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

Giancoli Douglas 5th edition

Ch. 25 - Electric Current and Resistance

Problem 74a

Chapter 24, Problem 74a

A microwave oven running at 72% efficiency delivers 950 W to the interior. Find the power drawn from the source.

Verified step by step guidance

Step 1: Understand the relationship between efficiency, output power, and input power. Efficiency (η) is defined as the ratio of the output power (P_out) to the input power (P_in), expressed as a percentage: η = (P_out / P_in) × 100.

Step 2: Rearrange the formula to solve for the input power (P_in). The formula becomes: P_in = P_out / (η / 100).

Step 3: Substitute the given values into the formula. Here, P_out = 950 W and η = 72%. The equation becomes: P_in = 950 / (72 / 100).

Step 4: Simplify the denominator by dividing 72 by 100 to convert the percentage into a decimal. Then divide 950 by this decimal to calculate the input power.

Step 5: The result of this calculation will give you the power drawn from the source, which is the input power (P_in).

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Key Concepts

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

Efficiency

Efficiency is a measure of how well an energy conversion process works, defined as the ratio of useful output energy to the input energy. In this context, the microwave oven operates at 72% efficiency, meaning that 72% of the electrical power drawn is converted into useful microwave energy, while the rest is lost as waste energy.

Power

Power is the rate at which energy is transferred or converted. It is measured in watts (W), where one watt equals one joule per second. In this problem, the useful power delivered to the interior of the microwave is 950 W, which represents the energy used to heat food.

Input Power Calculation

To find the input power drawn from the source, we can use the formula: Input Power = Output Power / Efficiency. Given the output power of 950 W and the efficiency of 72%, this calculation will reveal the total power consumed by the microwave from the electrical source, accounting for energy losses.

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Textbook Question

A 100-W, 120-V incandescent lightbulb has a resistance of 12 Ω when cold (20°C) and 150 Ω when on (hot). Calculate its power consumption (a) at the instant it is turned on, and (b) after a few moments when it is hot.

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A 2800-W oven is connected to a 240-V source. How long will it take to bring 150 mL of 15°C water to 100°C assuming 65% efficiency?

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A 0.65-mm-diameter copper wire carries a tiny current of 3.2 μA. Estimate the current density.

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What is the average current drawn by a 1.0-hp 120-V motor? (1 hp = 746 W.)

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