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- 2078 Chaitra · 8 marks
Cable and MCB size for two motors
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%.
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 |
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).
I = P / (√3 × V_L × pf)
Motor (a): 5 kW, pf 0.8
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
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
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)
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.
✓ Answer checked by Claude Opus 5.5 (high effort)
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