   Chapter 17.6, Problem 17.10QQ

Chapter
Section
Textbook Problem

The diameter of wire A is greater than the diameter of wire B, but their lengths and resistivities are identical. For a given voltage difference across the ends, what is the relationship between PA and PB, the dissipated power for wires A and B, respectively? (a) PA = PB (b) PA < PB (c) PA > PB

To determine
Compare the power dissipated by wires A and B.

Explanation

Given Info: The length and resistivity of wires A and B are same. The voltage across the wires A and B are also same. The diameter of wire A is greater than that of wire B.

Explanation:

Formula to calculate the power is,

P=(ΔV)2R

• P is the power dissipated by wire,
• ΔV is the voltage across the wire,
• R is the resistance of the wire,

Formula to find the resistance is,

R=4ρLπd2

• ρ is the resistivity of the wire,
• L is the length of the wire,
• d is the diameter of cross sect

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