Explain mutual inductance and its role in coupled circuits.

Mutual inductance (M) occurs when changing current in one coil induces voltage in another nearby coil through magnetic coupling. M = k*sqrt(L1*L2), where k is coupling coefficient (0 to 1). Tight coupling (k near 1) is desired in transformers; loose coupling is used in wireless charging and RF circuits. The induced voltage follows: V2 = M(dI1/dt). Mutual inductance can add (aiding) or subtract (opposing) from self-inductance depending on winding orientation.