Self-Inductance & RL Transient

When current in a coil changes, its own flux changes, inducing a back-EMF that opposes the change. The proportionality constant is the self-inductance L: ε = −L·dI/dt.

Unit: henry (H) = V·s/A. A 1 H inductor produces 1 V when its current changes at 1 A/s.

For a long solenoid of length ℓ, area A, N turns: L = μ₀·N²·A/ℓ. Adding a ferromagnetic core multiplies by μ_r.

L depends ONLY on geometry and core material — not on the current.

Energy stored in an inductor: U = ½LI². This is energy stored in the MAGNETIC FIELD.

Energy density of the field: u = B²/(2μ₀) — analogous to ε₀E²/2 for an E-field.

In a circuit, inductors resist sudden current changes (just like capacitors resist sudden voltage changes).