified. We can say that the body in this state has electric charges, and the bodies themselves are called charged. From the school curriculum, we know that all bodies are made up of tiny particles (molecules). A molecule is a particle of a substance that can be separated from a body and it will have all the properties inherent in this body. Molecules of complex bodies are formed from various combinations of atoms of simple bodies. For example, a water molecule consists of two simple ones: an oxygen atom and one hydrogen atom.

Atoms, neutrons, protons and electrons - what are they?

In turn, an atom consists of a nucleus and revolving around it electrons. Each electron in an atom has a small electrical charge. For example, a hydrogen atom consists of a nucleus of an electron revolving around it. The nucleus of an atom consists, in turn, of protons and neutrons. The nucleus of an atom, in turn, has an electric charge. The protons that make up the nucleus have the same electric charges and electrons. But protons, unlike electrons, are inactive, but their mass is many times greater than the mass of an electron. The particle neutron, which is part of the atom, has no electric charge, it is neutral. The electrons that revolve around the nucleus of an atom and the protons that make up the nucleus are carriers of equal electric charges. Between the electron and the proton there is always a force of mutual attraction, and between the electrons themselves and between the protons, the force of mutual repulsion. Because of this, the electron has a negative electric charge, and the proton positive. From this we can conclude that there are 2 kinds of electricity: positive and negative. The presence of equally charged particles in an atom leads to the fact that between the positively charged nucleus of the atom and the electrons rotating around it, there are forces of mutual attraction that hold the atom together. Atoms differ from each other in the number of neutrons and protons in the nuclei, which is why the positive charge of the nuclei of atoms of various substances is not the same. In atoms of different substances, the number of rotating electrons is not the same and is determined by the positive charge of the nucleus. The atoms of some substances are firmly bound to the nucleus, while in others this bond can be much weaker. This explains the different strengths of the bodies. Steel wire is much stronger than copper wire, which means that steel particles are more strongly attracted to each other than copper particles. The attraction between molecules is especially noticeable when they are close to each other. The most striking example is that two drops of water merge into one upon contact.

Electric charge

In the atom of any substance, the number of electrons revolving around the nucleus is equal to the number of protons contained in the nucleus. The electric charge of an electron and a proton are equal in magnitude, which means that the negative charge of the electrons is equal to the positive charge of the nucleus. These charges mutually balance each other, and the atom remains neutral. In an atom, electrons create an electron shell around the nucleus. The electron shell and the nucleus of an atom are in continuous oscillatory motion. When the atoms move, they collide with each other and one or more electrons fly out of them. The atom ceases to be neutral and becomes positively charged. Since its positive charge has become more negative (weak connection between the electron and the nucleus - metal and coal). In other bodies (wood and glass), the electronic shells are not broken. After breaking away from atoms, free electrons move randomly and can be captured by other atoms. The process of appearances and disappearances in the body is continuous. As the temperature increases, the speed of the vibrational movement of atoms increases, the collisions become more frequent, become stronger, the number of free electrons increases. However, the body remains electrically neutral, since the number of electrons and protons in the body does not change. If a certain amount of free electrons is removed from the body, then the positive charge becomes greater than the total charge. The body will be positively charged and vice versa. If a lack of electrons is created in the body, then it is additionally charged. If the excess is negative. The greater this deficiency or excess, the greater the electric charge. In the first case (more positively charged particles), bodies are called conductors (metals, aqueous solutions of salts and acids), and in the second (lack of electrons, negatively charged particles) dielectrics or insulators (amber, quartz, ebonite). For the continuous existence of an electric current, it is necessary to constantly maintain a potential difference in the conductor.

Well, that's a little physics course is over. I think you, with my help, remembered the school curriculum for the 7th grade, and we will analyze what the potential difference is in my next article. Until we meet again on the pages of the site.

electrolytes It is customary to call conductive media in which the flow of electric current is accompanied by the transfer of matter. Carriers of free charges in electrolytes are positively and negatively charged ions.

The main representatives of electrolytes widely used in technology are aqueous solutions of inorganic acids, salts and bases. The passage of electric current through the electrolyte is accompanied by the release of substances on the electrodes. This phenomenon has been named electrolysis (fig.9.10) .

Electric current in electrolytes is the movement of ions of both signs in opposite directions. Positive ions move towards the negative electrode ( cathode), negative ions - to the positive electrode ( anode). Ions of both signs appear in aqueous solutions of salts, acids and alkalis as a result of the splitting of some neutral molecules. This phenomenon is called electrolytic dissociation .

The law of electrolysis was experimentally established by the English physicist M. Faraday in 1833.

Faraday's first law determines the amount of primary products released on the electrodes during electrolysis: the mass m of the substance released on the electrode is directly proportional to the charge q that has passed through the electrolyte:

m = kq = kitit,

where kelectrochemical equivalent of a substance:

F = en A = 96485 C / mol. - Faraday constant.

Faraday's second lawelectrochemical equivalents of various substances include their chemical equivalents :

Unified Faraday's Law for electrolysis:

Electrolytic processes are classified as follows:

obtaining inorganic substances (hydrogen, oxygen, chlorine, alkalis, etc.);

obtaining metals (lithium, sodium, potassium, beryllium, magnesium, zinc, aluminum, copper, etc.);

cleaning of metals (copper, silver,…);

obtaining metal alloys;

obtaining galvanic coatings;

treatment of metal surfaces (nitriding, boriding, electropolishing, cleaning);

obtaining organic substances;

electrodialysis and water desalination;

film deposition by electrophoresis.

Practical application of electrolysis

Electrochemical processes are widely used in various fields of modern technology, in analytical chemistry, biochemistry, etc. In the chemical industry, chlorine and fluorine, alkalis, chlorates and perchlorates, persulfuric acid and persulfates, chemically pure hydrogen and oxygen, etc. are obtained by electrolysis. In this case, some substances are obtained by reduction at the cathode (aldehydes, para-aminophenol, etc.), others by electrooxidation at the anode (chlorates, perchlorates, potassium permanganate, etc.).

Electrolysis in hydrometallurgy is one of the stages in the processing of metal-containing raw materials, which ensures the production of marketable metals. Electrolysis can be carried out with soluble anodes - the electrorefining process or with insoluble ones - the electroextraction process. The main task in the electrorefining of metals is to ensure the required purity of the cathode metal at acceptable energy costs. In non-ferrous metallurgy, electrolysis is used to extract metals from ores and purify them.

Aluminum, magnesium, titanium, zirconium, uranium, beryllium, etc. are obtained by electrolysis of molten media. For refining (cleaning) the metal by electrolysis, plates are cast from it and placed as anodes 1 in the electrolyzer 3 (Fig. 9.11). When a current is passed, the metal to be purified 1 undergoes anodic dissolution, i.e., it passes into solution in the form of cations. Then these metal cations are discharged at the cathode 2, due to which a compact deposit of already pure metal is formed. Impurities in the anode either remain insoluble 4 or pass into the electrolyte and are removed.

Figure 9.11 shows a diagram of the electrolytic refining of copper.

Electroplating - the field of applied electrochemistry, which deals with the processes of applying metal coatings to the surface of both metal and non-metal products when a direct electric current passes through solutions of their salts. Electroplating is divided into electroplating and electroforming.

electroplating (from Greek cover) - is the electrodeposition on the surface of a metal of another metal, which is firmly connected (adhered) to the coated metal (object), which serves as the cathode of the electrolyzer (Fig. 9.12).

Electroplating can be used to cover a part with a thin layer of gold or silver, chrome or nickel. With the help of electrolysis, it is possible to apply the thinnest metal coatings on various metal surfaces. With this method of coating, the part is used as a cathode, placed in a salt solution of the metal from which the coating is to be obtained. A plate of the same metal is used as the anode.

Rice. 9.12Rice. 9.13
We recommend that you view the Electroforming demo.

Electrotype production of precise, easily detachable metal copies by electrolysis of considerable thickness from various non-metallic and metallic objects, called matrices (Fig. 9.13).

Busts, statues, etc. are made using electroforming. Electroplating is used to apply relatively thick metal coatings to other metals (for example, the formation of a "superimposed" layer of nickel, silver, gold, etc.).

What is electric current

Directional movement of electrically charged particles under the influence of . Such particles can be: in conductors - electrons, in electrolytes - ions (cations and anions), in semiconductors - electrons and so-called "holes" ("electron-hole conductivity"). There is also a "bias current", the flow of which is due to the process of charging the capacitance, i.e. change in the potential difference between the plates. Between the plates, no movement of particles occurs, but the current flows through the capacitor.

In the theory of electrical circuits, current is considered to be the directed movement of charge carriers in a conducting medium under the action of an electric field.

Conduction current (simply current) in the theory of electrical circuits is the amount of electricity flowing per unit time through the cross section of the conductor: i \u003d q / t, where i is the current. BUT; q \u003d 1.6 10 9 - electron charge, C; t - time, s.

This expression is valid for DC circuits. For alternating current circuits, the so-called instantaneous current value is used, equal to the rate of change of charge over time: i (t) \u003d dq / dt.

Electric current occurs when an electric field, or potential difference between two points of a conductor, appears in a section of an electrical circuit. The potential difference between two points is called voltage or voltage drop in this section of the circuit.


Instead of the term "current" ("current value"), the term "current strength" is often used. However, the latter cannot be called successful, since the current strength is not any force in the literal sense of the word, but only the intensity of the movement of electric charges in the conductor, the amount of electricity passing per unit time through the cross-sectional area of ​​\u200b\u200bthe conductor.
The current is characterized, which in the SI system is measured in amperes (A), and current density, which in the SI system is measured in amperes per square meter.
One ampere corresponds to the movement through the cross section of the conductor for one second (s) of an electricity charge of one pendant (C):

1A = 1C/s.

In the general case, denoting the current with the letter i, and the charge with q, we get:

i = dq / dt.

The unit of current is called the ampere (A). The current in the conductor is 1 A if an electric charge equal to 1 pendant passes through the cross section of the conductor in 1 second.

If a voltage acts along the conductor, then an electric field arises inside the conductor. When the field strength E, the electrons with charge e are affected by the force f = Ee. The values ​​f and E are vector. During the free path time, the electrons acquire a directed motion along with a chaotic one. Each electron has a negative charge and receives a velocity component directed opposite to the vector E (Fig. 1). Ordered motion, characterized by some average electron velocity vcp, determines the flow of electric current.

Electrons can also have directed motion in rarefied gases. In electrolytes and ionized gases, the flow of current is mainly due to the movement of ions. In accordance with the fact that in electrolytes positively charged ions move from the positive to the negative pole, historically the direction of the current was taken to be the opposite of the direction of electrons.

The current direction is taken to be the direction in which positively charged particles move, i.e. the direction opposite to the movement of electrons.
In the theory of electrical circuits, the direction of movement of positively charged particles from a higher potential to a lower one is taken as the direction of current in a passive circuit (outside energy sources). This direction was taken at the very beginning of the development of electrical engineering and contradicts the true direction of movement of charge carriers - electrons moving in conductive media from minus to plus.


The value equal to the ratio of the current to the cross-sectional area S is called the current density (denoted δ): δ= I/S

It is assumed that the current is uniformly distributed over the cross section of the conductor. Current density in wires is usually measured in A/mm2.

According to the type of carriers of electric charges and the medium of their movement, they are distinguished conduction currents and displacement currents. Conductivity is divided into electronic and ionic. For steady modes, two types of currents are distinguished: direct and alternating.

Electric current transfer called the phenomenon of the transfer of electric charges by charged particles or bodies moving in free space. The main type of electric current transfer is the movement in the void of elementary particles with a charge (the movement of free electrons in electron tubes), the movement of free ions in gas-discharge devices.

Electric displacement current (polarization current) called the ordered movement of bound carriers of electric charges. This kind of current can be observed in dielectrics.
Full electric current is a scalar value equal to the sum of the electrical conduction current, the electrical transfer current and the electrical displacement current through the considered surface.

A constant current is a current that can vary in magnitude, but does not change its sign for an arbitrarily long time. Read more about this here:

An alternating current is a current that periodically changes both in magnitude and in sign.The quantity characterizing the alternating current is the frequency (in the SI system it is measured in hertz), in the case when its strength changes periodically. High frequency alternating current pushed out to the surface of the conductor. High-frequency currents are used in mechanical engineering for heat treatment of surfaces of parts and welding, in metallurgy for melting metals.Alternating currents are divided into sinusoidal and non-sinusoidal. A sinusoidal current is a current that changes according to a harmonic law:

i = Im sin ωt,

The rate of change of alternating current is characterized by it, defined as the number of complete repetitive oscillations per unit time. Frequency is denoted by the letter f and is measured in hertz (Hz). So, the frequency of the current in the network 50 Hz corresponds to 50 complete oscillations per second. The angular frequency ω is the rate of change of current in radians per second and is related to frequency by a simple relation:

ω = 2πf

Steady (fixed) values ​​of direct and alternating currents designate with a capital letter I unsteady (instantaneous) values ​​- with the letter i. The conditionally positive direction of the current is considered the direction of movement of positive charges.

This is a current that changes according to the sine law over time.

Alternating current also means current in conventional single- and three-phase networks. In this case, the alternating current parameters change according to the harmonic law.

Since alternating current varies with time, simple problem solving methods suitable for direct current circuits are not directly applicable here. At very high frequencies, charges can oscillate - flow from one place in the circuit to another and back. In this case, unlike DC circuits, the currents in series-connected conductors may not be the same. Capacitances present in AC circuits amplify this effect. In addition, when the current changes, self-induction effects come into play, which become significant even at low frequencies, if coils with large inductances are used. At relatively low frequencies, AC circuits can still be calculated using , which, however, must be modified accordingly.

A circuit that includes various resistors, inductors, and capacitors can be considered as if it consisted of a generalized resistor, capacitor, and inductor connected in series.

Consider the properties of such a circuit connected to a sinusoidal alternator. In order to formulate rules for designing AC circuits, it is necessary to find the relationship between voltage drop and current for each of the components of such a circuit.

It plays completely different roles in AC and DC circuits. If, for example, an electrochemical element is connected to the circuit, then the capacitor will begin to charge until the voltage across it becomes equal to the EMF of the element. Then the charging will stop and the current will drop to zero. If the circuit is connected to an alternator, then in one half-cycle the electrons will flow from the left side of the capacitor and accumulate on the right, and vice versa in the other. These moving electrons are an alternating current, the strength of which is the same on both sides of the capacitor. As long as the frequency of the alternating current is not very high, the current through the resistor and the inductor is also the same.

In AC consuming devices, AC is often rectified by rectifiers to produce DC.

Electrical conductors

The material in which current flows is called. Some materials become superconductive at low temperatures. In this state, they offer almost no resistance to current, their resistance tends to zero. In all other cases, the conductor resists the flow of current and, as a result, part of the energy of the electrical particles is converted into heat. The current strength can be calculated using for a section of the circuit and Ohm's law for a complete circuit.

The speed of particles in conductors depends on the material of the conductor, the mass and charge of the particle, the ambient temperature, the applied potential difference and is much less than the speed of light. Despite this, the speed of propagation of the actual electric current is equal to the speed of light in a given medium, that is, the speed of propagation of the front of an electromagnetic wave.

How current affects the human body

Current passed through the human or animal body can cause electrical burns, fibrillation, or death. On the other hand, electric current is used in intensive care, for the treatment of mental illness, especially depression, electrical stimulation of certain areas of the brain is used to treat diseases such as Parkinson's disease and epilepsy, a pacemaker that stimulates the heart muscle with a pulsed current is used for bradycardia. In humans and animals, current is used to transmit nerve impulses.

According to safety precautions, the minimum perceptible current is 1 mA. The current becomes dangerous for human life starting from a strength of about 0.01 A. The current becomes fatal for a person starting from a strength of about 0.1 A. A voltage of less than 42 V is considered safe.

Any current appears only in the presence of a source with free charged particles. This is due to the fact that there are no substances in vacuum, including electric charges. Therefore, the vacuum is considered the best. In order for it to become possible for the passage of an electric current a, it is necessary to ensure the presence of a sufficient number of free charges. In this article we will look at what constitutes an electric current in a vacuum.

How electric current can appear in a vacuum

In order to create a full-fledged electric current in a vacuum, it is necessary to use such a physical phenomenon as thermionic emission. It is based on the property of a certain substance to emit free electrons when heated. Such electrons emerging from a heated body are called thermoelectrons, and the entire body is called an emitter.

Thermionic emission underlies the operation of vacuum devices, better known as vacuum tubes. The simplest design contains two electrodes. One of them is the cathode, which is a spiral, the material of which is molybdenum or tungsten. It is he who is heated by an electric current ohm. The second electrode is called the anode. It is in a cold state, performing the task of collecting thermionic electrons. As a rule, the anode is made in the form of a cylinder, and a heated cathode is placed inside it.

Application of current in vacuum

In the last century, vacuum tubes played a leading role in electronics. And, although they have long been replaced by semiconductor devices, the principle of operation of these devices is used in cathode ray tubes. This principle is used in welding and melting work in vacuum and other areas.

Thus, one of the varieties of current a is an electron flow flowing in vacuum. When the cathode is heated, an electric field appears between it and the anode. It is this that gives the electrons a certain direction and speed. According to this principle, an electronic lamp with two electrodes (diode) works, which is widely used in radio engineering and electronics.

The modern device is a cylinder made of glass or metal, from which air has been previously pumped out. Two electrodes, a cathode and an anode, are soldered inside this cylinder. To enhance the technical characteristics, additional grids are installed, with the help of which the electron flux is increased.

Current and voltage are quantitative parameters used in electrical circuits. Most often, these values ​​​​change over time, otherwise there would be no point in the operation of the electrical circuit.

Voltage

Conventionally, the voltage is indicated by the letter U. The work done to move a unit of charge from a point of low potential to a point of high potential is the voltage between these two points. In other words, this is the energy released after the transition of a unit of charge from a high potential to a small one.

Voltage can also be called the potential difference, as well as the electromotive force. This parameter is measured in volts. To move 1 coulomb of charge between two points that have a voltage of 1 volt, you need to do 1 joule of work. Coulombs measure electric charges. 1 pendant is equal to the charge of 6x10 18 electrons.

Voltage is divided into several types, depending on the types of current.

  • Constant pressure . It is present in electrostatic circuits and DC circuits.
  • AC voltage . This type of voltage is available in circuits with sinusoidal and alternating currents. In the case of a sinusoidal current, voltage characteristics such as:
    voltage fluctuation amplitude is its maximum deviation from the x-axis;
    instant voltage, which is expressed at a certain point in time;
    operating voltage, is determined by the active work of the 1st half-cycle;
    medium rectified voltage, determined by the modulus of the rectified voltage for one harmonic period.

When transmitting electricity through overhead lines, the arrangement of supports and their dimensions depend on the magnitude of the applied voltage. The voltage between phases is called line voltage , and the voltage between ground and each of the phases is phase voltage . This rule applies to all types of overhead lines. In Russia, in household electrical networks, the standard is a three-phase voltage with a linear voltage of 380 volts, and a phase voltage value of 220 volts.

Electricity

The current in an electrical circuit is the speed of electrons at a certain point, measured in amperes, and is indicated on the diagrams by the letter " I". Derived units of the ampere are also used with the appropriate prefixes milli-, micro-, nano, etc. A current of 1 ampere is generated by moving a unit of charge of 1 coulomb in 1 second.

Conventionally, it is considered that the current flows in the direction from the positive potential to the negative one. However, from the course of physics it is known that the electron moves in the opposite direction.

You need to know that the voltage is measured between 2 points on the circuit, and the current flows through one specific point of the circuit, or through its element. Therefore, if someone uses the expression "voltage in resistance", then this is incorrect and illiterate. But often we are talking about voltage at a certain point in the circuit. This refers to the voltage between ground and this point.

Voltage is formed from the impact on electrical charges in generators and other devices. Current is generated by applying voltage to two points in a circuit.

To understand what current and voltage are, it would be more correct to use. On it you can see the current and voltage, which change their values ​​over time. In practice, the elements of an electrical circuit are connected by conductors. At certain points, the circuit elements have their own voltage value.

Current and voltage obey the rules:

  • The sum of the currents entering the point is equal to the sum of the currents leaving the point (charge conservation rule). Such a rule is Kirchhoff's law for current. The point of entry and exit of current in this case is called a node. A consequence of this law is the following statement: in a series electrical circuit of a group of elements, the current for all points is the same.
  • In a parallel circuit of elements, the voltage across all elements is the same. In other words, the sum of voltage drops in a closed circuit is zero. This Kirchhoff's law applies to stresses.
  • The work done per unit time by the circuit (power) is expressed as follows: P \u003d U * I. Power is measured in watts. 1 joule of work done in 1 second is equal to 1 watt. Power is distributed in the form of heat, is spent on mechanical work (in electric motors), is converted into radiation of various types, and accumulates in tanks or batteries. When designing complex electrical systems, one of the challenges is the thermal load of the system.

Electric current characteristic

A prerequisite for the existence of current in an electrical circuit is a closed circuit. If the circuit breaks, then the current stops.

Everything in electrical engineering works on this principle. They break the electrical circuit with moving mechanical contacts, and this stops the flow of current, turning off the device.

In the energy industry, electric current occurs inside current conductors, which are made in the form of tires, and other parts that conduct current.

There are also other ways to create an internal current in:

  • Liquids and gases due to the movement of charged ions.
  • Vacuum, gas and air using thermionic emission.
  • due to the movement of charge carriers.
Conditions for the occurrence of electric current
  • Heating conductors (not superconductors).
  • Application to charge carriers of potential difference.
  • Chemical reaction with the release of new substances.
  • The effect of a magnetic field on a conductor.
Current Waveforms
  • Straight line.
  • Variable harmonic sine wave.
  • A meander that looks like a sine wave, but has sharp corners (sometimes the corners can be smoothed).
  • A pulsating form of one direction, with an amplitude that fluctuates from zero to the largest value according to a certain law.

Types of work of electric current

  • Light emitted by lighting devices.
  • Generating heat with heating elements.
  • Mechanical work (rotation of electric motors, action of other electrical devices).
  • Creation of electromagnetic radiation.

Negative phenomena caused by electric current

  • Overheating of contacts and current-carrying parts.
  • The occurrence of eddy currents in the cores of electrical devices.
  • Electromagnetic radiation to the external environment.

The creators of electrical devices and various circuits when designing must take into account the above properties of electric current in their designs. For example, the harmful effect of eddy currents in electric motors, transformers and generators is reduced by blending the cores used to transmit magnetic fluxes. Core blending is its manufacture not from a single piece of metal, but from a set of separate thin plates of special electrical steel.

But, on the other hand, eddy currents are used to operate microwave ovens, ovens, operating on the principle of magnetic induction. Therefore, we can say that eddy currents are not only harmful, but also beneficial.

An alternating current with a signal in the form of a sinusoid can vary in frequency of oscillation per unit of time. In our country, the industrial current frequency of electrical devices is standard, and is equal to 50 hertz. In some countries, the current frequency is 60 hertz.

For various purposes in electrical engineering and radio engineering, other frequency values ​​\u200b\u200bare used:

  • Low frequency signals with lower current frequency.
  • High frequency signals, which are much higher than the current frequency of industrial use.

It is believed that electric current occurs when electrons move inside a conductor, so it is called conduction current. But there is another type of electric current, which is called convection. It occurs when charged macrobodies move, for example, raindrops.

Electric current in metals

The movement of electrons under the influence of a constant force on them is compared with a parachutist who descends to the ground. In these two cases, uniform motion occurs. The force of gravity acts on the skydiver, and the force of air resistance opposes it. The electric field force acts on the movement of electrons, and the ions of the crystal lattices resist this movement. The average speed of the electrons reaches a constant value, as does the speed of the skydiver.

In a metal conductor, the speed of one electron is 0.1 mm per second, and the speed of an electric current is about 300,000 km per second. This is because electric current flows only where voltage is applied to the charged particles. Therefore, a high current flow rate is achieved.

When moving electrons in a crystal lattice, there is the following regularity. The electrons do not collide with all the oncoming ions, but only with every tenth of them. This is explained by the laws of quantum mechanics, which can be simplified as follows.

The movement of electrons is hindered by large ions that resist. This is especially noticeable when metals are heated, when heavy ions "swing", increase in size and reduce the electrical conductivity of the crystal lattices of the conductor. Therefore, when metals are heated, their resistance always increases. As the temperature decreases, the electrical conductivity increases. By reducing the temperature of the metal to absolute zero, the effect of superconductivity can be achieved.