The phenomenon of emf induction in any circuit when the current changes in a nearby other circuit is called mutual induction. The induced emf is called the mutual inductance emf, and its instantaneous value is denoted. The nature of mutual inductance is based on the fact that the magnetic field created by the flow of current occupies a larger volume than a coil with current. Therefore, the magnetic flux can penetrate the area of the turns and adjacent coils:
where is the flux created by the current of the first circuit, is the flux penetrating only the first circuit, is the flux that captures the second circuit (see transformer theory in Appendix 2).
The product of the flux created by the current and the number of turns of the coil is called the flux linkage. a common part flow, combining both circuits, creates flux linkage, which is proportional to the inducing current
IN linear systems the coefficient M does not depend on i and is called the mutual inductance of coils 1 and 2. The coupling coefficient of two magnetically coupled circuits with inductances and mutual inductance M is understood as the value
Obviously, the coupling coefficient cannot be greater than one.
Let's consider the sequential connection of two magnetically coupled coils with consonant inclusion (the field of the second coil amplifies the field of the first), shown in Fig. 2.1.
Applying Kirchhoff's second law, it is easy to get the connection between the instantaneous values of current and voltage in a common circuit:
Since the ratio of the EMF to the current created by it, by definition, is nothing more than the resistance of the circuit, and for harmonic oscillations
If the coils are connected in opposite directions (the current of the second coil weakens the field of the first one), obviously, it will be necessary to change the signs in front of M to minus, which is physically justified. In this case:
The expressions obtained show that inductors connected in series have a complex resistance, the real part of which, as expected, sums up the winding resistances direct current, and the imaginary part, preceded by the factor , is the inductance of the entire system of coils. Therefore, one can write
In this expression, plus refers to the case of consonant switching on of the windings, and minus refers to the opposite connection.
Having a device for measuring inductance, you can measure the inductance of coils with a series-consistent connection once, and then switch the windings in the opposite direction and measure the inductance again.
In the first case, it is measured 
In the second case 
Subtracting the second from the first expression, we get
Let's move on to the experiment. As an object of study, we use the FPE-05 module containing two coaxial coils. The larger diameter outer spool can move along the length of the inner spool and its position is controlled by a scale on the stem. The beginnings and ends of both windings are brought out to the rear wall of the module, the corresponding sockets are marked as H1, K1, H2, K2. By using connecting wires coils are connected to a high-frequency capacitance and inductance meter type E7-9 or E12-1a. Description of devices is in the folder "universal measuring instruments". By changing the position of the external coil with the help of a rod, we measure the corresponding inductances of consonant and counter-connection, calculate the corresponding values of M and build a graph M (mH)=F(Xcm).
General form installations |
