Chapter 30: Inductance

Students learn about mutual inductance, where current changes in one coil induce electromotive force in nearby coils, and self-inductance, where a circuit component opposes changes in its own current flow through the relationship between induced voltage and current rate of change. The chapter develops the concept of magnetic energy storage in inductors and derives the energy density expressions for magnetic fields in both vacuum and material media. Circuit analysis progresses through increasingly complex configurations, beginning with resistor-inductor circuits that exhibit exponential current growth and decay characterized by the time constant L/R. Students then explore inductor-capacitor circuits, which demonstrate oscillatory behavior as energy alternates between the electric field of the capacitor and magnetic field of the inductor, with angular frequency determined by the circuit parameters. The most comprehensive analysis covers resistor-inductor-capacitor series circuits, where the resistance value determines whether the system exhibits underdamped oscillations with gradually decreasing amplitude, critically damped behavior for fastest equilibrium return, or overdamped response with slow non-oscillatory decay. Throughout these analyses, students apply Kirchhoff's voltage law and develop differential equations that describe the temporal evolution of current and charge in these fundamental circuit configurations.