--- title: "Cable and MCB size for two motors (η = pf)" subject: "Industrial Power Distribution and Illumination" chapter: 5 key: "semester_6/industrial_power_distribution_and_illumination:motor-cable-mcb-efficiency" source: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/motor-cable-mcb-efficiency site: BCT Engineering --- # Cable and MCB size for two motors (η = pf) Industrial Power Distribution and Illumination · Chapter 5: Electrification of Industrial Building - Asked in: 2080 Chaitra, 8 marks - Video: [How To Select Right MCB and Over Load Relay Size For Motor @TheElectricalGuy](https://www.youtube.com/watch?v=DWUuKNjMf3E) — The Electrical Guy - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/motor-cable-mcb-efficiency - Whole chapter: https://www.bctengineer.com/md/semester_6/industrial_power_distribution_and_illumination/chapter-5 ## Question An industrial building has the following loads. i) 5kW, 415V, 3-phase motor, η = pf = 0.8 ii) 10kW, 415V, 3-phase motor, η = pf = 0.85 Determine the size of the cable from MDB to SDB and SDB to the individual motor if the length of each cable is 10m and MCB size. Standard MCB size available are 6A, 10A, 16A, 32A and 40A. | Conductor Area (mm²) | 1.5 | 2.5 | 4 | 6 | 10 | |---|---|---|---|---|---| | 3.5C XLPE Cu Cable Current ratings (A) | 21 | 27 | 36 | 45 | 60 | ## Short answer 5 kW motor: 16 A MCB, 1.5 mm² cable. 10 kW motor: 32 A MCB, 4 mm² cable. MDB-SDB: 40 A MCB, 6 mm² cable. All voltage drops are negligible (<0.5%); sizes chosen by current rating. ## Answer Here 5 kW and 10 kW are motor **output** ratings, so input power = output / η. A safety factor of 1.25 on full-load current is used for MCB selection, and the cable is chosen so that its rating is not less than the MCB rating (Ib ≤ In ≤ Iz). ```text Input power P_in = P_out / η Line current I = P_in / (√3 × V × pf) ``` #### Motor (i): 5 kW, η = pf = 0.8 ```text P_in = 5000 / 0.8 = 6250 W I1 = 6250 / (√3 × 415 × 0.8) = 10.87 A 1.25 × I1 = 13.59 A → MCB 16 A Cable: rating ≥ 16 A → 1.5 mm² (21 A) ``` #### Motor (ii): 10 kW, η = pf = 0.85 ```text P_in = 10000 / 0.85 = 11764.71 W I2 = 11764.71 / (√3 × 415 × 0.85) = 19.26 A 1.25 × I2 = 24.07 A → MCB 32 A Cable: rating ≥ 32 A → 4 mm² (36 A) ``` #### MDB to SDB ```text I_total = I1 + I2 = 10.87 + 19.26 = 30.12 A 1.25 × 30.12 = 37.66 A → MCB 40 A Cable: rating ≥ 40 A → 6 mm² (45 A) ``` (Arithmetic sum of currents is taken, which is slightly conservative since the power factors differ.) #### Voltage drop check (10 m, ρ = 0.0178 Ω·mm²/m) | Run | I (A) | Cable | ΔV (V) | ΔV % | |---|---|---|---|---| | SDB–motor (i) | 10.87 | 1.5 mm² | 1.79 | 0.43 | | SDB–motor (ii) | 19.26 | 4 mm² | 1.26 | 0.30 | | MDB–SDB | 30.12 | 6 mm² | 1.29 | 0.31 | All drops are well below 2.5 %, so the current rating decides the size. **Answer** | Circuit | MCB | Cable (3.5C XLPE Cu) | |---|---|---| | SDB to 5 kW motor | 16 A TP | 1.5 mm² | | SDB to 10 kW motor | 32 A TP | 4 mm² | | MDB to SDB | 40 A TP | 6 mm² | Use D-curve (motor) MCBs so that starting current does not cause nuisance tripping; overload protection of the motor is given by a thermal overload relay in the starter. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The 5 kW rating is output power with η = 0.8. What is the electrical input? A. 5000 x 0.8 = 4000 W B. 6250 W (output / η) C. 5000 W D. 5000 / 0.64 W Answer: B. Input = output/η = 5000/0.8 = 6250 W. (Key point: Input power) 2. With I1 = 10.87 A, how are the MCB and cable chosen? A. 1.25 x 10.87 = 13.59 A, so 16 A MCB and 1.5 mm² (21 A) B. 10.87 A, so 10 A MCB and 1.5 mm² C. 13.59 A, so 10 A MCB and 2.5 mm² D. 1.25 x 10.87, so 16 A MCB and 4 mm² Answer: A. Next standard MCB above 13.59 A is 16 A; 1.5 mm² (21 A) is at least 16 A. (Key point: Motor (i) selection) 3. Total current is 10.87 + 19.26 = 30.12 A. What MCB and cable are chosen? A. 32 A MCB and 4 mm² B. 40 A MCB and 6 mm² (45 A) C. 40 A MCB and 4 mm² (36 A) D. 30 A MCB and 10 mm² Answer: B. 1.25 x 30.12 = 37.66 A gives 40 A MCB; the cable rating must be at least 40 A, so 6 mm² (45 A). (Key point: MDB to SDB) 4. Why does current rating decide the cable size here? A. Short length (10 m) makes voltage drops far below 2.5 % B. Voltage drop is not relevant to motors C. The cables are armoured D. The MCBs are D curve Answer: A. Drops of 0.3-0.4 % are far below the limit, so the current rating controls. (Key point: Governing factor) ## Close variants set in other exams - [Cable and MCB size for two motors](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Amotor-cable-mcb-pf) — Industrial Power Distribution and Illumination, chapter 5, asked 2× ## Related in Industrial Power Distribution and Illumination - [Cable size MDB to SDB-1 (60 kW) and SDB-2 (75 kW)](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Acable-mdb-sdb-60kw-75kw) — Industrial Power Distribution and Illumination, chapter 5, asked 4× - [Selecting MCCB and MCB for MDB and SDB](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Amccb-mcb-selection-mdb-sdb) — Industrial Power Distribution and Illumination, chapter 5 - [Single-phase Cu cable for three loads](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Asingle-phase-cable-three-loads) — Industrial Power Distribution and Illumination, chapter 5 - [Cable size MDB to SDB1 (80 kW) and SDB2 (10 kW)](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Acable-mdb-sdb-80kw-10kw) — Industrial Power Distribution and Illumination, chapter 5, asked 5× - [Cable size MDB to SDB1 (70 kW) and SDB2 (90 kW)](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Acable-mdb-sdb-70kw-90kw) — Industrial Power Distribution and Illumination, chapter 5, asked 5×