Define mutual inductance and the coupling coefficient; what is the expression for mutual inductance M between two coils with self-inductances L1 and L2 and coupling coefficient k?

• A. M = L1 + L2
• B. M = k√(L1L2)
• C. M = sqrt(L1^2 + L2^2)
• D. M = k (L1 L2)

Answer: (B)

Mutual inductance quantifies how effectively energy from one coil’s magnetic flux links the other coil. It depends on how strong each coil is (their self-inductances) and how well the flux is shared between them, which is captured by the coupling coefficient k between 0 and 1. The coupling coefficient is defined as k = M / sqrt(L1 L2). Rearranging gives the expression for mutual inductance: M = k sqrt(L1 L2). This shows that when coupling is perfect (k = 1), M equals the geometric mean sqrt(L1 L2); with no coupling (k = 0), M is zero. The other forms do not reflect the correct dependence on both self-inductances or have incorrect units.