Ranking Lamps by Power and Energy Consumption

The question asks to arrange lamps based on increasing power rating and energy consumption required to produce the same level of illumination. For a constant illumination level, the power consumed by a lamp is inversely proportional to its efficacy (efficiency in converting electrical energy to light).

Efficacy is measured in lumens per watt (lm/W).

Lamp Efficacies Provided

• A. Incandescent Lamp: 10 lm/W
• B. Compact fluorescent lamp (CFL): 60 lm/W
• C. Halogen lamp: 20 lm/W
• D. Mercury vapour lamp: 40 lm/W
• E. Light Emitting diode (LED) lamp: 80 lm/W

Relationship Between Efficacy and Power Consumption

To achieve the same amount of light (luminous flux, $\Phi$), the power ($P$) required is calculated as:

$ P = \frac{\Phi}{\eta} $

where $\eta$ is the efficacy.

This formula shows that as efficacy ($\eta$) increases, the required power ($P$) decreases. Conversely, lower efficacy means higher power consumption for the same illumination.

Therefore, arranging lamps by increasing power consumption is equivalent to arranging them by decreasing efficacy.

Ordering Lamps by Decreasing Efficacy

The efficacies are:

• E (LED): 80 lm/W
• B (CFL): 60 lm/W
• D (Mercury vapour): 40 lm/W
• C (Halogen): 20 lm/W
• A (Incandescent): 10 lm/W

Arranging these from highest efficacy to lowest efficacy gives the order: E, B, D, C, A.

Conclusion

This order (E, B, D, C, A) represents the lamps from the most energy-efficient (highest efficacy) to the least energy-efficient (lowest efficacy). Consequently, it represents the order of increasing power rating and energy consumption for providing the same illumination level.