The book says that the for loop 2, the KVL is \$-j3 I_{1} + (12+j6)I_{2}=0\$ , but the loop 2 leaves the dot in its coil. Isn't it supposed to be \$-j3I_{1} + (12-j6)I_{2} =0\$ ?
Dot convention in Magnetically coupled circuits
currentmutual-inductance
Best Answer
The dot only determines the polarity of the mutual voltage, it won't affect other directions in the calculation. In figure (b), it shows the equivalent circuit take into the mutual voltage. Because the direction of \$I_{1}\$ in loop 1 is flow into coil 1, and the direction of \$I_2\$ is defined to flow out from coil 2. So the mutual voltage's polarity in loop 2 is positive at the dot side.