Electrical Theory, Circuits, and Calculations
What the exam is testing
The Electrical Theory, Circuits, and Calculations domain checks whether you can turn a load schedule into a current, a current into a protective device rating, and a circuit arrangement into a predictable voltage drop and fault level. The exam favours three-phase industrial calculations, power factor, efficiency, series and parallel networks, and the difference between design current and nominal current.
Core relationships
- Ohm's law: V = I x R. Power in a single-phase circuit: P = V x I x cos phi. Three-phase power: P = sqrt(3) x V_L x I_L x cos phi.
- For a balanced three-phase load, line current is the phase current in star, while in delta the line current is sqrt(3) times the phase current.
- Efficiency links output and input: input power = output power divided by efficiency. Use input power when calculating line current from a motor nameplate.
- Voltage drop by the mV/A/m method: Vdrop = mV/A/m x I x L / 1000, with L in metres. Compare the result with the permitted percentage of nominal voltage.
- Diversity is a design judgement supported by the load schedule and standard diversity factors; it is not permission to ignore the maximum demand of fixed industrial loads.
Worked example
A 15 kW, 400 V, three-phase motor has a power factor of 0.85 and an efficiency of 0.90. Find the line current. Input power = 15 / 0.90 = 16.67 kW. I = P / (sqrt(3) x V x cos phi) = 16670 / (1.732 x 400 x 0.85) = 28.3 A. The protective device must have a rating at least equal to this design current, the cable must carry that current after derating, and the starter overload must be set from the motor full-load current, not from the breaker rating. A common error is to use 15 kW directly, which gives 25.5 A and under-sizes the circuit.
Traps that cost marks
Omitting sqrt(3) in three-phase calculations; mixing kW and kVA; dividing by efficiency when converting from input to output; using 230 V for a 400 V three-phase line-to-line calculation; and checking voltage drop only after selecting the cable rather than as part of the selection.