AC Theory and AC Circuits
AC theory questions test sine-wave descriptions, RMS values, reactance, impedance, and phase relationships. You must convert between peak, RMS, and frequency values and calculate inductive and capacitive reactance.
Core rules
- A sine wave is described by peak value, frequency f, and phase; period T = 1/f.
- RMS value = peak / √2 for a sine wave; RMS gives the equivalent heating effect of DC.
- Average value of a full sine cycle is zero; the half-cycle average is 0.637 × peak.
- Inductive reactance X_L = 2πfL; capacitive reactance X_C = 1/(2πfC).
- Impedance Z combines resistance and reactance; in a series RLC circuit, Z = √(R² + (X_L − X_C)²).
- Power factor = cosφ, where φ is the phase angle between voltage and current.
Worked example
A voltage is v = 339 sin(314t). Find peak, RMS, and frequency, then the reactance of a 0.10 H inductor at that frequency. Peak = 339 V; RMS = 339 / √2 = 240 V. ω = 314 rad/s, so f = ω/(2π) = 314/6.283 = 50 Hz. X_L = 2πfL = 2π × 50 × 0.10 = 31.4 Ω. Reasoning: ω is angular frequency in rad/s, not frequency in hertz; divide by 2π before using reactance formulas.
Traps
- Calling the peak value the RMS value; RMS is lower by √2.
- Confusing peak-to-peak with peak.
- Using degrees per second instead of radians per second for ω.
- Forgetting that capacitive reactance falls as frequency rises while inductive reactance rises.