Active and inductive resistance of the coil. See what "inductive reactance" is in other dictionaries

26.02.2019

Inductor in a circuit alternating current

An inductor in an AC circuit behaves differently than a resistor. If resistors simply oppose the flow of electrons (the voltage across them is directly proportional to the current), then inductors oppose a change in the current passing through them (the voltage across them is directly proportional to the rate of change of current). According to Lenz's Law, the induced voltage always has a polarity that tries to maintain the current value of the current. That is, if the magnitude of the current increases, then the induced voltage will "slow down" the flow of electrons; if the magnitude of the current decreases, then the polarity of the voltage will reverse and will "help" the electron flow to remain at the same level. This resistance to a change in current is called reactance.

The mathematical relationship between the voltage across an inductor and the rate of change of current through it is as follows:

The ratio di/dt is the rate of change of the instantaneous current (i) over time and is measured in amperes per second. Inductance (L) is measured in henries and instantaneous voltage (u) is measured in volts. To show what happens to alternating current, let's analyze a simple inductive circuit:

A simple inductive circuit: the coil current lags the voltage by 90o.

If we plot current and voltage for this simple circuit, then it will look like like that:

As you remember, a change in voltage across an inductor is a response to a change in current passing through it. From this we can conclude that the instantaneous voltage is zero whenever the instantaneous current is at its peak (zero change, or zero slope of the current sine wave), and the instantaneous voltage is equal to its peak value whenever the instantaneous current is at the points of maximum change. (points of the steepest slope of the current wave, at which it crosses the zero line). All this leads to the fact that the voltage wave is 90 o out of phase with the current wave. The graph shows how the voltage wave gives a "handicap" to the current wave: the voltage "leads" the current, and the current "lags" behind the voltage.

If we plot the power values of our circuit on this graph, then everything will become even more interesting:

Since instantaneous power is the product of instantaneous voltage and instantaneous current (p = iu), it will be zero if the instantaneous voltage or current is zero. Whenever the instantaneous values of current and voltage are positive (above the zero line), the power will also be positive. Similar to the example with a resistive circuit, the power will take on a positive value even if the instantaneous current and voltage are negative (below the zero line). However, due to the fact that the voltage and current waves are out of phase by 90 o , there are cases when the current is positive and the voltage is negative (or vice versa), resulting in negative values of instantaneous power.

But what is negative power? Negative power means that the inductor is putting energy back into the circuit. Positive power means that the inductor is absorbing energy from the circuit. Since positive and negative power cycles are equal in magnitude and duration, during a complete cycle, the inductor gives back as much power back into the circuit as it draws from it. In a practical sense, this means that the reactance of the coil does not dissipate any energy, which is how it differs from the resistance of a resistor, which dissipates energy in the form of heat. However, all of the above is true only for ideal inductors, the wires of which do not have any resistance.

The resistance of an inductor that changes current strength is interpreted as resistance to alternating current as a whole, which, by definition, is constantly changing instantaneous magnitude and direction. This AC resistance is similar to conventional resistance, but differs from it in that it always leads to a phase shift between current and voltage, and also dissipates zero power. Because of these differences, given resistance has a slightly different name - reactance. Reactance, like usual, is measured in ohms, only it is denoted by the symbol X, and not R. For more specificity, the reactance of an inductor is usually denoted by a capital letter X with the letter L as an index: X L.

Since the voltage across an inductor is proportional to the rate of change of current, it will be greater for rapidly changing currents and less for slower changing currents. This means that the reactance of any inductor (in ohms) is directly proportional to the frequency of the alternating current. The exact formula for calculating reactance is as follows:

If a coil with an inductance of 10 mH is affected by frequencies of 60, 120 and 2500 Hz, then its reactance will take on the following values:

In the reactance equation, the expression “2πf” is important. It means a number in radians per second that characterizes the "rotation" of the alternating current (one complete cycle of the alternating current is one complete circular rotation). A radian is a unit of measurement for angles: there are 2π radians in one full circle, just like there are 360 o in it. If the alternator is bipolar, then it will make one complete cycle for every complete revolution of the shaft, which would mean 2π radians or 360o. If the constant 2π is multiplied by the frequency in hertz (cycles per second), the result is a number in radians per second, known as the angular (cyclic) frequency of the alternating current.

In addition to the expression 2πf, the angular frequency of an alternating current can be denoted by the lowercase Greek letter ω (Omega). In this case, the formula X L = 2πfL can be written as X L = ωL.

It must be understood that the angular frequency is an expression of how fast a complete cycle of a wave, equal to 2π radians, passes. It does not necessarily represent the actual shaft speed of the alternator producing alternating current. If the generator has more than two poles, its angular frequency will be a multiple of the shaft speed. For this reason, ω is sometimes expressed in units of electrical radians per second to distinguish it from mechanical motion.

In any way of expressing the angular frequency, it is obvious that it is directly proportional to the reactance of the inductor. With an increase in the frequency of the alternating current (or the speed of rotation of the generator shaft), the inductor will provide more resistance to the passage of current and vice versa. AC idle inductive circuit equals the voltage (in volts) divided by the reactance of the inductor (in ohms). As you can see, this is similar to the fact that a variable or D.C. in a simple resistive circuit is equal to the voltage (in volts) divided by the resistance (in ohms). As an example, let's consider the following schema:

However, we must keep in mind that voltage and current have different phases. As mentioned earlier, the voltage has a phase shift of +90 o with respect to the current (figure below). If we represent the phase angles of voltage and current mathematically (in the form of complex numbers), then we will see that the resistance of the inductor to alternating current has the following phase angle:

The current on the inductor lags behind the voltage by 90 o .

Mathematically, we can say that the phase angle of the resistance of the inductor to alternating current is 90 o. The phase angle of current reactance is very important in circuit analysis. This importance is especially evident in the analysis of complex AC circuits, where reactive and simple resistances interact with each other. It will also prove useful for representing the resistance of any component to an electric current in terms of complex numbers (rather than the scalar quantities of resistance and reactance).

INDUCTIVE RESISTANCE

In aerodynamics, part of the aerodynamic drag of a wing is due to vortices whose axes originate on the wing and are directed downstream. These, so-called. free, the vortices originate from the flow of air at the ends of the wing (Fig. 1) from the area under the wing to the area above the wing.

Rice. Fig. 1. Scheme of the appearance of an end vortex as a result of air flow from the area under the wing to the area above the wing.

The air flow at the ends causes a flow directed above the wing from the ends to the plane of symmetry, and under the wing - from the plane of symmetry to the ends; as a result, in the wake, or wake, behind the wing, each ch-tsy rotates around an axis passing through it and parallel to the local velocity vector v of the flow; the direction of rotation is opposite for the left and right half-wing (Fig. 2). Thus, a continuous system of vortices arises, extending from each point of the wing surface.

Rice. 2. Section of the flow behind the wing by a plane perpendicular to V.

Free vortices cause (induce) in the area between the ends of the wing flows directed downwards, which, superimposed on the oncoming flow, deflect the latter downward by an angle Da (the angle of the bevel of the flow).

Since the wing must be perpendicular to the oncoming flow, it deviates back by the same angle Yes (Fig. 3). Expanding this force into lengthwise and perpendicular to v, we obtain I. s. dQind and lift force dY. If the wing has an infinite span, I. s. absent.

Physical Encyclopedic Dictionary. - M.: Soviet Encyclopedia. . 1983 .

INDUCTIVE RESISTANCE

In an alternating current circuit - the reactive part of the resistance of a two-terminal network (see. Impedance), in Krom, the sinusoidal lags in phase with the applied voltage, just as it is the case for a self-induction coil. In the ideal case, when the self-induction coil can be characterized by unity. parameter - inductance L\u003d const, I. s. is defined as the ratio of voltage and current amplitudes and is equal to XL= w L(w - cyclic frequency). In this case, the current lags in phase with the voltage exactly by the angle p / 2, as a result of which, on average, no accumulation of electromagnet occurs over the period. energy in the coil, nor its dissipation: twice during the period it is pumped into the coil (mainly in the form of magnetic field energy) and twice returned back to the source (or to an external circuit). It is generally accepted that the reactance of an arbitrary two-terminal network (the imaginary part of its impedance Z=R+iX) has an inductive character if it is positive [X>0, with exp(iwt)-description of the time dependence of quantities]. It is this sign, and not proportionality X frequency w is characteristic for And. In principle, the function X(w) for I. s. can be arbitrary (known restrictions are imposed only Kramers - Kronig ratio); moreover, even the reactive energy associated with I. s. does not have to be predominantly magnetic. I. s. in microcircuits are quite often reproduced using phase shifters(gyrators). We also note that the same two-terminal network can behave differently in decomp. frequency ranges. Yes, hesitate. a circuit made up of parallel-connected self-induction coils (with inductance L) and a capacitor (with a capacitance WITH), at frequencies below the resonant w > w p = 1/ C LC behaves like an I.S., and when w > w p- How capacitance. M. A. Miller, G. V. Permitin.

Physical encyclopedia. In 5 volumes. - M.: Soviet Encyclopedia. Chief Editor A. M. Prokhorov. 1988 .

See what "INDUCTIVE RESISTANCE" is in other dictionaries:

Part of the aerodynamic drag (pressure drag) of a finite-span wing associated with the formation (induction of the name from here) of a vortex sheet behind the wing and determined by the energy costs to maintain a large-scale flow ... Encyclopedia of technology

Resistance to alternating current created in wires, electr. machines and transformers by self-induction. The value of I. s. proportional to the frequency of the AC inductance of the circuit. Technical railway dictionary. M .: State ... ... Technical railway dictionary

inductive reactance- reactance due to own inductance element electrical circuit and equal to the product of the values of inductance and angular frequency. [GOST R 52002 2003] EN inductive reactance reactance having a positive value is a value that characterizes the resistance to alternating current by the inductance of the circuit (its section), the unit of measurement is 1 Ohm; See also: resistance electrical resistance... Encyclopedic Dictionary of Metallurgy

We know that the self-induction current of the coil goes to meet the rising current of the generator. This the counteraction of the self-induction current of the coil to the increasing current of the generator is called inductive reactance.

Part of the alternating current energy of the generator is expended to overcome this opposition. All this part of the energy is completely converted into energy magnetic field coils. When the generator current decreases, the magnetic field of the coil will also decrease, cutting off the coil and inducing a self-induction current in the circuit. Now the self-induction current will go in the same direction as the decreasing generator current.

Thus, all the energy expended by the generator current to overcome the resistance of the self-induction current of the coil is completely returned to the circuit in the form of energy electric current. That's why inductive reactance is reactive, i.e., does not cause irretrievable energy losses.

The unit of inductive reactance is Ohm

Inductive reactance is denoted X L .

The letter X- means reactance, and L means that this reactance is inductive.

f- frequency Hz, L- coil inductance H, X L- inductive resistance Ohm

Relationship between phases U and I on X L

Since the active resistance of the coil is equal to zero by condition (purely inductive resistance), then all the voltage applied by the generator to the coil goes to overcome e. d.s. self-induction coil. This means that the graph of the voltage applied by the generator to the coil is equal in amplitude to the graph e. d.s. self-induction of the coil and is in antiphase with it.

The voltage applied by the generator to the purely inductive reactance and the current flowing from the generator through the purely inductive reactance are phase-shifted by 90 0, i.e. i.e. voltage leads current by 90 0.

A real coil, in addition to inductive resistance, also has active resistance. These resistances should be considered connected in series.

On active resistance coil voltage applied by the generator and the current coming from the generator are in phase.

On a purely inductive resistance, the voltage applied by the generator and the current coming from the generator are phase-shifted by 90 0. The voltage leads the current by 90 0 . The resulting voltage applied by the generator to the coil is determined by the parallelogram rule.