   Chapter 17.6, Problem 17.7QQ

Chapter
Section
Textbook Problem

A voltage ΔV is applied across the ends of a Nichrome heater wire having a cross-sectional area A and length L. The same voltage is applied across the ends of a second Nichrome heater wire having a cross-sectional area A and length 2L. Which wire gets hotter? (a) The shorter wire does. (b) The longer wire does. (c) More information is needed.

To determine
The nichrome heater wire which produce more heat.

Explanation

Given Info: First nichrome wire has area of cross section A and length L . Second nichrome wire has area of cross section A and length 2L . Same voltage ΔV applied across both wires.

Explanation:

Formula to calculate the power is,

P1=(ΔV)2R1

• P1 is the heat energy liberated in unit time in first wire,
• ΔV is the voltage across each wire,
• R1 is the resistance of the first wire,

Formula to calculate the resistance is,

R1=ρL1A

• ρ is the resistivity of nichrome,
• L1 is the length of first wire,
• A1 is the area of cross section of each wire

Substitute the equation for R in the previous equation to rewrite P1 ,

P1=A(ΔV)2ρL1 (I)

Formula to calculate the power generated in 2nd wire is,

P2</

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