Two coils `X` and `Y` are linked such that emf `E` is induced in `Y` when the current in `x` is changing at the rate `I' (= dI//dt)`. If a current `I_(0)` is now made to flow through `Y`, the flux linked with `X` will be

Options

A. `EI_(0) I'`
B. `(I_(0)I')/(E)`
C. `(EI')I_(0)`
D. `((E)/(I'))I_(0)`

Answer

D

Explanation

Let `M` be the mutual inductance between `X` and `Y`. By definition
`E = M(dI)/(dt) = MI', M = (E)/(I')`
The flux linked with `X` is `phi_(X) = MI_(0) = (E)/(I') I_(0)`