As a UK electrician, you must master three core calculations to ensure compliance, safety, and system performance. These calculations guarantee that the cable is right for the load, the voltage stays healthy, and the circuit trips quickly enough in a fault condition. UK electrician reference books PDF
1. Calculation for Overcurrent Protection: Current-Carrying Capacity ($I_z$)
This is the most fundamental calculation: ensuring the cable can handle the current being demanded without overheating. The cable's actual ability to carry current must be greater than or equal to the circuit's protective device rating ($I_n$).
The Formulaic Principle:
$I_n$ (Nominal Current): The rating of the protective device (e.g., a 32A MCB).
$I_z$ (Tabulated Current): The maximum current the cable can carry under standard conditions, found in BS 7671 Appendix 4 tables.
$C$ Factors (Correction Factors): These adjust the cable rating based on real-world conditions:
$C_a$ (Ambient Temperature): For example, a cable run through a boiler cupboard is derated.
$C_g$ (Grouping): A bundle of cables heats up more than a single cable, so the capacity is reduced.
$C_i$ (Insulation/Sheath): Applies if cables are surrounded by thermal insulation.
The Compliance Goal: You must prove that after applying all applicable $C$ factors, the maximum current the installed cable can safely carry ($I_z$ corrected) remains higher than the rating of the fuse or breaker ($I_n$) protecting it.
2. Calculation for Performance: Voltage Drop ($\Delta V$)
While cable sizing determines safety, the voltage drop calculation determines performance. If the voltage drops too much, equipment won't run efficiently or may fail altogether. BS 7671 (Regulation 525) sets limits on the maximum permissible voltage drop from the supply terminals to the farthest point of use.
The Formulaic Principle (Simplified):
$\Delta V$ (Voltage Drop): The voltage lost (in Volts) across the entire circuit length.
$I_b$ (Design Current): The maximum current the load will actually draw.
$L$ (Length): The total length of the circuit (in metres).
$mV$ (Millivolts per Ampere per Metre): A specific value for the cable type and size, found in BS 7671 Appendix 4 (Table 4D1B, etc.).
The Compliance Goal: The calculated voltage drop ($\Delta V$) must not exceed the maximum percentage allowed by the Regulations (typically 3% for lighting and 5% for other circuits in low voltage installations, though this varies by circuit type). If it's too high, you must increase the cable cross-sectional area (size) until it complies.
3. Calculation for Safety: Earth Fault Loop Impedance ($Z_s$)
This is the calculation that ensures the Automatic Disconnection of Supply (ADS) works fast enough to prevent a fatal shock. $Z_s$ measures the total resistance of the entire fault path, from the supply transformer back to the point of fault.
The Formulaic Principle:
$Z_s$ (Total Loop Impedance): The final measured or calculated impedance of the entire fault path.
$Z_e$ (External Loop Impedance): The impedance up to the intake terminals (supplied by the DNO/supplier).
$R_1 + R_2$ (Circuit Resistance): The resistance of the live ($R_1$) and earth ($R_2$) conductors of the specific circuit cable being calculated.
The Compliance Goal: The final calculated or measured value of $Z_s$ must be less than the Maximum Permissible Earth Fault Loop Impedance specified in BS 7671 Chapter 41 for the specific protective device ($I_n$) and disconnection time required (e.g., 0.4 seconds for most domestic final circuits). If the impedance is too high, the fault current won't be large enough to trip the device in time.
