AC and DC Circuit Theory and Analysis
AC and DC Circuit Theory and Analysis tests phasor arithmetic, impedance, power, transients, and network theorems as applied to test work. Level 4 questions often combine a simple circuit with a measurement or relay-loading scenario.
Core rules
- Use rms values for AC power; for a sine wave, peak = rms × √2.
- Series impedance adds as complex numbers: Z = R + j(XL − XC). Do not add magnitudes unless the circuit is purely resistive or purely reactive.
- Power triangle: P = VI cos θ, Q = VI sin θ, S = VI; power factor = cos θ. Inductive current lags; capacitive current leads.
- DC transients: τ = RC or L/R; after about five time constants the change is essentially complete.
- Thevenin equivalent uses the open-circuit voltage and the equivalent resistance seen from the test points; it is useful for meter and relay burden calculations.
Worked example
A series circuit has R = 6 Ω and XL = 8 Ω at 60 Hz, supplied at 120 V rms. Z = √(6² + 8²) = 10 Ω. I = 120/10 = 12 A. Power factor = R/Z = 0.6 lagging. Real power P = 120 × 12 × 0.6 = 864 W. Reactive power Q = 120 × 12 × 0.8 = 1,152 var. Apparent power S = 1,440 VA. The resistor voltage is 72 V and the inductor voltage is 96 V; they add as phasors, not arithmetically, to 120 V.
Traps
Adding 6 Ω and 8 Ω to get 14 Ω; using peak voltage in power formulas; assigning leading power factor to an inductive load; ignoring meter burden; mixing line-to-line and line-to-neutral voltages in three-phase calculations.