Worked Example: Residential Cable Sizing — Multi-Standard

Size a cable for a single-phase electric cooker in a residential kitchen. The full installation details are:

This example walks through the complete cable sizing procedure step by step, with full standard references at each stage, then compares the result across three international standards.

For a single-phase resistive load:

I_b = P / (V × PF) — (Eq. 1)

I_b = 7,200 / (230 × 1.0)

I_b = 31.3 A

The design current is the maximum sustained current the circuit is expected to carry. For a resistive load like a cooker, the power factor is 1.0, simplifying the calculation.

The protective device must have a rated current not less than the design current:

I_n ≥ I_b — (Eq. 2)

From the standard protective device ratings (6, 10, 16, 20, 25, 32, 40, 50, 63 A...), the next rating above 31.3 A is:

I_n = 32 A (MCB, Type B or C)

A Type B MCB trips at 3–5× rated current (instantaneous magnetic trip). Type C (5–10×) could also be used but Type B is more common for resistive loads in domestic installations.

The installation conditions differ from the standard reference conditions. We need to apply derating factors from AS/NZS 3008.1.1:2017:

Ambient temperature derating (k₁):

Reference ambient for AS/NZS 3008 is 40°C. Our ambient is 35°C, which is below the reference, so the temperature factor is actually greater than 1.0.

From Table 22, Row: 35°C, Column: 90°C rated cable:

k₁ = 1.04 (slight increase because ambient is below 40°C reference)

Grouping derating (k₂):

From Table 25, Row: 2 circuits, enclosed in conduit:

k₂ = 0.80

Combined derating factor:

k_total = k₁ × k₂ = 1.04 × 0.80 = 0.832

The cable must have a current-carrying capacity (after derating) at least equal to the protective device rating:

I_z ≥ I_n / k_total — (Eq. 3)

I_z ≥ 32 / 0.832

I_z ≥ 38.5 A

Now select from AS/NZS 3008 Table 13 (multicore cables), Column 6 (enclosed in wiring enclosure, V-90 insulation, copper conductor):

The minimum cable size based on current-carrying capacity is 6 mm², rated at 40 A from Table 13, Column 6.

However, we should verify that 6 mm² passes the voltage drop check before finalising this selection.

Check voltage drop for the 6 mm² cable first. From AS/NZS 3008 Table 35, for 6 mm² V-90 single-phase copper cable:

mV/A·m = 7.3 (at unity power factor)

ΔV = mV/A·m × I_b × L / 1000 — (Eq. 4)

ΔV = 7.3 × 31.3 × 22 / 1000

ΔV = 5.03 V

ΔV% = 5.03 / 230 × 100 = 2.19%

The AS/NZS 3000 Clause 3.6.2 limit for power circuits is 5%. This circuit at 2.19% passes comfortably.

Now let’s also check the 10 mm² option for comparison:

mV/A·m = 4.0 (Table 35, 10 mm²)

ΔV = 4.0 × 31.3 × 22 / 1000 = 2.75 V = 1.20%

Both 6 mm² and 10 mm² pass the voltage drop check. Since 6 mm² is the smaller and cheaper option and passes all checks, it is the correct selection for this scenario.

For completeness, verify the cable can withstand the prospective short circuit current at the consumer unit. Using the adiabatic equation:

k²S² ≥ I²t — (Eq. 5)

Where k = 115 (PVC insulated copper, initial temperature 90°C, final 250°C per AS/NZS 3008 Table 52), S = 6 mm², and I²t is determined by the protective device clearing time and fault current.

k²S² = 115² × 6² = 13,225 × 36 = 476,100 A²s

For a typical domestic installation with 16 kA prospective fault current and a 32 A Type B MCB tripping in approximately 5 ms at fault level, the energy let-through is well within the cable’s withstand. The 6 mm² cable passes the short circuit check.

Selected cable: 6 mm² V-90 TPS copper, protected by 32 A Type B MCB.

The governing factor is current-carrying capacity. The grouping derating (2 circuits) reduced the effective cable capacity enough that 4 mm² was insufficient, requiring a 6 mm² cable. Voltage drop was not the governing factor for this relatively short 22 m run.

Calculating the same circuit under different standards reveals how reference conditions and table values affect cable selection. Here is how this cooker circuit sizes across three standards: