(II) A certain copper wire has a resistance of 15.0 Ω. At what point along its length must the w

step 1 So essentially, we know that resistance is directly proportional to length. So if we have the re

(II) A certain copper wire has a resistance of 15.0 Ω. At...

(II) A certain copper wire has a resistance of 15.0 $\Omega$. At what point along its length must the wire be cut so that the resistance of one piece is 4.0 times the resistance of the other? What is the resistance of each piece?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Uniform Resistivity

For a uniform material, the resistance of a conductor can be defined using the formula R = ?L/A, where ? is the resistivity, L is the length, and A is the cross-sectional area. This formula highlights how resistance is inherently linked to the physical properties of the material and its dimensions.

Proportionality of Resistance to Length

When dealing with a uniform wire, the resistance is directly proportional to its length. This means that if the wire is divided into parts, each piece's resistance will be a fraction of the total resistance corresponding to its fraction of the total length. This principle is fundamental when solving problems where the resistance of one segment is defined in relation to another.

Series Resistance Addition

When segments of a wire are connected in series, as they would be after a cut, their individual resistances add to form the total resistance. Understanding this concept is important for solving problems where the sum of the segments' resistances must equal a known total resistance, especially when a specific ratio between parts is involved.

Transcript

Please give Ace some feedback