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Ch. 25 - Electric Current and Resistance
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 25 - Electric Current and ResistanceProblem 37
Chapter 24, Problem 37

At \$0.12/kWh, what does it cost to leave a 25-W porch light on day and night for a year?

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Determine the total energy consumed by the porch light in one year. Start by calculating the power usage in kilowatts: \( P = \frac{25}{1000} \, \text{kW} \).
Calculate the total time the light is on in one year. Since the light is on day and night, the total time is \( t = 365 \times 24 \, \text{hours} \).
Find the total energy consumed by multiplying the power by the time: \( E = P \times t \).
Determine the cost of the energy consumed by multiplying the total energy \( E \) by the cost per kilowatt-hour: \( \text{Cost} = E \times 0.12 \).
Substitute the values into the equations and simplify to find the total cost of leaving the light on for a year.

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Key Concepts

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

Power Consumption

Power consumption is the rate at which an electrical device uses energy, measured in watts (W). In this case, the porch light consumes 25 watts, which indicates how much energy it uses per hour. Understanding power consumption is essential for calculating the total energy used over time.
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Energy Cost Calculation

Energy cost calculation involves determining the total cost of electricity consumed by a device over a specific period. This is typically calculated by multiplying the power consumption (in kilowatts) by the time (in hours) the device is used and the cost of electricity per kilowatt-hour (kWh). This concept is crucial for finding the annual cost of running the porch light.
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Time Conversion

Time conversion is the process of converting time units to facilitate calculations. In this scenario, the light is on continuously for a year, which requires converting years into hours for accurate energy consumption calculations. There are 8,760 hours in a year (24 hours/day × 365 days/year), which is necessary for determining the total energy used by the light.
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Related Practice
Textbook Question

You buy a 75-W lightbulb in Europe, where electricity is delivered at 240 V. If you use the bulb in the United States at 120 V (assume its resistance does not change), how bright will it be relative to 75-W 120-V bulbs? [Hint: Assume roughly that brightness is proportional to power consumed.]

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Textbook Question

An electric car uses a 45-kW (160-hp) motor. If the battery pack is designed for 340 V, what current would the motor need to draw from the battery? Neglect any energy losses in getting energy from the battery to the motor.

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Textbook Question

A flashlight uses two AA 1.5-V batteries connected in series to provide 3.0 V across the bulb, as in Fig. 25–4b. The bulb draws 135 mA when turned on.

(a) Calculate the resistance of the bulb and the power dissipated.

(b) By what factor would the power increase if four AA batteries in series (total 6.0 V) were used with the same bulb? (Neglect heating effects of the filament.) Why shouldn’t you try this?

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Textbook Question

Calculate the peak current in a 2.5-k Ω resistor connected to a 220-V rms ac source.

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Textbook Question

The heating element of an electric oven is designed to produce 3.1 kW of heat when connected to a 240-V source. What must be the resistance of the element?

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Textbook Question

(II) A power station delivers 750 kW of power at 12,000 V to a factory through wires with total resistance 3.0 Ω. How much less power is wasted if the electricity is delivered at 50,000 V rather than 12,000 V?

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