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Currently stuck on this problem. In class we did not do an example of when the mutually induced inductors were in the same mesh, let alone one the inductors also being shared with another mesh. So I am pretty stumped. I need assistance in coming up with the KVL equation with each mesh. I'm not sure how to include the mutual inductance into the equations.
So far I have for I_1: 1 = 1*I_1 + j1*I_1 + j2*(I_1 - I_2) ...
For I_2: 0 = 2*I_2 - j1*I_2 + j2*(I_2 - I_1) ...
Normally with the two separated inductors, the mutual inductance would be as simple as add/subtracting the mutual inductance times the current going across the opposite inductor. Is that also somehow applied here? Would the mesh of I_1 have two mutual inductances added to the equation? Also how would I determine of the sign of mutual inductance caused by the shared inductor in the middle if the currents are coming in opposite directions (how do I know if the current is going towards or away from the dot)? Any advice would be appreciated to help steer me in the right direction. Thank you.
