LED Bulbs. LED bulbs are much more efficient at producing...

LED Bulbs. LED bulbs are much more efficient at producing light than are traditional incandescent bulbs. They initially cost much more, but they last far longer and use much less electricity. An LED bulb that produces as much light as a $100 \mathrm{~W}$ incandescent bulb uses only $12.5 \mathrm{~W}$ of power. The LED bulb lasts 15,000 hours, on the average, and costs $£ 8.00$, whereas the cost of an incandescent bulb was only $£ 0.80$, but it lasted just 750 hours. Assuming that electricity costs $£ 0.125$ per kilowatt-hour and that the bulbs are on for $4.0 \mathrm{~h}$ per day, (a) compare the total cost (including the price of the bulbs) of running each bulb for 3.0 years. (b) How much do you save over 3.0 years if you use an LED bulb instead of an incandescent bulb? (c) What is the resistance of a "100 W" LED bulb? (Remember, it actually uses only $12.5 \mathrm{~W}$ of power and operates across $230 \mathrm{~V}$.)

LED Bulbs. LED bulbs are much more efficient at producing light than are traditional incandescent bulbs. They initially cost much more, but they last far longer and use much less electricity. An LED bulb that produces as much light as a $100 \mathrm{~W}$ incandescent bulb uses only $12.5 \mathrm{~W}$ of power. The LED bulb lasts 15,000 hours, on the average, and costs $£ 8.00$, whereas the cost of an incandescent bulb was only $£ 0.80$, but it lasted just 750 hours. Assuming that electricity costs $£ 0.125$ per kilowatt-hour and that the bulbs are on for $4.0 \mathrm{~h}$ per day,
(a) compare the total cost (including the price of the bulbs) of running each bulb for 3.0 years. (b) How much do you save over 3.0 years if you use an LED bulb instead of an incandescent bulb? (c) What is the resistance of a "100 W" LED bulb? (Remember, it actually uses only $12.5 \mathrm{~W}$ of power and operates across $230 \mathrm{~V}$.)

Key Concepts

Electrical Resistance and Power Relations

This concept involves applying electrical formulas, such as Ohm’s Law and the power equation, to relate voltage, current, resistance, and power consumption. It is essential for determining characteristics like resistance in devices when the operating voltage and power are known.

LED Lighting Efficiency

This concept involves understanding how LEDs convert electrical power into light more efficiently than traditional incandescent bulbs. It includes recognizing that LEDs use significantly less energy to produce the same amount of light and typically generate less heat, leading to energy savings and lower operational costs over time.

Cost Analysis in Lighting

This involves evaluating both the initial purchase price and the long-term operating costs of lighting solutions. It includes analyzing factors such as energy consumption, bulb lifespan, and replacement frequency to determine the total cost of ownership over a specified period.

Energy Consumption Calculation

This concept requires calculating the amount of energy used by an electrical device based on its power rating and operating time. It typically involves converting power usage (in watts) and time (in hours) into energy units (kilowatt-hours) and using the cost per kilowatt-hour to assess total energy expenses.

Bulb Lifespan and Replacement Frequency

This pertains to understanding the expected operational duration of lighting devices and how often they need to be replaced. A longer lifespan means fewer replacements, which can offset higher upfront costs and reduce maintenance and replacement expenses.

Transcript

00:01 All right, so we're told that the led uses 12 .5 watts of power and can last 15 ,000 hours, and then each led bulb costs 8 pounds.

00:12 We're also told that the incandescent bulb takes 100 watts of power, and only lasts 750 hours, and it costs 0 .8 pounds per bulb.

00:24 So the first part, letter a, we are going to be looking at a three, year running cost for each bulb and comparing them.

00:35 So first thing we need to figure out is how many hours is that? so it's three years times 365 days per year, and then multiply that by four hours for every day, and we get 4 ,380 hours of runtime.

00:59 So if we look at the led from there, we're only going to need one led because, or one led bulb, because it can run for 15 ,000 hours, which is more than this.

01:16 So it's going to be able to run that whole time.

01:20 And so let's look at how many watts we would be using there.

01:25 So we have 12 .5 watts for every hour times 4 ,380 hours.

01:34 And we'll get 54 ,750 watt hours, which is the same as 54 .75 kilowatt hours.

01:49 Now we're also told that the cost of running, the cost of the electricity is 0 .125 pounds per kilowatt hour.

01:58 And so the total cost of running the led will be 0 .125 pounds, times 54 .75 kilowatt hours plus eight pounds for the actual cost of the bulb.

02:15 So that total will be 14 .84 pounds for the led.

02:29 Now let's look at the incandescent bulb.

02:32 So for the incandescent bulb that's going to be running for the same amount of hours.

02:36 However, it will run out with we'll need to get more bulbs.

02:41 So the first thing we need to figure out, how many bulbs will we need? so 4 ,380 hours, divide that by 750 hours per bulb, and we get 5 .84, which means we need six total bulbs.

02:57 So that'll come in later...

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