   Chapter 17, Problem 54AP

Chapter
Section
Textbook Problem

A given copper wire has a resistance of 5.00 Ω at 20.0°C while a tungsten wire of the same diameter has a resistance of 4.75 Ω at 20.0°C. At what temperature will the two wires have the same resistance?

To determine
The temperature at which Copper and Tungsten wires have the same resistance.

Explanation

Given Info: Copper wire has resistance 5.00Ω at 20.0°C Tungsten wire has resistance 4.75Ω at 20.0°C . Both wires have same diameter.

Explanation:

Formula to calculate the resistance of copper is,

RCu=R0Cu(1+αCu(TT0))

• RCu is the resistance of copper wire at temperature T ,
• R0Cu is the resistance of copper wire at some reference temperature T0 ,
• αCu is the temperature coefficient of resistivity of copper,

Formula to calculate the resistance of Tungsten is,

RW=R0W(1+αW(TT0))

• RW is the resistance of Tungsten wire at temperature T ,
• R0W is the resistance of Tungsten wire at some reference temperature T0 ,
• αW is the temperature coefficient of resistivity of Tungsten,

At temperature T , resistances RCu and RW are same. Equate the above relations for RCu and RW .

R0Cu(1+αCu(TT0))=R0W(1+αW(TT0))R0Cu+R0CuαCu(TT0)=R0W+R0WαW(TT0)(TT0

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