The basic idea is that a number of inductors connected
in series , magnetically linked or not , can be replaced by a single inductor
which produces the same current when same frequency voltage is applied across
it , as it produced in case of series connection .
Case-1 :- when inductors are not magnetically linked i.e magnetic flux of one inductor does not link any other inductor but itself.
First , lets take the series connection shown.
The emfs induced across the individual inductors will
be
i.e The equivalent
inductance of two or more series connected inductors equals the sum of all individual
inductances.
Case-2
:- when inductors are magnetically linked.
Case-2(a)
:- when inductors are magnetically linked and flux aids the local inductor
flux.
Leq = L1+L2+2M
i.e equivalent inductance is greater by 2M
factor when fluxes aid as compared to series connection without flux linkage.
Case-2(b)
:- when inductors are magnetically linked and flux oppose the local inductor
flux.
The whole procedure for
derivation is same except that emf induced in inductors L1 and L2 due to its own flux will be
of opposite sign repectively from emf induced in inductors L1 and L2
due to linking flux.
The final expression
would come out as
Leq = L1+L2-2M
Its left for your
practice !!
