Alternating Currents

AC voltage varies sinusoidally

AC voltage varies sinusoidally: V = Vm cos ωt, where Vm is peak voltage and ω is angular frequency. Similarly, current I = Im cos ωt. The RMS values a

In purely resistive AC circuits

In purely resistive AC circuits, voltage and current are in phase (φ = 0°). Current follows Ohm's law: I = V/R = (Vm/R)cos ωt. Average power consumed

In purely capacitive circuits

In purely capacitive circuits, current leads voltage by 90° (π/2 radians). Current I = -ωCVm sin ωt. Capacitive reactance XC = 1/(ωC) = 1/(2πfC) oppos

In purely inductive circuits

In purely inductive circuits, current lags voltage by 90°. Current I = (Vm/ωL)sin ωt. Inductive reactance XL = ωL = 2πfL increases with frequency. At

In series LCR circuits

In series LCR circuits, impedance Z = √[R² + (XL - XC)²] represents total opposition to AC current. Current I = V/Z, and voltage leads/lags current by