Solving a Mutual Inductance problem using Laplace

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Solving a Mutual Inductance problem using Laplace
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Usually M < sqrt(L1×L2)... Here I guess M < 4 is allowed. M=2 is maybe reasonable values. If L1-M negative would the current be in opposite phase? Extremely hard initial value setting case. I couldn't see it well how the voltage sources polarity was selected (that is below inductance M) - what if put above M rather than below M? Sign selected according to current I1+I2 direction. The handling of the mutual inductance seems risky or complicated.

jarikosonen
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This is from Nilsson and Riedel 11th ed, Chapter 13.

perezfranco
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What book is it? I appreciate if you say me that..!

bernardoroux