Discussion
When two coils having inductance of L1 and L2 are connected through mutual inductance M, the coefficient of coupling K is given by :
Answer: A
The coefficient of coupling is \(K = \frac{M}{\sqrt{L_{1}L_{2}}}\).
The mutual inductance between two coils can never exceed the geometric mean of their self-inductances; it reaches \(\sqrt{L_{1}L_{2}}\) only when every line of flux from one coil links the other. K measures how much of that ideal is achieved, so it is the ratio of M to \(\sqrt{L_{1}L_{2}}\) and always lies between 0 and 1.
The factor 2 in the other two square-root options is wrong: the version with 2M would give K = 2 for perfect coupling, which is impossible. L1L2/M has the units of inductance, not a pure number.
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