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Question

Two coils of self inductances L1 and L2 are placed so close together that effective flux in one coil is completely linked with the other. If M is the mutual inductance between them, then

A
M=L1L2
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B
M=L1/L2
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C
M=(L1L2)2
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D
M=(L1L2)
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Solution

The correct option is D M=√(L1L2)Consider two coils 1 and 2 When current I1 flows through coil 1 , L1=N1ϕ1I1 and M12=M=N2ϕ12I1where ϕ12=kϕ1 (Note : when current flows through one coil it produces flux; the whole flux may not link with the other coil coupled and this is due to leakage flux by a fraction k, known as coefficient of coupling)When current I2 flows through coil 2 , L2=N2ϕ2I2 and M21=M=N1ϕ21I2where ϕ21=kϕ2 Using above equations, M2=N2kϕ1I1×N1kϕ2I2=k2L1L2As the coils are completely link with each other so it is is called magnetically tightly coupled and so k=1.Thus, M2=L1L2 or M=√L1L2

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