AC Circuits — Formula Sheet

AC generator produces time-varying EMF

e = e₀ sin ωt where e₀ is peak EMF and ω is angular frequency

AC current similarly varies as

i = i₀ sin (ωt + φ) where φ is phase difference

Pure Resistor

Current and voltage in phase (φ = 0°), follows Ohm's law directly

Pure Inductor

Current lags voltage by 90° (φ = -90°), opposes change in current

Impedance Z = √[R² + (X_L - X_C)²] represents total opposition to AC current

Pure resistor

P_av = e_rms × i_rms (all power dissipated as heat)

Average value over half cycle = 0.637 × peak value.

RMS value = 0.707 × peak value = peak/√2.

Pure inductor

I lags V by 90°, XL = 2πfL.

Pure capacitor

I leads V by 90°, XC = 1/(2πfC).

Phase angle

tan φ = (XL - XC)/R.