The maximum value of the alternating current. Basic AC parameters
In this article we will talk about the parameters of alternating current. For example, a familiar household outlet is a source of alternating current and variable EMF.
The change in EMF and the change in the current of a linear load connected to such a source will occur according to a sinusoidal law. At the same time, variable EMF, alternating voltages and currents, can be characterized by their main four parameters:
period;
frequency;
amplitude;
effective value.
There are also auxiliary parameters:
angular frequency;
phase;
instant value.
The period T of an alternating current is the period of time during which the current or voltage makes one complete cycle of changes.
Since the generator is the source of alternating current, the period is related to the rotation speed of its rotor, and the higher the rotation speed of the coil or rotor of the generator, the shorter the period of the generated variable EMF, and, accordingly, the alternating current of the load.
The period is measured in seconds, milliseconds, microseconds, nanoseconds, depending on the specific situation in which this current is considered. The above figure shows how the voltage U changes over time, while having a constant characteristic period T.
The frequency f is the reciprocal of the period, and is numerically equal to the number of periods of current or EMF change in 1 second. That is, f = 1/T. The unit of frequency is hertz (Hz), named after the German physicist Heinrich Hertz, who made a significant contribution to the development of electrodynamics in the 19th century. The shorter the period, the higher the frequency of change in the EMF or current.
Today in Russia, the standard frequency of alternating current in electrical networks is 50 Hz, that is, 50 fluctuations of the mains voltage occur in 1 second.
In other areas of electrodynamics, higher frequencies are also used, for example, 20 kHz or more - in modern inverters, and up to units of MHz in narrower areas of electrodynamics. In the above figure, you can see that in one second there are 50 complete oscillations, each of which lasts 0.02 seconds, and 1 / 0.02 = 50.
According to the graphs of changes in sinusoidal alternating current over time, it can be seen that currents of different frequencies contain a different number of periods in the same time interval.
In one period, the phase of the sinusoidal EMF or sinusoidal current changes by 2pi radians or 360 °, so the angular frequency of the alternating sinusoidal current is:
The term "phase" means the stage of development of the process, and in this case, in relation to alternating currents and sinusoidal voltages, the phase is the state of the alternating current at a certain point in time.
In the figures you can see: the coincidence of the voltage U1 and the current I1 in phase, the voltages U1 and U2 are in antiphase, as well as the phase shift between the current I1 and the voltage U2. Phase shift φ is measured in radians, fractions of a period, in degrees. Thus, the phase shift between current I1 and voltage U2 is equal to φ = π radians, as well as between voltage U1 and voltage U2.
Amplitude Um and Im
Speaking about the magnitude of a sinusoidal alternating current or a sinusoidal variable EMF, the largest value of the EMF or current is called the amplitude or amplitude (maximum) value.
The largest value of a quantity that performs harmonic oscillations (for example, the maximum value of the current strength in alternating current, the deviation of an oscillating pendulum from the equilibrium position), the largest deviation of the oscillating quantity from a certain value, conventionally taken as the initial zero.
If we are talking about an alternating current generator, then the EMF at its terminals reaches the amplitude value twice per period, the first of which is +Em, the second -Em, respectively, during the positive and negative half-cycles. The current I behaves in a similar way, and is denoted accordingly by Im.
Instantaneous value of u and i
The value of the EMF or current in a particular this moment time is called the instantaneous value, they are denoted by small letters u and i. But since these values change all the time, it is inconvenient to judge alternating currents and EMF from them.
RMS I, E and U
The ability of alternating current to perform any useful work, for example, mechanically rotate the motor rotor or produce heat on a heating device, it is convenient to estimate by the effective values of the EMF and currents.
So, the meaning of such direct current, which, when passing through the conductor during one period of the considered alternating current, produces the same mechanical work or the same amount of heat as the given alternating current.
The effective values of voltages, emfs and currents are denoted by capital letters I, E and U. For sinusoidal alternating current and for sinusoidal AC voltage effective values are:
It is convenient to use the effective value of current and voltage to describe electrical networks. For example, a value of 220-240 volts is the effective voltage value in modern household outlets, and the amplitude is much higher - from 311 to 339 volts.
It is the same with current, for example, when they say that a current of 8 amperes flows through a household heating device, this means the effective value, while the amplitude is 11.3 amperes.
One way or another, mechanical work and electrical energy in electrical installations are proportional to the effective values of voltages and currents. A significant part of the measuring instruments shows exactly the effective values of voltages and currents.
Electricity- this is a directed or ordered movement of charged particles: electrons in metals, ions in electrolytes, and electrons and ions in gases. Electric current can be both direct and variable.
Definition of direct electric current, its sources
D.C(DC, in English Direct Current) is an electric current whose properties and direction do not change over time. Direct current and voltage are indicated in the form of a short horizontal dash or two parallel ones, one of which is dashed.
DC is used in cars and at home, in numerous electronic devices: laptops, computers, TVs, etc. The measured electric current from the socket is converted into direct current using a power supply or a voltage transformer with a rectifier.
Any power tool, device or device powered by batteries is also a consumer of direct current, because a battery or battery is only a source of direct current, which, if necessary, is converted into alternating current using special converters (inverters).
How AC works
Alternating current(AC in English Alternating Current) is an electric current that changes in magnitude and direction over time. On electrical appliances, it is conventionally indicated by a segment of the sinusoid "~".
Sometimes, after the sinusoid, the characteristics of the alternating current can be indicated - frequency, voltage, number of phases.
Alternating current can be either single or three-phase, for which the instantaneous values of current and voltage change according to a harmonic law.
Main characteristics alternating current - the effective value of the voltage and frequency.
note, as in the left graph for a single-phase current, the direction and magnitude of the voltage change with a transition to zero over a period of time T, and in the second graph for a three-phase current, there is a shift of three sinusoids by one third of the period. On the right graph, phase 1 is indicated by the letter "a", and the second by the letter "b". It is well known that the home socket is 220 volts. But few people know what it is effective value alternating voltage, but the amplitude or maximum value will be greater by the root of two, i.e. it will be equal to 311 volts.
Thus, if for direct current the voltage value and direction do not change over time, then for alternating current current - voltage constantly changing in magnitude and direction (a graph below zero is the opposite direction).
And so we approached to the concept of frequency- this is the ratio of the number of complete cycles (periods) to the unit of time of a periodically changing electric current. Measured in hertz. In our country and in Europe, the frequency is 50 Hertz, in the USA it is 60 Hz.
What does the frequency of 50 Hertz mean? It means that we have an alternating current changing its direction to the opposite and back (segment T- on the graph) 50 times per second!
AC sources are all sockets in the house and everything that is connected directly by wires or cables to the electrical panel. Many people have a question: why is there no direct current in the outlet? The answer is simple. In AC networks, the voltage value is easily and with minimal losses converted to the required level using a transformer in any volume. The voltage must be increased in order to be able to transmit electricity over long distances with the least losses in industrial scale. 
From the power plant, where there are powerful electric generators, a voltage of 330,000-220,000 comes out, then near our house at a transformer substation it is converted from a value of 10,000 Volts to a three-phase voltage of 380 Volts, which comes to an apartment building, and a single-phase voltage comes to our apartment , because between the voltage is 220 V, and between opposite phases in the electrical panel 380 volts.
And another important advantage of AC voltage is that AC asynchronous motors are structurally simpler and work much more reliably than DC motors.
How to make alternating current direct
For consumers operating on direct current, alternating current is converted using rectifiers.
DC to AC converter
If there are no difficulties with converting alternating current to direct current, then with the reverse conversion everything is much more complicated. For this at home inverter is used- This is a generator of periodic voltage from a constant, in shape close to a sinusoid.
Designations, parameters.
We know that a constant electric current is a current that does not change in time, both in magnitude and in the direction of electron movement. The main purpose of direct current is to power various radio and electronic equipment. DC sources include batteries, solar photovoltaic cells, batteries and DC generators.
In everyday life and industry, an alternating sinusoidal current is used. This is due to the fact that modern energy is based on the transmission of energy over long distances from hydro, thermal and nuclear power plants to the consumer. Alternating current generators are used to generate electrical energy in power plants. Transmission of alternating current is beneficial due to the advantages of its conversion and because of the low losses in power lines. Alternating electric current is easy to convert to direct current, as well as get any desired AC voltage. For example, the AC voltage transmitted through power lines is several thousand volts. In residential areas, the power line is connected to a transformer that converts the high voltage to a standard household voltage of 220 volts. It is this voltage that we have in the sockets of our apartments.
The standard frequency in a household electrical network is 50 Hz. In some foreign countries the standard frequency is 60 Hz. Just like direct current, alternating current is transmitted along two wires. If the direct current has two poles - plus and minus, then for alternating current one wire is current-carrying and is called "phase", and the second wire is common and is called "ground" or "zero". The voltage at a household electrical outlet is 220 volts.
Unlike direct current, alternating sinusoidal current (as well as alternating voltage) changes with time in amplitude (magnitude) and direction of electron movement. On the graph, the alternating current has the form of a sinusoid.
The distance between two adjacent vertices on the graph of an alternating sinusoidal current is called a period and is denoted by the letter T. A period is the time of one oscillation of the alternating current. The period is measured in seconds or in smaller units of time: milliseconds; microseconds; nanoseconds, etc. Value: period T=1 sec. to the minus first power (T -1) or 1 / T is called a frequency of 1 Hertz. The frequency is denoted by the letter f. In radio and electronic devices, depending on their purpose, the frequency can be in units of hertz (Hz or Hz), thousands of hertz (kHz or kHz), and so on.
Unlike direct current, alternating electric current (or voltage) changes its value over time, from a maximum to a minimum value. In this regard, the value of the alternating current or voltage will be slightly lower than the value of U or I. 
These values are called effective (effective) values of current or voltage and are designated Ieff and Ueff respectively (see figure). These are the values shown by AC meters.
An oscilloscope is the most suitable measuring device for investigating alternating current parameters. On the cathode ray tube of the oscilloscope - display (see figure) you can observe not only the shape of the alternating current, but also carry out a quantitative analysis of the signal under study. 
The X-axis of the display is graduated in time divisions, and the Y-axis is graduated in divisions of signal amplitude. In the figure, the "Time" switch is set to 0.01 microseconds per division along the X axis.
In the figure shown, the signal period is 2 divisions, therefore: T = 2 * 0.01 = 0.02 μS, and the signal frequency f = 1 / T = 1 / (0.02 -6) = 1 / 0.00000002 = 50000000 Hz = 50 MHz (MHz - megahertz ).
The "Y Value" switch is set to an amplitude of 10 volts per division along the Y axis. The signal has an amplitude of 6 divisions, so the signal voltage is 6 * 10 = 60 volts.
In conclusion of this topic, I would like to say that alternating sinusoidal current is used not only to power household and industrial electrical appliances. In radio and electronics, for example, high-frequency alternators for radio transmitters are widely used (both powerful for TV and radio studios, and low-power for cellular phones, pagers, etc.). In our subsequent topics, we will often encounter alternating electric current and the laws of its amplification, transformation, and so on.
Alternating current, in contrast to, continuously changes both in magnitude and in direction, and these changes occur periodically, that is, they are exactly repeated at regular intervals.
To induce such a current in the circuit, are used alternating current sources that create a variable emf, periodically changing in magnitude and direction. Such sources are called alternating current generators.
On fig. 1 shows a device diagram (model) of the simplest.
A rectangular frame made of copper wire is mounted on an axis and rotates in the field with the help of a belt drive. The ends of the frame are soldered to copper contact rings, which, rotating with the frame, slide along the contact plates (brushes).
Figure 1. Scheme of the simplest alternator
Verify that such a device is indeed source of EMF variable.
Suppose that a magnet creates between its poles, i.e., one in which the density of magnetic lines of force in any part of the field is the same. rotating, the frame crosses the lines of force magnetic field, and in each of its sides a and b.
The sides c and d of the frame are non-working, since when the frame rotates, they do not cross the magnetic field lines and, therefore, do not participate in the creation of the EMF.
At any moment in time, the EMF that occurs in side a is opposite in direction to the EMF that occurs in side b, but in the frame both EMFs act in accordance and in total make up the total EMF, i.e., induced by the entire frame.
It is easy to verify this if we use the known to us to determine the direction of the EMF rule right hand .
To do this, you need to position the palm of your right hand so that it faces the north pole of the magnet, and the bent thumb coincides with the direction of movement of that side of the frame in which we want to determine the direction of the EMF. Then the direction of the EMF in it will be indicated by outstretched fingers.
For whatever position of the frame we determine the direction of the EMF in sides a and b, they always add up and form a common EMF in the frame. In this case, with each revolution of the frame, the direction of the total EMF in it changes to the opposite, since each of the working sides of the frame passes under different poles of the magnet in one revolution.
The magnitude of the EMF induced in the frame also changes, as the speed at which the sides of the frame intersect the magnetic field lines changes. Indeed, at the time when the frame approaches its vertical position and passes it, the speed of crossing the lines of force by the sides of the frame is the greatest, and the largest EMF is induced in the frame. At those moments of time when the frame passes its horizontal position, its sides seem to slide along the magnetic lines of force without crossing them, and the EMF is not induced.
Thus, with a uniform rotation of the frame, an EMF will be induced in it, periodically changing both in magnitude and in direction.
The EMF that occurs in the loop can be measured with a device and used to create a current in an external circuit.
Graphical representation of direct and alternating currents
The graphical method makes it possible to visualize the process of changing one or another variable depending on time.
The construction of graphs of variables that change over time begins with the construction of two mutually perpendicular lines, called the axes of the graph. Then, on the horizontal axis, on a certain scale, time intervals are plotted, and on the vertical, also on a certain scale, the values \u200b\u200bof the quantity that they are going to graph (emf, voltage or current).
On fig. 2 graphically depicted direct and alternating currents. In this case, we plot the current values, and up the vertical from the point of intersection of the axes O, the current values \u200b\u200bof one direction, which is usually called positive, are plotted, and down from this point, the opposite direction, which is usually called negative.
Figure 2. Graphical representation of direct and alternating current
The point O itself serves simultaneously as the reference point for the values of current (vertically down and up) and time (horizontally to the right). In other words, this point corresponds to the zero value of the current and the initial moment of time from which we intend to trace how the current will change in the future.
Let us verify the correctness of the one constructed in Fig. 2, and a graph of a constant current of 50 mA.
Since this current is constant, that is, it does not change its magnitude and direction over time, the same current values, i.e., 50 mA, will correspond to different points in time. Consequently, at the moment of time equal to zero, i.e., at the initial moment of our observation of the current, it will be equal to 50 mA. Putting a segment up along the vertical axis equal to the current value of 50 mA, we will get the first point of our graph.
We must do the same for the next moment of time corresponding to point 1 on the time axis, i.e., to postpone a segment vertically upwards from this point, also equal to 50 mA. The end of the segment will determine the second point of the graph for us.
Having done a similar construction for several subsequent moments of time, we get a series of points, the connection of which will give a straight line, which is graphic representation of direct current 50 mA.
Let's move on to studying EMF variable graph. On fig. 3 at the top shows a frame rotating in a magnetic field, and at the bottom is a graphical representation of the emerging EMF variable.
Figure 3. Plotting the EMF variable
We begin to rotate the frame uniformly clockwise and follow the course of the change in the EMF in it, taking the horizontal position of the frame as the initial moment.
At this initial moment, the EMF will be zero, since the sides of the frame do not intersect the magnetic field lines. On the graph, this zero EMF value, corresponding to the moment t \u003d 0, will be represented by point 1.
With further rotation of the frame, an EMF will begin to appear in it and will increase in magnitude until the frame reaches its vertical position. On the graph, this increase in EMF will be depicted as a smooth upward curve, which reaches its top (point 2).
As the frame approaches the horizontal position, the EMF in it will decrease and fall to zero. On the graph, this will be depicted as a falling smooth curve.
Consequently, during the time corresponding to half the turn of the frame, the EMF in it managed to increase from zero to the maximum value and again decrease to zero (point 3).
With further rotation of the frame, the EMF will reappear in it and will gradually increase in magnitude, but its direction will already change to the opposite, as can be seen by applying the right-hand rule.
The graph takes into account the change in the direction of the EMF by the fact that the curve depicting the EMF crosses the time axis and is now located below this axis. The emf increases again until the frame takes up a vertical position.
Then the EMF will begin to decrease, and its value will become equal to zero when the frame returns to its original position, having completed one complete revolution. On the graph, this will be expressed by the fact that the EMF curve, having reached its peak in the opposite direction (point 4), will then meet with the time axis (point 5)
This ends one cycle of changing the EMF, but if we continue to rotate the frame, the second cycle immediately begins, exactly repeating the first, which, in turn, will be followed by the third, and then the fourth, and so on until we stop the rotation framework.
Thus, for each revolution of the frame, the EMF that arises in it makes a full cycle of its change.
If the frame is closed to some external circuit, then an alternating current will flow through the circuit, the graph of which will look the same as the EMF graph.
The wavy curve we got is called sinusoid, and the current, EMF or voltage that changes according to this law are called sinusoidal.
The curve itself is called a sinusoid because it is a graphic representation of a variable trigonometric quantity called a sine.
The sinusoidal nature of the current change is the most common in electrical engineering, therefore, speaking of alternating current, in most cases they mean a sinusoidal current.
To compare various alternating currents (EMF and voltages), there are quantities characterizing a particular current. They're called AC parameters.
Period, amplitude and frequency - AC parameters
Alternating current is characterized by two parameters - period and amplitude, knowing which we can judge what kind of alternating current it is and build a current graph.
Figure 4. Sinusoidal current curve
The period of time during which a complete cycle of current change takes place is called a period.
The period is denoted by the letter T and is measured in seconds.The period of time during which half of the full cycle of current change takes place is called a half-cycle. Therefore, the period of current change (EMF or voltage) consists of two half-cycles. It is quite obvious that all periods of the same alternating current are equal to each other.
As can be seen from the graph, during one period of its change, the current reaches twice its maximum value.
The maximum value of an alternating current (EMF or voltage) is called its amplitude or amplitude value of the current.
Im, Em and Um are generally accepted designations for the amplitudes of current, emf and voltage.
First of all, we paid attention to , however, as can be seen from the graph, there are countless intermediate values of it, smaller than the amplitude.
The value of the alternating current (EMF, voltage) corresponding to any chosen point in time is called its instantaneous value.
i, e and u are generally accepted designations for instantaneous values of current, emf and voltage.
The instantaneous value of the current, as well as its amplitude value, is easy to determine using a graph. To do this, from any point on the horizontal axis corresponding to the moment of interest to us, we draw a vertical line to the point of intersection with the current curve; the resulting segment of the vertical line will determine the value of the current in this moment, i.e. its instantaneous value.
Obviously, the instantaneous value of the current after the time T / 2 from the starting point of the graph will be equal to zero, and after the time - T / 4 to its amplitude value. The current also reaches its peak value; but already in the opposite direction, after a time equal to 3/4 T.
So, the graph shows how the current in the circuit changes over time, and that each moment of time corresponds to only one specific value of both the magnitude and direction of the current. In this case, the value of the current at a given point in time at one point in the circuit will be exactly the same at any other point in this circuit.
The number of complete periods completed by the current in 1 second is called AC frequency and is denoted by the Latin letter f.
To determine the frequency of an alternating current, that is, to find out how many periods of its change did the current make within 1 second, it is necessary to divide 1 second by the time of one period f = 1/T. Knowing the frequency of the alternating current, you can determine the period: T = 1/f
It is measured in a unit called hertz.
If we have an alternating current, the frequency of which is 1 hertz, then the period of such a current will be 1 second. Conversely, if the period of current change is 1 second, then the frequency of such a current is 1 hertz.
So we have defined AC parameters - period, amplitude and frequency, - which make it possible to distinguish various alternating currents, emfs and voltages from each other and to build, when necessary, their graphs.
When determining the resistance of various circuits to alternating current, use another auxiliary value that characterizes alternating current, the so-called angular or circular frequency.
Circular frequency denoted by the letter ω and is related to the frequency f as ω = 2π f
Let's explain this dependence. When constructing a graph of the variable EMF, we saw that during one complete revolution of the frame, a complete cycle of change in the EMF occurs. In other words, in order for the frame to make one revolution, i.e. turn 360 °, it takes time equal to one period, i.e. T seconds. Then in 1 second the frame makes 360°/T turns. Therefore, 360°/T is the angle through which the frame rotates in 1 second, and expresses the rate of rotation of the frame, which is commonly called angular or circular speed.
But since the period T is related to the frequency f by the ratio f=1/T, the circular speed can also be expressed in terms of the frequency and will be equal to ω = 360°f.
So, we came to the conclusion that ω = 360°f. However, for the convenience of using the circular frequency in all kinds of calculations, the angle of 360 ° corresponding to one revolution is replaced by a radial expression equal to 2π radians, where π = 3.14. Thus, we finally obtain ω = 2π f. Therefore, to determine the circular frequency of alternating current (), it is necessary to multiply the frequency in hertz by a constant number of 6.28.
Electricity
Variable and its application in medicine.
- Alternating current, its types and main characteristics.
Alternating current is such a current, the direction and numerical value of which change over time (alternating current).
Note: the shape of the current curve, the frequency, the duration of its change are not specified.
In practice, alternating current most often means periodic alternating current.
The physical essence of alternating current is reduced to fluctuations of electric charges in a medium (conductor or dielectric).
Types of current:
Conduction current.
bias current.
Conduction current- this is such a current, which is due to oscillations of electrons and ions in the medium.
Bias current- this is the current that is due to the displacement of electric charges at the conductor-dielectric interface (for example, the current through a capacitor).
The displacement current is associated with the change in time of the electric field at the conductor-dielectric interface and has the following features:
The amplitude of the displacement current and its direction are in phase with those of the conduction current.
In value, it is always equal to the conduction current.
A special case of the displacement current is the polarization current. The polarization current is a displacement current not in a vacuum, but in a material dielectric medium.
The sum of the bias and polarization currents is total bias current.
In medical practice, the following types of currents are used according to the shape of the current curve:
needle-exponential
The simplest is a periodic sinusoidal current. It is easily described mathematically and graphically, its shape is not distorted in electrical circuits with R, C, L elements.
Basic characteristics of alternating current.
Period– time of one cycle of current change in direction and numerical value (T, s).
Frequency is the number of cycles of current change per unit time.
\u003d 1 / T (the reciprocal of the period from -1, Hz)
Circular frequency( , 2 /T radians/s)
Phase( ) is a value that determines the relationship between current and voltage in an electrical circuit in time.
Instantaneous value of current and voltage- the value of these quantities at a given time (i, u).
Peak value of current and voltage- this is the maximum value of these quantities for the half-period (I m , U m).
RMS (effective, effective) value of current and voltage- is calculated as a positive square root of the average value of the squared voltage or current according to the formulas.
I = I 2 cp
U = U 2 cp
Mean value (U Wed ) for the period (constant component)- this is the arithmetic average of instantaneous current or voltage values for a period.
In practice, the root mean square value is determined by the effective (effective) value. (I cp, U cp), which for a sinusoidal current is calculated by the formulas:
I eff \u003d I \u003d 0.707 I m
U eff \u003d U \u003d 0.707 U m
In some cases, the medical application of electric current, you have to take into account other characteristics (for example, the amplitude factor K a, and the shape factor K f).
For practice, the following formulas for the relationship of characteristics are important:
i(u) ≤I m (U m)
I eff \u003d I \u003d I m / 2 \u003d 0.707 I m I m \u003d 1.41 I eff
U eff \u003d U \u003d U m / 2 \u003d 0.707 U m U m \u003d 1.41 U eff
2. AC circuits with active resistance, inductance, capacitance and their features.
Electrical circuit- this is a real or conceivable set of physical elements that transmit electrical energy from one point in space to another.
The physical elements of electrical circuits are conductors, resistors, capacitors, inductors. The elements of the circuit are also the elements of its connection, and, in addition, implement the corresponding properties of resistance, capacitance and inductance.
Types of electrical circuits:
Simple chains contain only single R, C, L elements, while complex chains have them in various amounts and combinations.
A common feature of the elements of an electrical circuit is that when an alternating current passes, they show resistance, which is called active (R), inductive (X l), capacitive (X c).
Singularities of simple ideal chains.
A circuit consisting of a current generator and an ideal resistor is called a simple resistance circuit.
The chain ideality condition:
Active resistance is not equal to zero,
its inductance and capacitance are zero.
R 0
C 
r=0~R
Peculiarities:
No phase shift ( ) between current and voltage.
This means that the current and voltage simultaneously pass their maximum (amplitude) and zero values.
On the R-element, energy is lost in the form of heat release.
Circuit with inductance- this is an electrical circuit consisting of an alternator and an ideal L - an inductor element.
At 
chain ideality conditions:
Coil inductance is not zero
Its capacitance and resistance are zero.
L 0
Chain features:
X L = L = 2 L
The circuit has a phase shift between voltage and current: V leads I in phase by an angle /2
Inductive reactance does not consume energy, because. it is stored in the magnetic field of the coil, and then given to the electrical circuit. Therefore, inductive resistance is called apparent or imaginary.
Chain with capacity- this is an electrical circuit consisting of an alternator and an ideal C - element - capacitor.
Chain ideality conditions:
The capacitance of a capacitor is not equal to zero, and its active resistance and inductance are equal to zero. C 0, R C = 0, L C = 0.
Features of the circuit with capacitance:
1
. Ohm's law is observed.
2. Capacitance provides resistance to alternating current, which is called capacitive. It is denoted by X s and decreases with increasing frequency non-linearly.
The circuit has a phase shift between voltage and current: V lags behind I in phase by an angle /2
Capacitance does not consume energy, because. it is stored in the electric field of the capacitor, and then given to the electric circuit. Therefore, capacitive resistance is called apparent or imaginary.
- Complete AC circuit and its types. Impedance and its formula. Features of the impedance of living tissue.
A complete alternating current circuit is a circuit from a generator, as well as R, C, and L elements, taken in various combinations and quantities.
To analyze the processes taking place in electrical circuits, complete serial and parallel circuits are used.
A series circuit is a circuit where all the elements can be connected in series, one after the other.
In a parallel circuit, R, C, L elements are connected in parallel.
Complete circuit features:
Ohm's law is respected
A complete circuit offers resistance to alternating current. This resistance is called total (imaginary, apparent) or impedance.
The impedance depends on the resistance of all elements of the circuit, denoted by Z and is calculated not by simple, but by geometric (vector) summation. For series-connected elements, the impedance formula has the following meaning:
Z is the series circuit impedance,
R - active resistance,
X L - inductive and X C - capacitive resistance,
L - coil inductance (henry),
C is the capacitance of the capacitor (farad).
Since the capacitive and inductive reactances give the voltage a phase shift in the opposite direction, it is possible that X L \u003d X C. In this case, the algebraic sum of the modules will be equal to zero, and the impedance will be the smallest.
The condition in which capacitive reactance is equal to inductive reactance in an alternating current circuit is called voltage resonance. The frequency at which X L \u003d X C is called the resonant frequency. This frequency p can be determined by the Thomson formula:
- Features of the impedance of living tissue and its equivalent electrical circuit.
When current is passed through living tissue, it can be considered as an electrical circuit consisting of certain elements.
It has been experimentally established that this circuit has the properties of active resistance and capacitance. This is evidenced by the release of heat and the decrease in tissue impedance with increasing frequency. The properties of inductance in living tissue are practically not found. Thus, living tissue is a complex, but not a complete electrical circuit.
The impedance of a living tissue can be considered for both series and parallel connection of its elements.
When connected in series, the currents through the elements are equal, the total applied voltage will be the vector sum of the voltages on the R and C elements, and the series circuit impedance formula will be:
Z_ - series circuit impedance,
R is its active resistance,
X C - capacitance.
When connected in parallel, the voltages on R and C elements are equal, the total current will be the vector sum of the currents of each element, and the impedance formula will be as follows:
The theoretical formulas for the impedance of a living tissue with parallel and series connection of its elements differ from the experimental ones as follows:
With a series connection, practical data give large deviations at low frequencies.
With a parallel circuit, these measurements show the final value of Z, although theoretically it should tend to zero.
Equivalent electrical circuit of living tissue - e This is a conditional model that approximately characterizes living tissue as an alternating current conductor.
The scheme allows you to judge:
What electrical elements does the fabric have
How are these elements connected?
How will the properties of the tissue change when the frequency of the current changes.
The scheme is based on three principles:
The extracellular environment and the contents of the cell are ionic conductors with an active resistance of the environment Rav and cells Rk.
The cell membrane is a dielectric, but not ideal, but with a small ionic conductivity, and, consequently, the resistance of the membrane Rm.
The extracellular environment and the contents of the cell, separated by a membrane, are capacitors Cm of a certain capacity (0.1 - 3.0 μF / cm 2).
If we take a liquid tissue medium as a model of living tissue - blood containing only erythrocytes, then when drawing up an equivalent circuit, it is necessary to take into account the paths of electric current.
Bypassing the cell, through the extracellular environment.
Through the cage.
The path around the cell is represented only by the resistance of the medium Rav.
The path through the cell by the resistance of the contents of the cell Rk, as well as the resistance and capacitance of the membrane. Rm, See.
If we replace the electrical characteristics with the corresponding designations, we will obtain equivalent circuits of varying degrees of accuracy:
Fricke scheme (ionic conductivity is not
taken into account).
Schwan scheme (ionic conductivity is taken into account as membrane resistance)
Designations on the diagram:
Rcp - active resistance of the cellular environment
Rk - Cell content resistance
Cm - membrane capacitance
Rm is the resistance of the membrane.
An analysis of the circuit shows that with an increase in the current frequency, the conductivity of cell membranes increases, and the total resistance of the tissue medium decreases, which corresponds to practical measurements.
5. Living tissue as a conductor of alternating electric current. Dispersion of electrical conductivity and its quantitative assessment.
The following features of living tissue as an alternating current conductor have been experimentally established:
1. The resistance of living tissue to alternating current is less than direct current.
2. The electrical characteristics of the tissue depend both on its type and on the frequency of the current.
3. With increasing frequency, the impedance of living tissue decreases non-linearly to a certain value, and then remains almost constant (mostly at frequencies above 10 6 Hz)
4. At a certain frequency, the impedance also depends on the physiological state (blood filling), which is used in practice. The study of peripheral circulation based on the measurement of electrical resistance is called rheography (impedance plethysmography).
5. When living tissue dies, its resistance decreases and does not depend on frequency.
6. When alternating current passes through living tissues, a phenomenon is observed, which is called the dispersion of electrical conductivity.
D 
dispersion of electrical conductivity is a phenomenon of the dependence of the total (specific) resistance of living tissue on the frequency of alternating current.
Graphs of such dependence are called dispersion curves. Dispersion curves are built in a rectangular coordinate system, where the values of the total (Z) or resistivity are plotted vertically, and the frequency on a logarithmic scale (Lg ) is plotted horizontally.
The frequency dependences in the shape of the curve for different tissues are similar, but differ in the resistance value.
There are several frequency ranges where the dispersion is especially pronounced. One of them corresponds to the interval 10 2 -10 6 Hz
Dispersion features:
1. Inherent only in living tissues.
2. More pronounced at frequencies up to 1 MHz.
3. In practice, it is used to assess the physiological state and viability of tissues.
Quantitative assessment of the dispersion is carried out by the coefficient of dispersion (K).
The dispersion coefficient is a dimensionless quantity equal to the ratio of low-frequency (10 2) total (or specific) resistance to high-frequency (10 6 Hz).
Z 1 - impedance at a frequency of 10 2 Hz
Z 2 - impedance at a frequency of 10 6 Hz
1 , 2 - resistivity at these frequencies
The value of the dispersion coefficient depends on the type of tissue, its physiological state, and the evolutionary stage of the animal's development. For example, for the liver of an animal, K = 9 -10 units, and for the liver of a frog, 2 -3 units. As the tissue dies, the dispersion coefficient tends to unity.
The phenomenon of dispersion is associated with the presence of polarization in living tissues, which, with increasing frequency, has less effect on the impedance. Therefore, the dispersion coefficient is often called the polarization coefficient.
In addition to frequency dependences in living tissues, phase shifts are noted between current and voltage, which also, but to a lesser extent, depend on frequency.
Phase shifts also decrease with tissue death and, in the future, can be used for practical purposes.
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