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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 √L1L2Let 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. ThusM12=N2ϕB2i1 and M21=N1ϕB1i2andL1=N1ϕB1i1 and L2=N2ϕB2i2If all the flux of coil 2 links coil 1 and vice versa, thenϕB2=ϕB1As M12=M21=MThus we getM12M21=M2=N1N2ϕB1ϕB2i1i2=L1L2orM=√L1L2(assuming that there is no flux leakage)Mutual inductance is inductance of emf in a coil due to change in current in another casefor two coils which are mutually coupled has mutual inductance in =√L1L2This is a general result assuming that there is no flux leakage.

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