AC through Inductor

A pure inductor opposes changes in current. Driven by v = V₀ sin(ωt), current is i = (V₀/X_L) sin(ωt − π/2).

Current LAGS voltage by exactly 90° (φ = +π/2). At the instant V is at its peak, I is zero and rising.

Inductive reactance: X_L = ωL = 2πfL. Units: Ω. Rises linearly with frequency.

At DC (f = 0): X_L = 0 (inductor acts as a wire). At very high f: X_L → ∞ (inductor BLOCKS AC).

No power is dissipated on average: P_avg = V_rms·I_rms·cos(π/2) = 0. Energy oscillates between source and inductor's magnetic field.

Phasor: I lags V by 90° — current phasor is 90° clockwise from voltage phasor.

Inductors are 'frequency-dependent resistors' — but they STORE energy, they don't dissipate it.