This is a problem from Engineering circuit analysis , practice problem 13.4, pg 431

Goal of the problem:
To calculate w(t) which is ,
\(
w(t)=0.5L_1i_1+0.5L_2i_2\)±\(Mi_1i_2\)

where,
\(L_1,L_2 \)are the self inductances and M is the mutual inductance,=\(k.(L_1.L_2)^{\frac{1}{2}}\)

I do not understand how i can calculate \(i_2\)?
pls help

 

Unless you draw the equivalent circuit showing the mutual inductance voltage sources you will have difficulty answering the question.

It's curious that there are apparently two answers for the total stored energy but the question asks only for a solution at one time - at t=0 sec. Was there another time or condition mentioned in the question that we can't see in the post?

It turns out the solution at t=0 sec is quite simple but you need to follow through with some work (as suggested above) for this to become apparent.

Your formula (correct or otherwise) includes a '±' sign term which relates to the equivalent inductance looking into the mutually coupled network - which sign will you actually apply?