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Circuit and electromagnetism basics

Two coils with self-inductances L1 = 4 mH and L2 = 9 mH are magnetically coupled with a coupling coefficient k = 0.5. What is the mutual inductance M?

  1. A6 mH
  2. B6.5 mH
  3. C3 mH
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Answer: C. 3 mH

The mutual inductance is M = k√(L1L2): 0.5 × √(4 × 9) = 0.5 × 6 = 3 mH. The coupling coefficient k lies between 0 and 1, reaching k = 1 for ideal coupling with no leakage flux. Connecting the two coils in series so that their fluxes aid gives L1 + L2 + 2M = 19 mH; connecting them so that their fluxes oppose gives L1 + L2 − 2M = 7 mH.

  • A. 6 mH is √(L1L2), forgetting to multiply by k.
  • B. 6.5 mH is the average of L1 and L2, not the mutual-inductance formula.
  • C. Correct. 0.5 × √(4 × 9) = 3 mH.
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