There are two stationary loops with mutual inductance `L_(12)`. The current is one of the loops starts to be varied as `I_(1) = alpha t` where `alpha` is a current, `t` is time. Find the time dependence `I_(2) (t)` of the current in the other loop whose inductance is `L_(2)` and resistance `R`.

Explanation

When the current in one of the loop is `I_(1) = alpha t`, and `e.m.f. L_(12) (d I_(1))/(dt) = L_(12) alpha` is, induced in the other loop. Then if the current in the other loop is `I_(2)` we must have,
`L_(2) (d I_(2))/(dt) + R I_(2) = L_(12) alpha`
This familar equaction has the solution,
`I_(2) = (L_(12) alpha)/(R) (1 - e^((-tR)/(L_(2))))` which is the required current.