Mutual inductance M is related to self-inductances L1, L2 and coupling coefficient k by which expression?

• A. M = sqrt(L1 L2)
• B. M = k sqrt(L1 L2)
• C. M = L1 L2 / k
• D. M = k (L1 + L2)

Answer: (B)

Mutual inductance depends on how well the magnetic flux from one coil links the other, and the coupling coefficient k captures how complete that linkage is (0 ≤ k ≤ 1). The right relationship is M = k times the geometric mean of the two self-inductances, which is M = k sqrt(L1 L2). This makes intuitive sense: if the coils are perfectly coupled (k = 1), M reaches its maximum value sqrt(L1 L2); if the coupling is partial (k < 1), M is proportionally smaller. The units also line up: sqrt(H × H) = H, and multiplying by the dimensionless k gives henries.

Seeing why the other forms don’t fit helps reinforce the concept. M = sqrt(L1 L2) would assume perfect coupling and ignore k. M = L1 L2 / k would not only misstate the dependence on coupling but also produce the wrong units under typical inductance values. M = k (L1 + L2) uses the sum of self-inductances and a linear term, which doesn’t reflect how mutual coupling relates to the self-inductances.