Ch.1 - Matter, Measurement & Problem Solving

Problem 131

Chapter 1, Problem 131

A length of #8 copper wire (radius = 1.63 mm) has a mass of 24.0 kg and a resistance of 2.061 ohm per km (Ω / km). What is the overall resistance of the wire?

Verified step by step guidance

Convert the mass of the copper wire to its volume using the density of copper (8.96 g/cm³).

Calculate the length of the wire using the volume and the cross-sectional area (A = πr², where r is the radius).

Convert the length of the wire from meters to kilometers to match the units of resistance per kilometer.

Use the given resistance per kilometer to find the total resistance by multiplying it by the length of the wire in kilometers.

Ensure all units are consistent and check calculations for any errors.

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Key Concepts

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

Resistance

Resistance is a measure of the opposition to the flow of electric current in a conductor. It is influenced by the material's properties, length, and cross-sectional area. The formula for resistance (R) is R = ρ(L/A), where ρ is the resistivity, L is the length, and A is the cross-sectional area. Understanding resistance is crucial for calculating how much current will flow through a wire for a given voltage.

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). It is expressed as V = IR. This fundamental principle helps in understanding how voltage, current, and resistance interact in electrical circuits, which is essential for solving problems related to wire resistance.

Cross-sectional Area

The cross-sectional area of a wire is the area of its circular end face, which affects its resistance. It can be calculated using the formula A = πr², where r is the radius of the wire. A larger cross-sectional area results in lower resistance, allowing more current to flow. This concept is vital when determining the overall resistance of a wire, as it directly influences the resistance value.

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Textbook Question

The diameter of a hydrogen atom is 212 pm. Find the length in kilometers of a row of 6.02×10²³ hydrogen atoms. The diameter of a ping pong ball is 4.0 cm. Find the length in kilometers of a row of 6.02×10²³ ping pong balls.

The daily recommended intake of calcium for an average adult is 1,000 mg. There is 125 mg of calcium in 100 grams of milk. If a 150 g smoothie contains 75 grams of milk, how many grams of smoothie should an adult consume to meet the daily recommended intake?

Lead metal can be extracted from a mineral called galena, which contains 86.6% lead by mass. A particular ore contains 68.5% galena by mass. If the lead can be extracted with 92.5% efficiency, what mass of ore is required to make a lead sphere with a 5.00-cm radius?

Rolls of aluminum foil are 304 mm wide and 0.016 mm thick. What maximum length of aluminum foil can be made from 1.10 kg of aluminum?

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