Principles and Calculations
This domain tests the design calculation chain that sits behind every circuit: design current, protective device rating, cable current-carrying capacity with derating factors, voltage drop, shock protection and thermal constraint. The exam expects the steps in order, with the factor values named and the outcome stated as a pass or fail.
The chain
- Design current Ib: the load current, from P/V for a single appliance or a diversity calculation for a whole installation.
- Device rating In: In greater than or equal to Ib.
- Tabulated capacity It: It greater than or equal to In, where It is the tabulated value multiplied by every applicable correction factor.
- Factors to check: Ca ambient temperature, Cg grouping, Ci thermal insulation, Cd depth of burial, and the rewirable fuse factor if relevant.
- Voltage drop: mV/A/m times Ib times length divided by 1000, limited to 3 per cent lighting and 5 per cent other circuits for a public supply, measured from the origin.
- Shock protection: the maximum Zs from the device tables, adjusted for conductor operating temperature.
- Thermal constraint: k squared S squared greater than or equal to I squared t for the protective conductor, and the adiabatic check on the live conductors.
Worked example
An 8.5 kW shower at 230 V, cable run 18 m, clipped direct alongside one other loaded circuit, in a 30 degree ambient. Ib = 8500 / 230 = 37.0 A, so a 40 A type B MCB is selected. 6 sq mm twin and earth, reference method C, has a tabulated capacity of 47 A. Cg for two circuits is 0.80 and Ca is 1.0, so It = 47 times 0.80 = 37.6 A, which is less than the 40 A device: fail on capacity. 10 sq mm has 65 A tabulated, so It = 65 times 0.80 = 52 A, which is greater than 40 A: pass. Voltage drop for 10 sq mm is 4.4 mV/A/m: 4.4 times 37 times 18 divided by 1000 = 2.93 V, well under the 6.9 V (3 per cent) limit. Zs must not exceed 1.09 ohm for a 40 A type B device at 0.4 s, so the measured value plus the temperature allowance is compared against that figure.
Traps
Choosing the cable from the tabulated figure alone and forgetting the factors; applying Cg when the circuits are not loaded simultaneously without saying so; using 5 per cent for a lighting circuit; forgetting that the device rating must not exceed the derated cable capacity; applying diversity to a single fixed appliance; omitting the thermal check on the circuit protective conductor.