Why is the mutual inductance term negative in the loop equations?

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SUMMARY

The discussion centers on the sign convention for mutual inductance in loop equations involving a circuit with inductors. The user initially formulated loop equations but was advised that the mutual inductance term, represented as j12, should be negative. The user clarified that their model current I2 enters the dot while I3 exits, leading to the conclusion that the correct application of the mutual inductance term should reflect the sign convention, specifically using jwL - M = 0 instead of jwL + M = 0. Ultimately, the user confirmed that their loop equations were correctly adjusted to reflect this understanding.

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I am running my loop current equations for this circuit and have.
-1+-j6*(I1-I2)=0
-j6*(I2-I1)+j20*I2 +j12*I3=0
(j30-j2+j5+4)*I3+j12*I2=0

But i am being told that the mutual inductance term j12 should be negative in both.
My model current I2 is going into the dot and I3 is coming out of the dot, so
jwL+M=0 should apply
not
jwL-M=0

what am i missing?
o wait... is it the sign of the 1V i have backwards?
 
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what is the question?
 
I am reviewing questions from old studies.
I believe it was to find Zeq at the terminals of the left hand inductor, by using a 1V test.
But i think I answered my own question.
For I1 running from - to + potential the loop equation needs to read
1+-j6*(I1-I2)=0
so that second loop equation is
-j6*(I2-I1)+j20*I2 +j12*I3=0
 

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