GATE 2024 IN – Question 63
Two magnetically coupled coils have total inductance 500 mH in series aiding and 300 mH in series opposing. Their self-inductances are equal. The coupling coefficient is ______ (two decimal places).
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Show answer and explanation
Correct answer: 0.25 to 0.25
Explanation
Equal self-inductances give $2L+2M=500$ mH and $2L-2M=300$ mH. Adding gives $L=200$ mH; subtracting gives $M=50$ mH.
Therefore $k=M/\sqrt{L_1L_2}=50/200=\boxed{0.25}$.