A capacitor and a coil in an AC circuit

If a lamp and a coil are connected in series to a DC source, the coil (with small active resistance) is almost no obstacle; with alternating current of the same effective voltage the lamp is dimmer. The reason is that when the current changes, a self-induced EMF appears in the coil and opposes the change. If i = Iₘcosωt, the EMF is e = –L·Δi/Δt = ωLIₘsinωt; for R = 0 the coil voltage is u = –e = –ωLIₘsinωt = ωLIₘcos(ωt + π/2). Thus the voltage leads the current by π/2 (the current lags the voltage). The amplitudes obey Uₘ = ωL·Iₘ, that is Iₘ = Uₘ/X_L, where the inductive reactance X_L = ωL = 2πνL (in Ω). The larger the frequency and inductance, the larger X_L; for direct current (ν = 0) X_L = 0. X_L is also a reactive resistance: energy is not turned into heat but stored as magnetic field energy and returned (mean power zero). Coils are used as chokes to block high-frequency currents.