What Is Electropathy?

Inductance is a property of a closed loop and is a physical quantity. After the coil passes the current, magnetic field induction is formed in the coil, and the induced magnetic field will generate an induced current to resist the current passing through the coil. The interaction between this current and the coil is called the inductive reactance of the electric power, which is also the inductance. The unit is "Henry (H)", named after the American scientist Joseph Henry. It is a circuit parameter describing the induced electromotive force effect in this coil or in another coil due to a change in coil current. Inductance is a general term for self and mutual inductance. A device that provides inductance is called an inductor. ^[1]
Right!

A property of a conductor, measured by the ratio of the electromotive force or voltage induced in the conductor to the rate of change of the current that produces the voltage. A steady current produces a stable magnetic field, and a constantly changing current (AC) or a fluctuating DC produces a changing magnetic field. The changing magnetic field in turn induces an electromotive force in a conductor in this magnetic field. The magnitude of the induced electromotive force is directly proportional to the rate of change of the current. The scaling factor is called inductance and is represented by the symbol L and the unit is Henry (H). ^[2]

Inductance symbol: L

Inductance unit: Henry (H), milli-Henry (mH), micro-Henry (H), the conversion relationship is:

1H = 1000mH 1mH = 1000H

Inductive self-inductance

A coil (or loop) with a current of I is passed, and the sum of the interlinking magnetic fluxes of each turn is called the magnetic flux of the coil. If the magnetic flux of each coil is and the number of turns of the coil is N, then the magnetic flux of the coil = N. When the coil current I changes with time, the flux linkage also changes with time. According to the law of electromagnetic induction, the self-induced electromotive force EL will be induced in the coil, and its value will be

The self-inductance L of the coil is defined as the ratio of the time derivative dI / dt of the self-inductive electromotive force eL and the current, and is given a negative sign, that is,

In the above two formulas, the positive directions of and eL, and the positive directions of and I all conform to the right-hand spiral rule. Knowing the inductance L, the self-inductive emf can be calculated from dI / dt. In addition, self-induction can also be defined as follows

Four self-inductance calculation formulas for linear magnetic media

From an engineering point of view, media other than ferromagnetic materials can be considered linear magnetic media, and their permeability is approximately equal to the vacuum permeability 0. The self-inductance of the coil placed in this medium is only related to the shape and size of the coil and its turn conductor, and has nothing to do with the amount of current.

The formula for calculating the self-inductance L of four coils or circuits with simple geometric shapes is as follows:

(1) Self-inductance of long solenoid (ignoring end effect and radial dimension of turns)

Where l is the length of the solenoid; S is the cross-sectional area of the solenoid; N is the total number of turns.

(2) Self-inductance of a toroidal close-wound coil without a magnetic core (the cross section of the ring is square, and the average radius of the ring is R)

Where b is the side length of the square cross-section; N is the total number of turns. If Rb, it is approximately L ₀ Nb / 2R, which is the same form as the long solenoid self-inductance calculation formula.

(3) Self-inductance of coaxial cable (ignoring end effects)

Where R ₁ and R ₂ are the radius of the inner and outer conductors of the coaxial cable; l is the cable length; Li and Lo are called the internal and external self-inductance of the coaxial cable, respectively. The length of the conductor inside the cable is related to its radius.

(4) Self-inductance of two-wire transmission line (ignoring end effects)

Where R is the radius of the two wires; l is the length of the transmission line; D is the distance between the axes of the two wires.

Mutual inductance

Suppose there are two adjacent coils in a linear magnetic medium. There is a current I _{1 in the} coil _{1 .} The part of the magnetic flux generated by _I1 that is interlinked with the coil 2 forms a mutual inductance magnetic link ₂₁ . When the current I ₁ changes with time, ₂₁ also changes with it; according to the law of electromagnetic induction, a mutual induction electromotive force M2 will appear in the coil 2

Define the mutual inductance M ₂₁ of coil 1 to coil 2 as

or

Similarly, if there is a current I 2 in the coil 2, it generates a mutual inductance magnetic link ₁₂ and the coil 1 is linked. When I ₂ changes, mutual inductance E _M1 appears in coil 1

In the formula, M ₁₂ refers to the mutual inductance of the coil 2 to the coil 1. The above formula is the definition of M ₁₂ .

If the current I ₁ is a constant current, or I ₁ is a time-varying current with a low rate of change, the mutual inductance flux ₁₂ is proportional to I ₁ , and the proportionality factor (normal number) is the mutual inductance M _{21 of} coil 1 to coil 2, And

21 = _M21I1

Similarly, if the current I ₂ is a constant current or a time-varying current with a low rate of change, ₂ is proportional to I ₂ , and the proportionality factor is the mutual inductance M _{12 of} coil 2 to coil 1, and

₁₂ = M ₁₂ I ₂

The theory proves that M ₁₂ = M _{21 and} use M to represent them, then

Time-varying currents are applied to coils 1 and 2 at the same time. When they are I _{1 and} I ₂ respectively, the induced electromotive force e ₁ and e ₂ in the coil are the sum of the self-inductive electromotive force and the mutual inductive electromotive force.

Two formulas for calculating mutual inductance in linear magnetic media

The mutual inductance M is not only related to the shape and size of the coil and its conductor, and the vacuum permeability 0, but also to the mutual position of the two coils.

(1) Mutual inductance between two coaxial long solenoids (ignoring the end effect, the radius of the two solenoids is approximately the same value R, and the lengths of the two solenoids are l ₁ and l ₂ respectively, and l ₁ > l ₂ )

In the formula, N ₁ and N ₂ are the number of turns of the two solenoids, respectively.

(2) Mutual inductance between two pairs of transmission lines (Suppose two pairs of two-line transmission lines AA and BB are parallel to each other, ignoring the end effect and the influence of the wire radius)

Where DAB , DAB, DAB, DAB are the distances between the corresponding wires between two pairs of transmission lines, as shown in the figure; l is the length of the transmission line.

Inductance of three-phase balanced transmission line

There is mutual inductance between the three power lines. After using the three-phase transmission line transposition technology, the phases are balanced. After considering the effects of the self-inductive magnetic flux and the mutual-inductive magnetic flux, the equivalent inductance L per unit length of the transmission line transmission line of each pair of two parallel pairs is

Where D =

(DAB, DBC, and DCA are the distances between the corresponding phase lines, respectively). The geometric mean distance is called; R is the wire radius.