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 29

Chapter 24, Problem 29

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?

Verified step by step guidance

Identify the relationship between power, voltage, and resistance using the formula:

P = V^{2} / R

, where

P

is power,

V

is voltage, and

R

is resistance.

Rearrange the formula to solve for resistance:

R = V^{2} / P

Substitute the given values into the formula:

V = 240 \, V

and

P = 3.1 \, kW = 3100 \, W

Calculate the square of the voltage:

V^{2} = 240^2

Divide the squared voltage by the power to find the resistance:

R = 240^2 / 3100

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Key Concepts

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

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. It is mathematically expressed as V = I * R. This relationship is fundamental in electrical circuits and is essential for calculating resistance when voltage and current are known.

Power in Electrical Circuits

The power (P) consumed by an electrical device is defined as the rate at which it converts electrical energy into another form of energy, such as heat. It is calculated using the formula P = V * I, where P is power in watts, V is voltage in volts, and I is current in amperes. Understanding this concept is crucial for determining the resistance of the heating element based on its power rating and the voltage supplied.

Resistance

Resistance (R) is a measure of the opposition to the flow of electric current in a circuit. It is measured in ohms (Ω) and can be calculated using Ohm's Law. In the context of the heating element, knowing the resistance allows us to understand how much current will flow when a specific voltage is applied, which is necessary for ensuring the element operates safely and effectively at its rated power.

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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

The filament of an incandescent lightbulb has a resistance of 12 Ω at 20°C and 140 Ω when hot.

(a) Calculate the temperature of the filament when it is hot, and take into account the change in length and area of the filament due to thermal expansion (assume tungsten for which the thermal expansion coefficient is ≈ 5.5 10⁻⁶ C°⁻¹ ).

(b) In this temperature range, what is the percentage change in resistance due to thermal expansion, and what is the percentage change in resistance due solely to the change in ρ? Use Eq. 25–5.

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Textbook Question

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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Textbook Question

A rectangular solid made of carbon has sides of lengths 1.0 cm, 2.0 cm, and 4.0 cm, lying along the x, y, and z axes, respectively (Fig. 25–36). Determine the resistance for current that passes through the solid in the y direction, (Assume the resistivity is ρ = 3.0 x 10⁻⁵ Ω•m).

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Textbook Question

Neglect the internal resistance of a battery unless the problem refers to it. Ten 7.0-W Christmas tree lights are connected in series to each other and to a 120-V source. What is the resistance of each bulb?

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