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Circuit in question

I have a question regarding the dot convention, or more-so want to find out where I am getting it wrong. I start by defining the currents I1, I2, and I3. I1 goes through R1 and L1, while I2 is the current through L2 and I3 goes through R2.

I then set up two equations using KVL, where I find that the magnetic inductance on L1 and L2 respecitively should be -XM*I2 and -XMI1. Would this be correct?

My thought process was that the current I2 enters at the dot, meaning the dotted terminal of L1 is positive, implying that the mutual inductance is negative. For the mutual inductance of L2 we see that I1 leaves the dotted terminal, meaning the dot at L2 is negative, which would imply a negative mutual inductance

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The dot convention for coupled coils is this:Current entering one coil marked with a dot produces current exitting the coupled coil at its dotting end or: If the voltage of one coil is higher at its end marked with a dot ,it produces a voltage drop from the dotted end of the coupled coil to the undotted end of the coupled coil.

In your case I1 enters L1 at its not-dotted end and L2 at its dotting end so:

the voltage drop across L1 due to the mutual inductance will be in the opposite direction from the voltage drop across L1 due to its self inductance and the voltage drop across L2 due to the mutual inductance will be in the opposite direction from the voltage drop across L2 due to its self inductance.

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