

§5 Currents after closing and opening the circuit Consider a circuit consisting of a source current EMF ?, the resistance R, inductance L and the key K. The circuit current flows At time t = 0 disable EMF, closing the circuit shorted (key in position 2). As soon as the current begins to decrease selfinduced emf arises that prevents this decrease.
Potentiation
At t = 0
time constant determines the rate of decrease (increase) in the circuit
therefore, τ  the time during which the current in the circuit is reduced by a factor e. The more or less L R (ie, the greater τ), the slower the current in the circuit decreases. , in the chain, except EMF E will act selfinduced emf, which prevents the instantaneous current rise. or
inhomogeneous linear differential equation. His solution is the total solution of the homogeneous differential equation and any particular solution of the inhomogeneous equations. The general solution homogeneous equations
Particular solution of the nonhomogeneous
The general solution of the nonhomogeneous
at t = 0 I = 0, hence , I_{0} = const,then
§6 Mutual induction. Transformers Consider two fixed circuit (1 and 2), located close enough to each other. If the loop current flows one I1, then the magnetic flux generated by this current is proportional to I1. We denote the part of the Ô_{21}_{ }thread that runs through circuit 2. Then
where L_{21}  proportionality factor . If the current I_{1}is changed, the circuit 2 is induced emf E_{i2} _{2} _{ } Similarly, during the flow of current in the circuit 2 I2 magnetic flux pervades circuit  Ô_{12}
If I_{2}is changed, then
The phenomenon emergence the EMF in a circuit when changing current in the other is called mutual induction. Proportionality coefficients L_{12} and L_{21}are called mutual inductance L_{12} = L_{21}. L_{12} and L_{21}are dependent on the geometric shape, size, relative position of the contours and the magnetic permeability of the medium surrounding contours [L_{12}] =Ãí. Calculate the mutual inductance of two coils wound on a common toroid. Magnetic induction field generated by the coil 1 to the number of turns N_{1},the magnetic permeability μ core
where is the length of the core in the midline The magnetic flux through one turn of coil 2: :
The total magnetic flux
Consequently, the
2. Transformers (converter)  a device to increase, decrease, electrical isolation, etc. voltage and current. It is based on the phenomenon of mutual induction. Primary and secondary windings with N_{1} and N_{2}turns, respectively, mounted on a closed iron core. Change in the flux in the coil 1 is connected to a variable emf is in the secondary appearance EMF mutual induction, and in the primary  EMF of selfinduction. Primary current I_{1}is determined by Ohm's law
R_{1} the resistance of the primary winding , I_{1}R_{1 }small in comparison and in variable fields. Consequently,
EMF mutual induction in the secondary
Consequently,
Sign “  “means that the phases and opposite .  transformation ratio. k > 1 stepup transformer ; k < 1 stepdown transformer.
Therefore, the currents in the windings are inversely proportional to the number of turns in these coils. A transformer consists of one winding is called autotransformer..
