Two coils of self-inductance `L_(1)` and `L_(2)` are placed closed to each other so that total flux in one coil is completely linked with other. If `M` is mutual inductance between them, then

Options

A. ` M = L _ 1 // L _ 2 `
B. ` M = L _ 1 L _ 2 `
C. ` M = sqrt( L _ 1 L _ 2 ) `
D. ` M = ( L _ 1 L _ 2 ) ^ 2 `

Answer

C

Explanation

We know that, ` M = - ( e _ 2 )/( di _ 1 // d t ) = - ( e _ 1 )/( di_2//dt ) `
Also, ` e _ 1 = - L _ 1 ( di _ 1 )/( dt ) and e _ 2 = - L _ 2 ( di _ 2 )/( dt ) `
` rArr M ^ 2 = ( e _ 1 e _ 2 ) /(( ( di _ 1 )/( dt ) ) ( ( d i _ 2)/( dt ))) = L _ 1 L _ 2 `
` rArr M = sqrt (L _ 1 L _ 2 ) `