Alternating Current

v(t) = V₀ sin(ωt). Rotating phasor projects onto sine wave. V_rms = V₀/√2.

I in phase with V (φ = 0°). I₀ = V₀/R.

I lags V by 90°. X_L = ωL grows with frequency.

I leads V by 90°. X_C = 1/(ωC) falls with frequency.

Z = √(R² + (X_L − X_C)²). Phasor + impedance triangle live.

I peaks at f₀ = 1/(2π√LC). Q-factor and bandwidth Δf = f₀/Q.

P_avg = V_rms·I_rms·cosφ. Watch p(t) = v·i and the average line.

q(t) = q₀cos(ω₀t). Energy bounces between capacitor and inductor.

V_s/V_p = N_s/N_p. Step-up vs step-down with animated flux in core.

ε(t) = NBAω sin(ωt). Rotating coil between magnetic poles.

X_L (linear ↑) and X_C (1/f ↓) crossing at resonance frequency f₀.

V_rms = V₀/√2 — DC equivalent for power. Mains 230 V is RMS, peak 325 V.

Vector sum: V = √(V_R² + (V_L − V_C)²). Tune each and see V_net.