Discussion
A 40 mH coil is connected in series with a 90 mH coil. If the mutual inductance between the two coils is 30 mH, find the coefficient of coupling.
Answer: A
The coefficient of coupling is 0.5. It is the ratio of the mutual inductance to the geometric mean of the two self inductances.
\[ k = \frac{M}{\sqrt{L_1 L_2}} \]
\[ = \frac{30}{\sqrt{40 \times 90}} = \frac{30}{60} = 0.5 \]
The values 0.6, 0.7 and 0.8 do not equal 30 divided by 60. The fact that the coils are connected in series does not change the formula for k. So the first option is correct.
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