Inductances
Consider two neighbouring coils, C1 (of N1 turns) and C2 (of N2 turns)
Bounding surfaces S1 and S2 as shown in the diagram below. If a
current I1 flows in C1, a magnetic field B1 will be created. All flux links
C1 and some of the flux will link C2, and the flux linkages can be
calculated by
From the Biot-Savart law, we know that the flux density and hence
the flux linkage is proportional to the current I1. We write
the flux linkage is proportional to the current I1. We write
where L11 and L12 are defined as the self inductance of coil 1 and
the mutual inductance between the two coils, respectively. The self
inductance of coil 2 can be obtained similarly by introducing a current
in it. It can be shown that the mutual inductances calculated from both
sides are equal or L21=L12.
the mutual inductance between the two coils, respectively. The self
inductance of coil 2 can be obtained similarly by introducing a current
in it. It can be shown that the mutual inductances calculated from both
sides are equal or L21=L12.
where N1 and N2 are absorbed in the contour integrals over C1 and C2,
and R is the distance between dl1 and dl2.
Circuital Symbols of Inductors
The circuital symbol for an inductor of a single coil is
and R is the distance between dl1 and dl2.
Circuital Symbols of Inductors
The circuital symbol for an inductor of a single coil is
In the case of magnetically coupled coils, a dot convention is
commonly employed to mark the reference directions of the magnetic
fields generated by the currents in those coils. As shown below, the
terminals of two coils, A and B, are marked such that a positive current
IA entering the dot marked terminal of circuit A produces in circuit B a
flux in the same direction as would positive current IB entering the dot
marked terminal of circuit B.
commonly employed to mark the reference directions of the magnetic
fields generated by the currents in those coils. As shown below, the
terminals of two coils, A and B, are marked such that a positive current
IA entering the dot marked terminal of circuit A produces in circuit B a
flux in the same direction as would positive current IB entering the dot
marked terminal of circuit B.
The circuital symbol for a magnetic coupling between two circuits or
coils is
coils is
where L11 and L22 are the self inductances of coils 1 and 2, and L12 is
the mutual inductance between two coils. Note that L12=L21.
Source ( pdf )
http://services.eng.uts.edu.au/cempe/subjects_JGZ/ems/ems_ch4_nt.pdf
Inductance
Consider a two coil magnetic system as shown below. The magnetic flux
linkage of the two coils can be express as
where the first subscript indicates the coil of flux linkage and the secondthe coil carrying current. By defining the self and mutual inductances of
the two coils as
where Ljk is the self inductance of the jth coil when j=k, the mutualinductance between the jth coil and the kth coil when jk, and Ljk = Lkj,
the flux linkages can be expressed as
The above definition is also valid for a n coil system. For a linearmagnetic system, the above calculation can be performed by switching
on one coil while all other coils are switched off such that the magnetic
circuit analysis can be simplified. This is especially significant for a
complex magnetic circuit. For a nonlinear magnetic system, however,
the inductances can only be calculated by the above definition with all
coils switched on.
Source ( pdf )
http://services.eng.uts.edu.au/cempe/subjects_JGZ/eet/eet_ch4.pdf
Inductance relates flux-linkage to current
http://services.eng.uts.edu.au/cempe/subjects_JGZ/eet/eet_ch4.pdf
Inductance relates flux-linkage to current
