Electrical Fundamentals and Circuit Theory
What this domain tests
Circuit analysis with numbers: Ohm's law and Kirchhoff's laws, series and parallel networks, impedance, AC power in kW, kVA and kvar, power factor, and balanced three-phase relationships. Questions are usually short calculations where unit discipline decides the mark.
Core rules
- Ohm's law extends to AC as V = IZ, with Z = √(R² + (X_L − X_C)²), X_L = 2πfL and X_C = 1/(2πfC).
- Single phase: P = VI cos φ, Q = VI sin φ, S = VI.
- Balanced three phase: P = √3 × V_L × I_L × cos φ; in star V_L = √3 V_ph and I_L = I_ph; in delta I_L = √3 I_ph and V_L = V_ph.
- Energy in kWh = kW × hours; a 3 kW load for 4 hours uses 12 kWh.
- Series elements share current and add voltage; parallel elements share voltage and add current.
- Power factor correction reduces line current and kVA, but leaves the kW demand unchanged.
Worked example
A 400 V three-phase 15 kW motor runs at 0.85 power factor and 90% efficiency. Find the line current. Input power = 15/0.90 = 16.67 kW. I = 16 670/(1.732 × 400 × 0.85) = 28.3 A. The reasoning: the nameplate kW is shaft output, so it must be divided by efficiency before the power formula is applied; the result is line current only because the motor is treated as a balanced load.
Traps
- Feeding output kW into the current formula, which understates current by the efficiency margin.
- Mixing line and phase quantities in delta-connected loads.
- Treating kVA as kW when the power factor is below unity.
- Forgetting that a reduced power factor raises current and cable loading for the same kW.