In the lumen method, which expression gives the number of luminaires N?

N = E x A / (lumens per luminaire x UF x MF)

N = E x A x UF x MF / lumens per luminaire

N = E x A x MF / (lumens per luminaire x UF)

N = A / (E x UF x MF x lumens per luminaire)

The calculation gives N = 37.2. Why does the answer use a 10 x 4 = 40 grid?

It is the nearest regular grid not below 37.2 that keeps spacing within the limit

The number is rounded down to 36 to save cost

40 is always used for rooms of 600 m^2

Because the supply is 3-phase, N must be a multiple of 10

How is the incomer MCB rating chosen for the most loaded phase (504 W)?

Iph = 504/(230 x 0.9) = 2.43 A, then 1.25 x Iph rounded up to 6 A

Iph = 504/400 = 1.26 A, then a 2 A MCB

Iph = 1440/230 = 6.26 A, then a 6 A MCB

Iph = 504 x 230 x 0.9, then a 25 A MCB

2070 Bhadra · 8 marks

Room 40 × 15 m, 75 lux FTL design

Short answer

By lumen method, required luminaires N = 75×600/(2160×0.8×0.7)=37.2, rounded to 40 single 36 W FTL, arranged 10×4. Spacing 4 m×3.75 m within 6 m limit, actual illuminance 80.6 lux.

An illumination on the working plane of 75 lux is required in a room 40m × 15m in size. The luminaries are required to be hung 4m above the work bench. Assuming a suitable space height ratio, a utilization factor of 0.8, a lamp efficiency of 60 lumen per watt and maintenance factor is 0.7. Estimate the number and disposition of lamp and switches. Design the sub-circuits, distribution board if supply system is 3 phase 4 wire system and consider 1 × 36 watt FTL with electronic ballast.

Given: room 40 m × 15 m, E = 75 lux, Hm = 4 m, UF = 0.8, MF = 0.7, 1 × 36 W FTL with electronic ballast at 60 lm/W, 3-phase 4-wire supply. Assumptions: suitable space–height ratio 1.5 → maximum spacing 1.5 × 4 = 6 m; pf 0.9 with electronic ballast, ballast loss neglected.

Number of luminaires

Lumen method: N = (E × A) / (φ × UF × MF), where φ is the output of one luminaire.

Area A        = 40 × 15 = 600 m²
φ per luminaire = 36 W × 60 lm/W = 2160 lm
Total lumens  = E × A / (UF × MF)
              = 75 × 600 / (0.8 × 0.7)
              = 80357 lm
N             = 80357 / 2160 = 37.2

Rounding up and fitting a regular grid: 10 × 4 = 40 luminaires (10 along the 40 m side, 4 along the 15 m side).

Arrangement and spacing

Spacing along length = 40/10 = 4 m
Spacing along width  = 15/4 = 3.75 m
End spacing (to wall) = half of these
Max spacing = SHR × Hm = 1.5 × 4 = 6 m
4 m and 3.75 m ≤ 6 m  → OK
Actual E = 40 × 2160 × 0.8 × 0.7 / 600
         = 80.6 lux (≥ 75 lux required)

Layout diagram

Plan 40 m × 15 m (letter = phase of lamp circuit)
+---------------------+
| R R R R R R R Y Y Y |
| B B B B B B Y Y Y Y |
| B R R R R R R R Y Y |
| B B B B B B Y Y Y Y |
+---------------------+
[DB]  [SB]  <- entrance: DB and switch board
       S S S S ... one switch per sub-circuit

Each light sub-circuit is controlled by one 6 A one-way switch; all switches are grouped on a switch board (SB) next to the entrance, and the DB is mounted beside it.

Sub-circuits

Rule (IS 732 / NEA practice): a light sub-circuit carries at most 10 points and 800 W. Here one luminaire is 36 W, so up to 10 luminaires per sub-circuit. Number of circuits is made a multiple of 3 for phase balance.

Circuit	Luminaires	Load (W)	Current (A)	Phase	MCB
L1	7	252	1.22	R	6 A
L2	7	252	1.22	Y	6 A
L3	7	252	1.22	B	6 A
L4	7	252	1.22	R	6 A
L5	6	216	1.04	Y	6 A
L6	6	216	1.04	B	6 A

Distribution board design

Phase	Circuits	Load (W)	Current (A)
R	L1, L4	504	2.43
Y	L2, L5	468	2.26
B	L3, L6	468	2.26

Total connected load = 1440 W (lighting)
Most loaded phase    = 504 W
Iph = 504 / (230 × 0.9) = 2.43 A
Main MCB ≥ 1.25 × 2.43 = 3.04 A → 6 A TPN MCB

DB specification: 4-way-per-phase TPN DB (12 ways in all, spares included) with 6 A TPN MCB as incomer, 25 A 4-pole RCCB (100 mA) for earth-leakage protection, 6 A SP MCBs (B-curve) for light circuits. Incoming cable: 4-core 1.5 mm² Cu PVC (rating 21 A ≥ 6 A), plus earth continuity conductor.

3-phase, 400/230 V, 4-wire supply
        |
   [Energy meter]
        |
   [6 A TPN MCB]
        |
   [25 A 4P RCCB]
        |
==R====Y====B====N== busbars
  |    |    |    |    |
  L1   L2   L3   L4   L5  ...

✓ Answer checked by Claude Opus 5.5 (high effort)

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