Hi, in this part of the circuit i am not sure on how to reduce the inductors to a single one, i need this to solve de ODE for t>=0, i have tried to reduce it using parallel and series asumptions but i have the problem with the 4mH inductor on the center could someone give me a hand? thanks


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Perhaps this will give you an idea.

http://en.wikipedia.org/wiki/Y-Δ_transform

 

of course i forgot about delta-star transform, thanks

 

And if you find yourself in a similar situation and don't recall that transform (or whatever trick makes it easy), you can always fall back on the fundamentals. You know that inductances add like resistors, so analyze the equivalent resistance (as seen between the top and bottom rails) of the circuit that has the inductors replaced with the same numerically valued resistors.

Symmetry then dictates that no current flows in the bridging component, and so you have two strings, each with a 4Ω and 0.5Ω component in series, connected in parallel. Hence, by inspection, you have (4.5/2)Ω or 2.25Ω, which translates to an equivalent inductance of 2.25mH. Is that what you got after applying the delta-wye transform?

 

Yes i obtain 2.25 mH. That is an interesting approach, i really appreciate it.