Electrical Science
Electrical Science underpins every calculation in the practical exam: circuit resistance, power, the a.c. behaviour of coils and capacitors, and three-phase relationships. Questions are short and numerical, so marks come from quoting the formula, substituting with consistent units, and giving the answer with its unit.
d.c. fundamentals
- Ohm's law: V = IR. Power: P = VI = I squared R = V squared over R.
- Series: resistances add, current is common, voltage divides. Parallel: the reciprocal of the total equals the sum of reciprocals, voltage is common.
- Kirchhoff: currents at a node sum to zero; voltages round a closed loop sum to zero.
a.c. quantities
- Nominal 50 Hz, 230 V line to neutral, 400 V line to line. r.m.s. = peak divided by root two, so peak = 1.414 times r.m.s.
- Reactance: XL = 2 pi f L; XC = 1 over (2 pi f C). In series, Z = square root of (R squared plus (XL minus XC) squared).
- Power factor = cos phi = R/Z. True power P = VI cos phi; apparent power S = VI; reactive power Q = VI sin phi.
- Three-phase star: VL = root three times Vph and IL = Iph. Delta: IL = root three times Iph and VL = Vph. Power = root three times VL times IL times cos phi.
Worked example
A coil of resistance 8 ohm and inductive reactance 6 ohm is connected to 230 V a.c. Find the current, power factor and true power. Z = square root of (64 + 36) = 10 ohm. I = 230 / 10 = 23 A. Power factor = R/Z = 0.8. True power = I squared R = 529 times 8 = 4232 W, which checks against 230 times 23 times 0.8 = 4232 W. Apparent power = 230 times 23 = 5290 VA and reactive power = square root of (5290 squared minus 4232 squared) = 3174 var. Working P by both routes is a useful self-check.
Magnetism, induction and machines
Current in a conductor creates a magnetic field, and a changing flux induces an e.m.f. Transformers change voltage by the turns ratio N1/N2 = V1/V2. Motors and RCDs both depend on this: an RCD compares the flux from live and neutral in a toroid and trips when the residual current exceeds its sensitivity.
Traps
Mixing r.m.s. and peak values; adding R and X arithmetically instead of vectorially; using P = VI on an inductive load; confusing line and phase values in delta; forgetting that copper resistance rises about 20 per cent between 20 and 70 degrees Celsius.