Question

A uniform illumination of 150 lux is to be obtained on the floor of a room measuring 15m x 15m by arranging electric lights suitably. Calculate the number of lamps and wattage of each lamp if lamp efficiency is 20 lumens/watt. Assume and write suitable values of constants required for this calculation.

Answer 1

To determine the number of lamps and the wattage of each lamp needed to achieve a uniform illumination of 150 lux in a room measuring 15 meters by 15 meters, we can follow these steps:

### Step 1: Calculate the Total Illuminance Required

1. **Calculate the Area of the Room:**
   \[
   \text{Area} = \text{Length} \times \text{Width} = 15\, \text{m} \times 15\, \text{m} = 225\, \text{m}^2
   \]

2. **Calculate the Total Luminous Flux Required:**
   \[
   \text{Total Illuminance (Lux)} = 150\, \text{lux}
   \]
   \[
   \text{Total Luminous Flux (Lumens)} = \text{Total Illuminance (Lux)} \times \text{Area (m}^2\text{)}
   \]
   \[
   \text{Total Luminous Flux} = 150\, \text{lux} \times 225\, \text{m}^2 = 33,750\, \text{lumens}
   \]

### Step 2: Calculate the Required Wattage of Lamps

3. **Determine Lamp Efficiency:**
   - Given lamp efficiency is 20 lumens per watt.

4. **Calculate Total Watts Needed:**
   \[
   \text{Total Watts} = \frac{\text{Total Luminous Flux}}{\text{Lamp Efficiency}} = \frac{33,750\, \text{lumens}}{20\, \text{lumens/watt}} = 1,687.5\, \text{watts}
   \]

### Step 3: Determine the Number of Lamps

5. **Choose Wattage of Each Lamp:**
   - Let’s assume we will use 100-watt lamps (a common choice for brightness).
   \[
   \text{Luminous Output of a 100-watt lamp} = 100\, \text{watts} \times 20\, \text{lumens/watt} = 2,000\, \text{lumens}
   \]

6. **Calculate the Number of Lamps Needed:**
   \[
   \text{Number of Lamps} = \frac{\text{Total Luminous Flux}}{\text{Luminous Output per Lamp}} = \frac{33,750\, \text{lumens}}{2,000\, \text{lumens/lamp}} = 16.875
   \]
   Since the number of lamps must be a whole number, round up to 17 lamps.

### Summary of Results

- **Total Luminous Flux Required:** 33,750 lumens
- **Total Power Required:** 1,687.5 watts
- **Lamp Wattage Used:** 100 watts per lamp
- **Number of Lamps Required:** 17 lamps

### Conclusion

To achieve a uniform illumination of 150 lux in a room measuring 15m x 15m, you would need **17 lamps of 100 watts each**, given that each lamp produces 2,000 lumens at an efficiency of 20 lumens per watt. This arrangement ensures that the total illumination meets the required standard for the space.

Answer 2

To calculate the number of lamps and the wattage of each lamp required to achieve a uniform illumination of 150 Lux on a room floor, you can follow these steps:

### Given Data:
- Illumination level (\( E \)) = 150 Lux
- Room dimensions = 15 m × 15 m
- Lamp efficiency = 20 Lumens/Watt

### Constants:
- Area of the room (\( A \)) = 15 m × 15 m = 225 m²
- Illuminance (\( E \)) is defined as:
  \[ E = \frac{\text{Total Luminous Flux (Φ)}}{\text{Area (A)}} \]
  Therefore:
  \[ \text{Total Luminous Flux (Φ)} = E \times A \]

### Steps:

1. **Calculate the Total Luminous Flux Required:**

   \[ \text{Total Luminous Flux (Φ)} = 150 \, \text{Lux} \times 225 \, \text{m}^2 \]
   \[ \text{Total Luminous Flux (Φ)} = 33750 \, \text{Lumens} \]

2. **Determine the Wattage of Each Lamp:**

   The luminous flux provided by a lamp is given by:
   \[ \text{Luminous Flux per Lamp} = \text{Lamp Efficiency} \times \text{Wattage} \]

   Rearranging to find the Wattage:
   \[ \text{Wattage} = \frac{\text{Luminous Flux per Lamp}}{\text{Lamp Efficiency}} \]
   \[ \text{Luminous Flux per Lamp} = 20 \times \text{Wattage} \]
   \[ \text{Wattage} = \frac{\text{Luminous Flux per Lamp}}{20} \]

3. **Calculate the Number of Lamps:**

   Total luminous flux required by all lamps:
   \[ \text{Number of Lamps} \times \text{Luminous Flux per Lamp} = \text{Total Luminous Flux} \]
   \[ \text{Number of Lamps} \times (20 \times \text{Wattage}) = 33750 \, \text{Lumens} \]
   \[ \text{Number of Lamps} = \frac{33750}{20 \times \text{Wattage}} \]

4. **Select a Practical Wattage and Compute:**

   Let's choose a practical wattage value for calculation. For instance, if each lamp is 60 Watts:
   \[ \text{Luminous Flux per Lamp} = 20 \times 60 = 1200 \, \text{Lumens} \]
   \[ \text{Number of Lamps} = \frac{33750}{1200} \approx 28.125 \]

   Since you can't have a fraction of a lamp, round up to the nearest whole number:
   \[ \text{Number of Lamps} = 29 \]

### Summary:

- **Number of Lamps:** 29
- **Wattage of Each Lamp:** 60 Watts

These values are based on a lamp efficiency of 20 Lumens/Watt and will provide a uniform illumination of 150 Lux in the room.