# Self Inductance and Mutual Inductance

Consider a circuit consisting of n-coils that are magnetically coupled with each other. Under linear conditions, the total flux linking any one coil is the sum of self flux and mutual flux due to (n-1) coils.
To find

• the self flux of a coil, excite that coil alone.
• the mutual flux in a coil due to other coils, excite all other coils except that coil.

Now apply superposition to find total flux due self and mutual flux in the coil.

Consider the case where coil alone is excited. The current flowing through the coil produces a total flux of . Out of the flux , a part of this flux links with all other coils called magnetizing flux( ) and rest of flux that links to itself is called leakage flux( ).

(1) Consider the case where all the coils except coil are excited. The flux produced by all other coils, links with coil produces a total mutual flux of (2) where is the flux produced by -coil linking with -coil.

By superposition theorem, the total flux linking with coil is,

(3) If the -coil has turns, then flux linkages is given by,

(4) Inductance is defined as rate of change of flux linkages( ) with current.

(5) If is the reluctance offered to the flux( ), then it is related to magneto-motive force( ) as, . The reciprocal of reluctance is permeance( ). Therefore

(6) For an N-turn -coil, by Ampere’s law,

(7) Using Eq-(5) to Eq-(7), for -coil we can define

• Leakage inductance,

(8) • Magnetizing inductance,

(9) • Self-inductance,

(10) Mutual inductance bewteen and coil is

(11) and

(12) but, .
Therefore, From EQ-11 and EQ-12,

(13)  Leakage coefficient is This site uses Akismet to reduce spam. Learn how your comment data is processed.