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Question

Two coils of inductances L1 , and L2 are linked such that their mutual inductance is M. Then M=

A
L1+L2
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B
12(L1+L2)
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C
(L1±L2)
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D
L1L2
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Solution

The correct option is D L1L2
Let us first consider a case when the total flux associated with one coil links with the other, i.e. a case of maximum flux linkage. Consider two coils placed adjacent to each other. Thus

M12=N2ϕB2i1 and M21=N1ϕB1i2

and
L1=N1ϕB1i1 and L2=N2ϕB2i2

If all the flux of coil 2 links coil 1 and vice versa, then
ϕB2=ϕB1
As M12=M21=M
Thus we get

M12M21=M2=N1N2ϕB1ϕB2i1i2=L1L2

or
M=L1L2(assuming that there is no flux leakage)
Mutual inductance is inductance of emf in a coil due to change in current in another case
for two coils which are mutually coupled has mutual inductance in =L1L2
This is a general result assuming that there is no flux leakage.

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