Correct answer: C — M = k√(L₁L₂)
Relation between self and mutual inductance
Self-inductance describes the flux linkage a coil produces in itself for a given current. Mutual inductance describes the flux linkage produced in one coil by current in the other. Not all the flux generated by one coil necessarily links the second coil; some may follow leakage paths.
The coupling coefficient k expresses the degree of magnetic coupling. For the magnitude of mutual inductance in the usual passive two-coil model:
k = M/√(L₁L₂)
M = k√(L₁L₂), with 0 ≤ k ≤ 1
L₁, L₂ and M are measured in henrys, while k is dimensionless. When k = 0, the coils have no magnetic coupling. When k = 1, coupling is perfect and M reaches √(L₁L₂). Intermediate values represent partial coupling.
Example of using the relation
If L₁ = 4 H, L₂ = 9 H and k = 0.5, first find the geometric mean of the two self-inductances, then apply the coupling factor:
√(L₁L₂) = √(4 × 9) = 6 H
M = 0.5 × 6 = 3 H
The induced voltage due to mutual coupling has magnitude M|di/dt|. Its polarity is determined by the dot convention and reference directions, rather than by changing the magnitude relation above.
