---
title: "Cable and MCB size for two motors"
subject: "Industrial Power Distribution and Illumination"
chapter: 5
key: "semester_6/industrial_power_distribution_and_illumination:motor-cable-mcb-pf"
source: https://www.bctengineer.com/q/semester_6/industrial_power_distribution_and_illumination/motor-cable-mcb-pf
site: BCT Engineering
---

# Cable and MCB size for two motors

Industrial Power Distribution and Illumination · Chapter 5: Electrification of Industrial Building

- Asked in: 2078 Chaitra, 8 marks
- Video: [CABLE SIZE SELECTION FOR RUN MOTOR](https://www.youtube.com/watch?v=wktkMA_WhMQ) — SN TECHNICAL
- 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-pf
- Whole chapter: https://www.bctengineer.com/md/semester_6/industrial_power_distribution_and_illumination/chapter-5

## Question

An industrial building has the following loads.
a) 5kW, 415V, 3-phase motor, pf = 0.8
b) 10kW, 415V, 3-phase motor, pf = 0.85
Determine the size of the cable from MDB to SDB and SDB to the individual motor if the length of the 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 (pf 0.8): 16 A MCB, 1.5 mm² cable. 10 kW motor (pf 0.85): 32 A MCB, 4 mm² cable. MDB-SDB: 40 A MCB (for discrimination), 6 mm² cable. Total current 25.06 A, drop <0.3%.

## Answer

Efficiency is not given, so the 5 kW and 10 kW ratings are taken as the electrical input power of the motors (η = 1). MCBs are chosen with a 1.25 safety factor on full-load current, and cables so that their rating is not less than the MCB rating (Ib ≤ In ≤ Iz).

```text
I = P / (√3 × V_L × pf)
```

#### Motor (a): 5 kW, pf 0.8
```text
Ia = 5000 / (√3 × 415 × 0.8) = 8.70 A
1.25 × 8.70 = 10.87 A → MCB 16 A
Cable rating ≥ 16 A → 1.5 mm² (21 A)
```

#### Motor (b): 10 kW, pf 0.85
```text
Ib = 10000 / (√3 × 415 × 0.85) = 16.37 A
1.25 × 16.37 = 20.46 A → MCB 32 A
Cable rating ≥ 32 A → 4 mm² (36 A)
```

#### MDB to SDB
```text
I = 8.70 + 16.37 = 25.06 A
1.25 × 25.06 = 31.33 A → 32 A would be enough,
but for discrimination with the 32 A motor MCB
the next size is taken → MCB 40 A
Cable rating ≥ 40 A → 6 mm² (45 A)
```

#### Voltage drop check (10 m, Cu, ρ = 0.0178 Ω·mm²/m)
```text
ΔV = √3 × I × ρ × L × cosφ / A
Motor (a): √3 × 8.70 × 0.0178 × 10 × 0.8 / 1.5
         = 1.43 V (0.34 %)
Motor (b): √3 × 16.37 × 0.0178 × 10 × 0.85 / 4
         = 1.07 V (0.26 %)
MDB–SDB : about 1.1 V (0.26 %)
```
All are far below 2.5 %, so the current rating governs.

**Answer**
| Circuit | Current (A) | MCB | Cable |
|---|---|---|---|
| SDB to motor (a) | 8.70 | 16 A | 1.5 mm² |
| SDB to motor (b) | 16.37 | 32 A | 4 mm² |
| MDB to SDB | 25.06 | 40 A | 6 mm² |

If the 5 kW and 10 kW are output ratings, the currents rise by the efficiency factor; with a typical η of about 0.85 the same MCB and cable sizes still apply.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Efficiency is not given. How are the 5 kW and 10 kW ratings treated?
   A. As electrical input power (η = 1)
   B. As output with η = 0.5
   C. As apparent power in kVA
   D. As power at unity pf
   Answer: A. The answer takes the ratings as input power, so I = P/(√3 V pf). (Key point: Assumption)

2. What are the current and MCB for the 5 kW, pf 0.8 motor at 415 V?
   A. 10.87 A, MCB 10 A
   B. 8.70 A, 1.25 x 8.70 = 10.87 A, MCB 16 A
   C. 8.70 A, MCB 6 A
   D. 6.02 A, MCB 10 A
   Answer: B. I = 5000/(√3 x 415 x 0.8) = 8.70 A; with 1.25 factor 10.87 A, next standard size is 16 A. (Key point: Motor (a))

3. I = 25.06 A gives 31.33 A with the 1.25 factor. Why is 40 A taken, not 32 A?
   A. 32 A is not a standard size
   B. 32 A would overload the 6 mm² cable
   C. For discrimination with the 32 A motor MCB, the upstream device must be larger
   D. 40 A is needed for voltage drop
   Answer: C. The upstream MCB must be bigger than the downstream 32 A MCB to discriminate, so 40 A is used, with 6 mm² (45 A). (Key point: MDB to SDB MCB)

4. What does the voltage drop check show?
   A. Motor (a) cable fails the drop limit
   B. Drops are 0.26-0.34 %, far below 2.5 %, so current rating governs
   C. The MDB-SDB cable needs 10 mm²
   D. Drop can be ignored for all lengths
   Answer: B. The 10 m runs have tiny drops, so sizes follow the current rating. (Key point: Voltage drop check)

## Close variants set in other exams

- [Cable and MCB size for two motors (η = pf)](https://www.bctengineer.com/question.md?key=semester_6%2Findustrial_power_distribution_and_illumination%3Amotor-cable-mcb-efficiency) — 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