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)//dt)=-(e_(1))/(di_(2)//dt)`
Also, `e_(1)=-L_(1)(di_(1))/(dt) and e_(2)=-L_(2)(di_(2))/(dt)`
`implies M^(2)=(e_(1)e_(2))/(((di_(1))/(dt))((di_(2))/(dt)))=L_(1)L_(2) implies M=sqrt(L_(1)L_(2))`