Compact Fluorescent Bulbs. Compact fluorescent bulbs are...

Compact Fluorescent Bulbs. Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They initially cost much more, but they last far longer and use much less electricity. According to one study of these bulbs, a compact bulb that produces as much light as a $100 \mathrm{~W}$ incandescent bulb uses only $23 \mathrm{~W}$ of power. The compact bulb lasts 10,000 hours, on the average, and costs $\$ 11.00,$ whereas the incandescent bulb costs only $\$ 0.75$, but lasts just 750 hours. The study assumed that electricity costs $\$ 0.080$ per kilowatt-hour and that the bulbs are on for $4.0 \mathrm{~h}$ per day. (a) What is the total cost (including the price of the bulbs) to run each bulb for 3.0 years? (b) How much do you save over 3.0 years if you use a compact fluorescent bulb instead of an incandescent bulb? (c) What is the resistance of a "100 W" fluorescent bulb? (Remember, it actually uses only $23 \mathrm{~W}$ of power and operates across $120 \mathrm{~V} .$ )

Key Concepts

Energy Efficiency

This concept involves comparing how effectively devices convert energy into a desired output, such as light. In the context of bulbs, energy efficiency is illustrated by comparing the amount of electrical power consumed by a light source to the luminescence produced, with more efficient bulbs producing the same light output at lower power consumption.

Life Cycle Cost Analysis

Life cycle cost analysis evaluates the total cost of using an appliance over its entire life, including initial purchase price, replacement costs, energy consumption, and operating expenses. In the case of light bulbs, this analysis compares the higher upfront cost but longer lifespan and lower electricity usage of compact fluorescent bulbs against the lower upfront cost but higher replacement frequency and greater energy consumption of incandescent bulbs.

Power Consumption and Wattage

Wattage indicates the rate at which a device uses electrical energy. In lighting, a bulb’s wattage helps to determine its energy use over time. Understanding the difference between the rated wattage and actual power consumption, as seen in the comparison between a 100 W incandescent bulb and a compact fluorescent operating at 23 W for equivalent light output, is essential for analyzing energy efficiency and operating costs.

Electrical Energy Consumption Calculation

This concept involves computing the energy used by an appliance over a period, typically measured in kilowatt-hours (kWh). It encompasses translating the device's wattage into energy consumption based on the duration of use and then using the electricity cost per kWh to determine the operating cost. This calculation is a fundamental tool in cost comparisons and energy budgeting.

Electrical Resistance Calculation

Electrical resistance relates the voltage across a device to the current flowing through it and is utilized to calculate power consumption using formulas such as P = V^2/R. In scenarios where a device’s power rating is given, such as a bulb operating at a specific wattage and voltage, the resistance can be deduced to understand its electrical properties and behavior.

Transcript

00:02 Hi, here in the given problem, we made two columns to compare the cost of running two bulbs.

00:13 The first column is for compact bulb and the second column is for incandescent bulb.

00:31 First of all, the cost of this compact bulb is $11 .00.

00:41 And the cost of this incandescent bulb is just $0 .75.

00:47 The power consumed by a compact bulb is just 23 watt.

00:56 And the power consumed by incandescent bulb is 100 watt.

01:03 Then as these bulbs, both of the bulbs are used for four hours a day, hence energy consumed by both the bulbs in three years will be, cost of all, this 23 watt should be converted into kilowatt by dividing it by 1 ,000.

01:27 So this is 23 by 1 ,000 kilowatt into to find the total duration in hours.

01:35 This is 365 days in one year.

01:40 Then these are three years.

01:42 And four hours per day.

01:48 So it comes out to be 100 .74 kilowatt hour.

01:58 Similarly here for incandescent, the power in kilowatt, then the duration is same.

02:09 365 days into three years into four hours per day.

02:14 And it comes out to be 438 kilowatt hour.

02:22 Now, the rate of power consumption is given as $0 .080 per kilowatt hour.

02:36 So using that, the total cost of running these two bulbs finally comes out to be 4 .4 .4 .4...