- Asked 2/20
- 2080 Chaitra · 8 marks
Cable and MCB size for two motors (η = pf)
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.
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 |
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).
Input power P_in = P_out / η
Line current I = P_in / (√3 × V × pf)
Motor (i): 5 kW, η = pf = 0.8
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
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
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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