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Two coils of self-inductances $L_1$ and $L_2$ are coupled with mutual inductance $M$ and coupling coefficient $K$. The relation between them is:
A$M = \sqrt{L_1 L_2}/K$
B$M = K L_1 L_2$
C$M = K(L_1 + L_2)$
D$M = K\sqrt{L_1 L_2}$, with $0 \le K \le 1$
Answer & Solution
Correct answer: D. $M = K\sqrt{L_1 L_2}$, with $0 \le K \le 1$
The coupling coefficient is defined as $K = M / \sqrt{L_1 L_2}$, hence $M = K\sqrt{L_1 L_2}$. $K = 1$ corresponds to perfect flux linkage between the two coils, $K = 0$ to no coupling, and most real transformers have $K$ close to but less than $1$.
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