   Chapter 17.4, Problem 17.6QQ

Chapter
Section
Textbook Problem

Suppose an electrical wire is replaced with one having every linear dimension doubled (i.e., the length and radius have twice their original values). Does the wire now have (a) more resistance, (b) less resistance, or (c) the same resistance than before?

To determine
The new resistance of electrical wire on doubling each linear dimension.

Explanation

Given Info: Every linear dimension of electrical wire is doubled that is length and radius have twice their original values.

Explanation:

Formula to calculate the resistance before doubling of linear dimensions is,

Rbefore=ρLπr2

• Rbefore is the resistance of the wire before doubling of linear dimensions,
• ρ is the resistivity of the material of the wire,
• L is the length of the wire,
• r is the radius of cross section of wire,

Formula to calculate the resistance after doubling of linear dimensions is,

Rafter=ρ2Lπ(2r)2

• Rafter is the resistance of the wire after doubling of linear dimensions,

Divide (II) by (I) to calculate the ratio Rafter/Rbefore

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