Cable Sizing for a Buried Supply
You are asked to install a 230 V single-phase supply to a detached garage 35 m from the house. The load is a 3 kW heater, a 1.5 kW compressor, and lighting totalling 200 W. The cable will be buried direct in the garden at a depth of 600 mm, passing under a paved path. The soil is sandy and the ambient temperature is 20 °C. The consumer unit has a 16 A MCB available, and the earthing system is TN-S with a Ze of 0.35 Ω. The garage has a metal consumer unit and the circuits include a 13 A socket and a 6 A lighting circuit. You must select a suitable cable and verify protection.
1. Calculate the design current and select an appropriate cable size, showing your reasoning.
Read the worked answer
Total load: 3 kW + 1.5 kW + 0.2 kW = 4.7 kW. Design current Ib = P / U = 4700 / 230 ≈ 20.4 A.
However, the heater and compressor may not run simultaneously; apply diversity if appropriate. For a garage supply, a common approach is to size for the full load or apply a diversity factor. If we assume the compressor and heater can run together, Ib ≈ 20.4 A. A 16 A MCB would be too small; we need a 20 A or 25 A device.
Cable selection: for direct burial in sandy soil, use a PVC/SWA cable. Reference method D (buried direct) applies. For a 4 mm² two-core SWA, the tabulated current-carrying capacity (It) for method D is approximately 37 A (for 70 °C PVC, 2-core). Apply correction factors:
- Ambient temperature 20 °C: Ca = 1.0 (reference 30 °C for buried, but for 20 °C Ca ≈ 1.05; conservatively 1.0).
- Soil thermal resistivity: sandy soil may be poorer; use a derating factor of about 0.9 if not known.
- Depth of burial 600 mm: no correction if ≥0.5 m.
So Iz = It × Ca × Cs ≈ 37 × 1.0 × 0.9 ≈ 33.3 A. This exceeds Ib (20.4 A) and In (20 A), so 4 mm² is adequate. A 2.5 mm² cable would give It ≈ 24 A, derated to ≈21.6 A, which is marginal and not recommended for a 20 A MCB with a 20.4 A load. Select 4 mm² SWA.
2. Verify that the selected cable and MCB provide adequate protection against overload and short circuit, and check voltage drop.
Read the worked answer
Overload protection: In = 20 A, Ib = 20.4 A. The rule is Ib ≤ In ≤ Iz. Here 20.4 ≤ 20 is not satisfied (Ib slightly exceeds In). Use a 25 A MCB: 20.4 ≤ 25 ≤ 33.3, which is satisfactory. Alternatively, apply diversity to reduce Ib below 20 A. For a garage, diversity may allow Ib ≈ 16 A, but the heater alone is 13 A, so a 20 A MCB is reasonable if the compressor is intermittent. Recommend a 20 A MCB with a 4 mm² cable and note that the compressor should not run with the heater at full load; otherwise use a 25 A MCB.
Short-circuit protection: The MCB must interrupt the prospective short-circuit current. At the garage, Zs = Ze + R1+R2. For 4 mm² SWA, R1+R2 ≈ (4.61 + 7.41) mΩ/m × 35 m ≈ 0.42 Ω. So Zs ≈ 0.35 + 0.42 = 0.77 Ω. Prospective fault current ≈ 230 / 0.77 ≈ 299 A. A 20 A MCB (Type B) has a magnetic trip at 5×In = 100 A, so 299 A will trip instantaneously. Satisfactory.
Voltage drop: For 4 mm², mV/A/m ≈ 11 mV/A/m. Vd = 11 × 20.4 × 35 / 1000 ≈ 7.85 V, which is 3.4% of 230 V. The limit for a final circuit is 5% (11.5 V), so satisfactory. For lighting, the 6 A circuit is short and within limits.
3. State the earthing and bonding requirements for the garage and explain how the TN-S system affects your design.
Read the worked answer
The garage is fed from a TN-S system, so the supply neutral and earth are separate at the origin. The garage consumer unit must have a main switch and the earthing conductor from the house must be sized according to the supply neutral conductor (typically 16 mm² for TN-S). The SWA cable's armour can be used as the CPC if it meets the adiabatic requirement, but for a 4 mm² cable the armour is often adequate; however, a separate CPC is preferable for a garage supply.
Bonding: the garage has metal parts (metal consumer unit, possibly water pipes if present). Main protective bonding is required for extraneous conductive parts at the garage, sized 10 mm² if the supply is TN-S and the earthing conductor is 16 mm². If there are no metallic services, bonding may not be required. The metal consumer unit must be earthed.
Because it is TN-S, the earth fault loop impedance is low enough for MCB operation, so no RCD is strictly required for the garage supply, but a 30 mA RCD is recommended for socket outlets and for protection against direct contact. The SWA armour must be earthed at the supply end.