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. `sqrt(L_(1)L_(2))`
B. `sqrt((L_(1))//(L_(2)))`
C. `L_(1)+ L_(2)`
D. `L_(1)- L_(2)`

Answer

A

Explanation

When a rod of length l is rotated about one of its ends in a plane perpendicular to uniform magnetic field B with angular velocity `omega` then emf induced between its ends can be written as follows:
`"emf"= (1)/(2)Bomegal^(2)` ...(i)
In case, rod is not straight then represents minimum distance between the ends of rod and emf induced is not dependent on shape. In given case direct distance between a and c can be written as follows:
`l= sqrt(L^(2)+4R^(2))`
Substituting above in equation (1) we get the following:
`"emf" = (1)/(2)Bomega (L^(2)+4R^(2))`
Hence, option (b) is correct.