Basic Electrical Theory and Fundamentals
Scope
This domain tests DC circuit laws, AC waveform values and three-phase power - the calculations that recur in cable sizing, machine rating and instrument selection. Expect numerical questions rather than definitions alone.
Core rules
- Ohm's law: V = IR; power P = VI = I²R = V²/R.
- Series: same current, voltages add, R_total = R₁ + R₂ + … Parallel: same voltage, currents add, 1/R_total = 1/R₁ + 1/R₂.
- KCL: algebraic sum of currents at a node is zero. KVL: algebraic sum of voltages round a closed loop is zero.
- AC values: V_rms = V_m/√2 = 0.707 V_m; half-wave average = 0.637 V_m; form factor = 1.11; crest factor = 1.414.
- Single-phase P = VI cos φ; three-phase P = √3 V_L I_L cos φ; Q = √3 V_L I_L sin φ.
- Star: V_L = √3 V_ph, I_L = I_ph. Delta: I_L = √3 I_ph, V_L = V_ph.
Worked example
A 415 V three-phase motor draws 12 A at 0.85 power factor lagging. Input power P = √3 × 415 × 12 × 0.85 = 7,332 W ≈ 7.33 kW. If efficiency is 88%, shaft output = 7.33 × 0.88 = 6.45 kW. Apparent power S = √3 × 415 × 12 = 8.63 kVA; reactive power Q = √(8.63² − 7.33²) = 4.55 kvar. The line voltage is used because the motor is connected to a 415 V three-phase supply; in star the winding would see 415/√3 = 240 V.
Traps that cost marks
Using 230 V in a three-phase formula, omitting √3, entering power factor as 85 instead of 0.85, and mixing peak with RMS values in power calculations. In star–delta questions, label line and phase quantities before substituting.