GCSE Physics

New Technology: LED Bulb Payback Time Answers

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Phew - some of that was hard! Check your answers below.

Data for 8 LampsHalogenDimmable LED
Power (W)40042
Power (kW)0.400.042
Daily Use (h)22
Daily Energy Use (kWh)0.800.084
Annual Energy Use (kWh)29230.7
Annual Energy Cost ()40.884.30

  1. What is the cost of 8 LED lamps for the kitchen example above?
    At £16 each, this is an easy calculation: 8 × 16 = £128.
  2. How much money is saved per year if they're used for 2 hours a day on average
    8 halogen lamps cost £40.88 to run for 2 hours a day over a year. The LEDs cost £4.30 so the saving is £40.88 - £4.30 = £36.58
  3. Calculate the payback time, in years, for buying 8 lamps, used for 2 hours a day.
    The energy saved each year saves us £36.58, but we spent £128 on the new LED lamps. The time to make this money back (payback time), is the total spent divided by the annual saving:
    128 ÷ 36.58 = 3.5 years.
  4. Totalight's website suggests an LED lamp "pays for itself in 18 months". How many hours would the kitchen LED lamps have to be used for a payback time of 18 months?
    This is much harder than a GCSE question! We need to save £128 in 18 months, which would mean saving £85.33 in a year.
    At 14p for a kWh, this would be an annual energy saving of 609.5 kWh. Or 1.67 kWh per day.
    The best way forward is to look at the power saving in kW for the 8 LEDs from the 8 halogens, which is 0.4-0.042 = 0.358 kW.
    Now using Energy = Power × Time we can find the time:

    1.67 kWh = 0.358 kW × time
    time = 1.67 / 0.358 = 4.66 hours.

    So, the lamps would have to be on for 4 hours 40 minutes each day on average in order to pay for themselves in 18 months.

    [Editor's Note: since this question was written, the price of the lamps has fallen, so the payback time will be shorter, or the time they'd need to be used for, less!]

  5. Explain whether or not a payback time of less than 18 months would be achievable in a school or office using LEDs instead of halogens.
    A payback time of less than 18 months would easily be achieved in an office or school as lights would be typically turned on for much longer than 5 hours a day on average, even taking into account weekends and holidays.

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