Question

There are two stationary loops with mutual inductance L₁₂. The current in one of the loops starts to be varied as I₁ = αt, where α is a constant, t is time. Find the time dependence I₂ (t) of the current in the other loop whose inductance is L₂ and resistance R.

Answer 1

When the current in one of the loop is  I₁ = αt, an e.m.f.  is induced in the other loop. Then if the current in the other loop is I₂ we must have,

This familiar equation has the solution,

 which is the required current.