Self-Inductance & RL Transient
L = μ₀N²A/ℓ. RL circuit current I(t) = I∞(1 − e^(−t/τ)), τ = L/R.
Key Notes
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).
Formulas
Defining relation
Back-EMF; opposes change in current.
Solenoid self-inductance
Tightly-wound, long-solenoid approximation. With core: L = μ_r·μ₀·N²·A/ℓ.
Energy stored
Stored in the surrounding magnetic field.
Field energy density
Local energy per unit volume in a B-field.
RL transient (rising current)
When a battery is connected to RL in series.
Important Points
L is a GEOMETRIC property — like capacitance C. Doesn't depend on the current.
Doubling N (turns) QUADRUPLES L because L ∝ N².
Iron-core inductors can have L hundreds of times larger than air-core for the same geometry.
Sudden interruption of current through an inductor (e.g., opening a switch) produces a HUGE back-EMF (V = L·dI/dt) — that's why inductive arcs are dangerous and why diodes are added across relay coils ('flyback diodes').
Time constant τ = L/R sets how fast the current rises (or falls) in an RL circuit — at t = τ, current reaches 63% of final value.
Inductor behaves like an open circuit at t = 0⁺ and like a short circuit at steady state in DC.
Self-Inductance & RL Transient notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.