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

AI Thread Summary
The discussion revolves around the confusion regarding the sign of the mutual inductance term in loop equations for a circuit. The user initially set up the equations but was informed that the mutual inductance term should be negative. They clarified that their model for current I2 is entering the dot and I3 is exiting, which led to questioning the application of the mutual inductance sign convention. The user speculated that the issue might stem from the polarity of a voltage source in their analysis. Ultimately, they concluded that adjusting the loop equation for I1's direction resolved the confusion about the mutual inductance term.
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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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