AC through Inductor
I lags V by 90°. X_L = ωL grows with frequency.
Key Notes
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.
Formulas
Inductive reactance
Resistance-like quantity (Ω) — measures opposition to AC.
Peak / rms current
Just like Ohm's law with X_L in place of R.
Current waveform
Lags voltage by 90° (T/4 in time).
Average power
cos(π/2) = 0 — pure inductor is 'wattless'.
Instantaneous power
Positive and negative halves cancel over a full cycle.
Important Points
Mnemonic 'CIVIL': in a C, I leads V; in an L, V leads I. So for an inductor, current LAGS.
X_L is a function of frequency — same inductor 'looks bigger' at higher f.
Inductors are open-circuit at high frequency (block AC), short-circuit at DC (steady state).
Zero average power doesn't mean the current is zero — energy just sloshes back and forth.
Real inductors have some resistance too; the 'pure L' is an idealisation but a useful one.
Industrial loads (motors) are heavily inductive — utilities require power-factor correction to keep cos φ near 1.
AC through Inductor 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.