In Fig, the mutual inductance of a coil and a very long straight wire is `M`, coil has resistance `R` and self-inductance `L`. The current in the wire varies according to the law `I = at`, where `a` is a constant and `t` is the time, the time dependence of current in the coil is

Options

A. `(M)/(aR)`
B. `maR e^(-Rt//L)`
C. `(M)/(R ) e^(-tR//L)`
D. `(Ma)/(R ) (1 - e^(-tR//L))`

Answer

D

Explanation

`E = (Mdi)/(dt) = Ma`, `I = (Ma)/(R )(1 - e^(-tR//L))`