Electrical Fundamentals and Circuit Theory
This domain tests whether you can apply Ohm's law, series–parallel reduction, AC quantities and three-phase relationships to real panel and wiring situations rather than recite formulas.
Core relationships
- Ohm's law: V = IR; power P = VI = I²R = V²/R for DC and purely resistive AC loads.
- Series: same current, R = R1 + R2 + ...; parallel: same voltage, 1/R = 1/R1 + 1/R2.
- Kirchhoff: current into a node equals current out (KCL); the algebraic sum of voltages round a closed loop is zero (KVL).
- AC: RMS = 0.707 × peak, form factor 1.11; declared supply is 230 V single-phase and 415 V three-phase.
- Three-phase: V_line = √3 × V_phase in star; I_line = √3 × I_phase in delta; P = √3 V_L I_L cos φ.
- Impedance Z = √(R² + X²); power factor cos φ = R/Z; true power VI cos φ, reactive power VI sin φ (var).
Worked example
A 7.5 kW, 415 V three-phase motor has efficiency 0.88 and power factor 0.8. Find the line current. Input power = 7500/0.88 = 8523 W. Then I_L = 8523/(1.732 × 415 × 0.8) = 8523/575 = 14.8 A, so a 16 A overload setting on a 20 A frame is sensible. Forgetting efficiency gives 7500/575 = 13.0 A - a 12% error that would set the relay low and cause nuisance tripping.
Traps that cost marks
- Using peak values where RMS is required, or vice versa.
- Adding parallel resistances directly instead of using reciprocals.
- Ignoring efficiency when calculating motor input current.
- Mixing line and phase values in a delta-connected load.
- Treating a short circuit as an ordinary resistance in a series–parallel problem.