AC Fundamentals and Single-Phase Circuits
Scope
AC Fundamentals and Single-Phase Circuits tests sinusoidal waveforms, RMS and average values, form factor, frequency, reactance, impedance, phase angle, power factor, series RLC behaviour and resonance.
Core rules
- For v = Vm sin(2πft), f = 1/T and ω = 2πf.
- For a sine wave: RMS = Vm/√2 = 0.707Vm; half-cycle average = 2Vm/π = 0.637Vm; form factor = 1.11; peak factor = 1.414.
- XL = 2πfL and XC = 1/(2πfC).
- Series RLC: Z = √[R² + (XL − XC)²]; φ = tan⁻¹[(XL − XC)/R].
- P = VI cos φ, Q = VI sin φ, S = VI; power factor = cos φ.
- At resonance XL = XC, Z = R, current is maximum and power factor is unity.
Worked example
A 230 V, 50 Hz supply feeds R = 6 Ω in series with XL = 8 Ω. Z = √(6² + 8²) = 10 Ω. I = 230/10 = 23 A. cos φ = R/Z = 0.6 lagging, so P = 230 × 23 × 0.6 = 3174 W; check with I²R = 529 × 6 = 3174 W. Reactive power Q = 230 × 23 × 0.8 = 4232 var. The 0.8 is sin φ, not the power factor.
Traps
- Adding 6 Ω and 8 Ω arithmetically to get 14 Ω instead of using the impedance triangle.
- Substituting peak voltage where RMS is required in power calculations.
- Calling an inductive circuit’s power factor leading.
- Confusing reactive power in var with active power in watts.