Magnetically coupled inductors an AC circuits

[iceman_ch]

Homework Statement

I've actually uploaded the question.

When solving problems with magnetically coupled inductors I like to add dependent sources so that I can keep everything straight. My question is when I add the dependent sources does there need to be a specific polarity to them. With the way that AC works I would think that it doesn't matter what polarity you assign them because in the end the angle is what determines the poliarity. I could make it so that when I do the mesh the sources come out positive. Is this the best way to solve this problem or is there another way.

Thanks

 

[The Electrician]

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