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Ch 28: Fundamentals of Circuits
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 28: Fundamentals of CircuitsProblem 39
Chapter 28, Problem 39

It seems hard to justify spending \$5.00 for an LED lightbulb when an ordinary incandescent bulb costs 50¢. To see if this makes sense, compare a 60 W incandescent bulb that lasts 1000 hours to a 10 W LED bulb that has a lifetime of 15,000 hours. Both bulbs produce the same amount of visible light. If electricity costs \$0.15/kWh, what is the total cost—purchase price plus energy—to get 15,000 hours of light from each type of bulb? This is called the life-cycle cost.

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Step 1: Calculate the total energy consumption for each type of bulb over 15,000 hours. For the incandescent bulb, use the formula \( E = P \times t \), where \( P \) is the power in watts and \( t \) is the time in hours. Convert the result to kilowatt-hours (kWh) by dividing by 1000. Repeat the same calculation for the LED bulb.
Step 2: Determine the energy cost for each bulb by multiplying the total energy consumption (in kWh) by the cost of electricity, \( \$0.15/\text{kWh} \). This gives the total energy cost for each bulb over 15,000 hours.
Step 3: Calculate the number of incandescent bulbs needed to last 15,000 hours. Since each incandescent bulb lasts 1,000 hours, divide 15,000 by 1,000 to find the total number of bulbs required. For the LED bulb, only one bulb is needed since it lasts 15,000 hours.
Step 4: Compute the total purchase cost for each type of bulb. For the incandescent bulb, multiply the number of bulbs needed by the cost of one bulb (\$0.50). For the LED bulb, the purchase cost is simply \$5.00 since only one bulb is required.
Step 5: Add the energy cost and the purchase cost for each type of bulb to find the total life-cycle cost. Compare the results to determine which bulb is more cost-effective over 15,000 hours.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Life-Cycle Cost

Life-cycle cost refers to the total cost of owning and operating a product over its entire lifespan. In this context, it includes both the initial purchase price of the lightbulb and the ongoing costs associated with energy consumption. By calculating the life-cycle cost, one can make informed decisions about which product is more economical in the long run.
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Energy Consumption

Energy consumption is the amount of electrical energy used by a device over time, typically measured in watts (W) or kilowatt-hours (kWh). For the bulbs in question, the incandescent bulb consumes 60 W, while the LED bulb consumes only 10 W. Understanding energy consumption is crucial for calculating the operational costs associated with each bulb over its lifetime.
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Cost of Electricity

The cost of electricity is the price paid for electrical energy, usually expressed in terms of dollars per kilowatt-hour (kWh). In this scenario, the electricity cost is $0.15/kWh. This rate is essential for calculating the total energy cost incurred by each type of bulb during its operational life, allowing for a comprehensive comparison of their life-cycle costs.
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