Active resistance, inductance and capacitance in an alternating current circuit. Reactance XL and XC

We know that the self-induction current of the coil meets the increasing current of the generator. This the opposition 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 spent to overcome this counteraction. All this part of the energy is completely converted into the energy of the magnetic field of the coil. 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 flow in the same direction as the decreasing generator current.

Thus, all the energy expended by the generator current to overcome the counteraction of the self-induction current of the coil is completely returned to the circuit in the form of electric current energy. Therefore, inductive reactance is reactive, i.e., it does not cause irreversible energy losses.

The unit of inductive reactance is Ohm

Inductive reactance is denoted by 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 reactance Ohm

Relationship between phases U and I on X L

Since the active resistance of the coil is equal to zero (purely inductive resistance), then all the voltage applied by the generator to the coil is used to overcome the e. d.s. self-inductance of the coil. This means that the graph of the voltage applied by the generator to the coil is equal in amplitude to the graph of 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 shifted in phase by 90 0, i.e. that is, the voltage leads the current by 90 0.

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

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

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

click on the picture to enlarge

The resulting voltage applied by the generator to the coil always leads the current by an angle less than 90 0.

The magnitude of the angle φ depends on the values ​​of the active and inductive resistance of the coil.

About the resulting coil resistance

The resulting resistance of the coil cannot be found by summing the values ​​of its active and reactive resistances.

The resulting coil resistance Z is

In an alternating current circuit, under the influence of a continuously changing voltage, changes in this current occur. In turn, these changes cause the generation of a magnetic field that periodically increases or decreases. Under its influence, a counter voltage is induced in the coil, preventing changes in current. Thus, the flow of current occurs under a continuous counteraction, called inductive reactance.

This value is directly related to the frequency of the applied voltage (f) and the inductance value (L). The formula for inductive reactance will look like this: XL = 2πfL. Direct proportional dependence, if necessary, allows you to calculate the frequency or inductance value by transforming the basic formula.

What does inductive reactance depend on?

Under the influence of alternating current passing through a conductor, an alternating magnetic field is formed around this conductor. The action of this field leads to the induction of an electromotive force in the opposite direction in the conductor, also known as self-induction emf. The opposition or resistance of the EMF to alternating current is called reactive inductive reactance.

This value depends on many factors. First of all, it is influenced by the current value not only in its own conductor, but also in neighboring wires. That is, an increase in resistance and leakage flux occurs as the distance between the phase wires increases. At the same time, the impact of adjacent wires is reduced.

There is such a thing as linear inductive reactance, which is calculated by the formula: X0 = ω x (4.61g x (Dav/Rpr) + 0.5μ) x 10-4 = X0' + X0'', in which ω is angular frequency, μ - magnetic permeability, Dav - the geometric mean distance between the phases of the power line, and Rpr - the radius of the wire.

The quantities X0’ and X0’’ represent two components of the linear inductive reactance. The first of them, X0’, is an external inductive reactance, depending only on the external magnetic field and the size of the power line. Another quantity - X0’’ is the internal resistance, depending on the internal magnetic field and magnetic permeability μ.

On high voltage power lines of 330 kV or more, the passing phases are split into several separate wires. For example, at a voltage of 330 kV, the phase is divided into two wires, which reduces the inductive reactance by approximately 19%. Three wires are used at a voltage of 500 kV - inductive reactance can be reduced by 28%. The 750 kV voltage allows phase separation into 4-6 conductors, which helps reduce resistance by approximately 33%.

The linear inductive reactance has a value depending on the radius of the wire and is completely independent of the cross-section. If the radius of the conductor increases, then the value of the linear inductive reactance will correspondingly decrease. Conductors located nearby have a significant influence.

Inductive reactance in an AC circuit

One of the main characteristics of electrical circuits is resistance, which can be active or reactive. Typical representatives of active resistance are considered to be ordinary consumers - lamps, incandescent lamps, resistors, heating coils and other elements in which electricity.

Reactive reactance includes inductive and capacitive reactance, located in intermediate electricity converters - inductive coils and capacitors. These parameters must be taken into account when performing various calculations. For example, to determine the total resistance of a circuit section, . Addition is carried out geometrically, that is, in a vector way, by constructing a right triangle. In it, both legs are both resistances, and the hypotenuse is total. The length of each leg corresponds to the effective value of one or another resistance.

As an example, we can consider the nature of inductive reactance in the simplest alternating current circuit. It includes a power source with EMF (E), a resistor as an active component (R) and a coil with inductance (L). The appearance of inductive resistance occurs under the influence of self-inductive emf (Emf) in the coil turns. Inductive reactance increases in accordance with the increase in inductance of the circuit and the value of the current flowing through the circuit.

Thus, Ohm’s law for such an alternating current circuit will look like the formula: E + Esi = I x R. Next, using the same formula, you can determine the value of self-induction: Esi = -L x Ipr, where Ipr is the derivative of the current with time. The minus sign means the opposite direction of Esi in relation to the changing current value. Since such changes occur constantly in the alternating current circuit, there is significant opposition or resistance on the part of Esi. With constant current, this dependence is absent and all attempts to connect the coil to such a circuit would lead to a normal short circuit.

To overcome the self-induction EMF, such a potential difference must be created at the coil terminals by the power source so that it can at least minimally compensate for the resistance Eci (Ucat = -Esi). Since an increase in alternating current in the circuit leads to an increase in the magnetic field, an eddy field is generated, which causes an increase in the opposite current in the inductance. As a result, a phase shift occurs between current and voltage.

Coil inductive reactance

An inductor is classified as a passive component used in electronic circuits. It is capable of storing electricity by turning it into a magnetic field. This is its main function. An inductor in its characteristics and properties resembles a capacitor that stores energy in the form of an electric field.

Inductance, measured in Henry, is the appearance of a magnetic field around a current-carrying conductor. In turn, it is associated with the electromotive force, which counteracts the applied alternating voltage and current in the coil. This property is inductive reactance, which is in antiphase with the capacitive reactance of the capacitor. The inductance of the coil can be increased by increasing the number of turns.

In order to find out what the inductive reactance of the coil is, it should be remembered that it, first of all, opposes alternating current. As practice shows, each inductive coil itself has a certain resistance.

The passage of an alternating sinusoidal current through the coil leads to the appearance of an alternating sinusoidal voltage or EMF. As a result, inductive reactance arises, determined by the formula: XL = ωL = 2πFL, in which ω is the angular frequency, F is the frequency in hertz, L is the inductance in henry.

Active resistance R is a physical quantity equal to the ratio of power to the square of current, which is obtained from the expression for power. At low frequencies it is practically independent of frequency and coincides with the electrical resistance of the conductor. http://www.sip2-kabel.ru/ litkult wire ppsrvm 1 characteristics.

Let a coil be connected to an alternating current circuit. Then, when the current changes according to the law, a self-inductive emf appears in the coil. Because Since the electrical resistance of the coil is zero, then the EMF is equal to minus the voltage at the ends of the coil created by an external generator (??? What other generator???). Therefore, a change in current causes a change in voltage, but with a phase shift . The product is the amplitude of voltage oscillations, i.e. . The ratio of the amplitude of voltage oscillations across the coil to the amplitude of current oscillations is called inductive reactance .

Let there be a capacitor in the circuit. When it is turned on, it charges for a quarter of the period, then discharges for the same amount, then the same thing, but with a change in polarity. When the voltage across the capacitor changes according to the harmonic law the charge on its plates is equal to . The current in the circuit occurs when the charge changes: , similar to the case with a coil, the amplitude of the current fluctuations is equal to . The value equal to the ratio of the amplitude to the current strength is called capacitive reactance .

We know that the self-induction current of the coil meets the increasing current of the generator. This the opposition 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 spent to overcome this counteraction. All this part of the energy is completely converted into the energy of the magnetic field of the coil. 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 flow in the same direction as the decreasing generator current.

Thus, all the energy expended by the generator current to overcome the counteraction of the self-induction current of the coil is completely returned to the circuit in the form of electric current energy. Therefore, inductive reactance is reactive, i.e., it does not cause irreversible energy losses.

The unit of inductive reactance is Ohm

Inductive reactance is denoted by 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 reactance Ohm

Relationship between phases U and I on X L

Since the active resistance of the coil is equal to zero (purely inductive resistance), then all the voltage applied by the generator to the coil is used to overcome the e. d.s. self-inductance of the coil. This means that the graph of the voltage applied by the generator to the coil is equal in amplitude to the graph of 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 shifted in phase by 90 0, i.e. that is, the voltage leads the current by 90 0.

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

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

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

click on the picture to enlarge

The resulting voltage applied by the generator to the coil always leads the current by an angle less than 90 0.

The magnitude of the angle φ depends on the values ​​of the active and inductive resistance of the coil.

About the resulting coil resistance

The resulting resistance of the coil cannot be found by summing the values ​​of its active and reactive resistances.

The resulting coil resistance Z is

Electric current in conductors is continuously associated with magnetic and electric fields. Elements that characterize the conversion of electromagnetic energy into heat are called active resistances (denoted R). Typical representatives of active resistances are resistors, incandescent lamps, electric ovens, etc.

Inductive reactance. Formula of inductive reactance.

Elements associated with the presence of only a magnetic field are called inductances. Coils, windings and etc. have inductance. Inductive reactance formula:

where L is inductance.

Capacitance. Capacitance formula.

Elements associated with the presence of an electric field are called capacitances. Capacitors, long power lines, etc. have capacitance. Capacitance formula:

where C is capacity.

Total resistance. Total resistance formulas.

Real consumers of electrical energy may also have a complex value of resistance. In the presence of active R and inductive L resistances, the value of the total resistance Z is calculated using the formula:

Similarly, the total resistance Z is calculated for the circuit of active R and capacitive resistance C:

Consumers with active R, inductive L and capacitive resistance C have a total resistance: