AC Circuits and Single-Phase/Three-Phase Systems
What this domain tests
This domain checks your handling of alternating quantities: RMS and peak values, reactance, impedance, power factor, and the star–delta relationships used in three-phase supply. Numerical questions on impedance and power are common.
Core rules
- For a sine wave, RMS = peak/√2 and average = 0.637 × peak; form factor = RMS/average = 1.11 and peak factor = 1.414.
- Frequency f = 1/T; inductive reactance XL = 2πfL rises with frequency, while capacitive reactance XC = 1/(2πfC) falls.
- Impedance Z = √(R² + (XL − XC)²); current I = V/Z; power factor cos φ = R/Z.
- Real power P = VI cos φ, reactive power Q = VI sin φ, apparent power S = VI.
- Star: line voltage = √3 × phase voltage, line current = phase current. Delta: line current = √3 × phase current, line voltage = phase voltage. Three-phase power = √3 VLIL cos φ.
Worked example
A coil of R = 6 Ω and XL = 8 Ω is connected to 230 V, 50 Hz. Z = √(36 + 64) = 10 Ω, so I = 23 A. Power factor = 6/10 = 0.6. Real power = 230 × 23 × 0.6 = 3174 W, and apparent power = 5290 VA. The difference is reactive power, about 4232 var, which a capacitor bank could partly supply.
Traps that cost marks
Substituting peak voltage into V = IZ instead of RMS; adding R and X arithmetically; mixing line and phase values in delta; and treating power factor as efficiency, which it is not.