Electrical Theory and Principles
Theory questions reward fluency with a handful of relationships and punish unit sloppiness.
Core relationships
Ohm's law (E = I × R), power (P = E × I = I²R = E²/R), and three-phase power (P = √3 × E_line × I_line × power factor). In series circuits the current is common, voltages divide and resistances add; in parallel the voltage is common, currents add and resistances combine reciprocally. In AC, impedance is the vector sum Z = √(R² + X²); inductive reactance X_L = 2πfL makes current lag voltage, capacitive reactance X_C = 1/(2πfC) makes current lead. Transformers trade voltage for current at constant volt-amperes through the turns ratio, and a balanced three-phase wye load carries zero neutral current.
Traps candidates fall into
- Peak versus RMS: 120 V is an RMS value, and its peak is about 169 V (√2 × RMS).
- Real versus apparent power: kW and kVA are only equal at unity power factor, so a low-PF load draws more current than the kW rating suggests.
- Mixing series and parallel rules mid-calculation, especially assuming current splits in a series string.
- Forgetting that non-linear loads (harmonics) can add in the neutral of a balanced system rather than cancel.
- Using line-to-line voltage where line-to-neutral belongs, or forgetting √3 in three-phase calculations.
Worked example
A 10 kW single-phase load at 240 V and 0.8 PF draws I = 10,000 ÷ (240 × 0.8) = 52 A. The same load supplied at 208 V three-phase draws I = 10,000 ÷ (1.732 × 208 × 0.8) = 34.7 A. Rule of thumb: at 240 V single-phase and unity power factor, 1 kW is about 4.2 A.