Question #25626

A tungsten wire has a radius of and is heated from 20.0 to . The temperature coefficient of resistivity is . When is applied across the ends of the hot wire, a current of is produced. How long is the wire? Neglect any effects due to thermal expansion of the wire.
resistivity at 20.0celcius is 5.6x10^-8 ohms/m

Expert's answer

It's known that R= p x L/A where R is the resistance, p is the proportionality constant known as the resistivity of the material, L is the length, and A is the area. the book sa5.6x10^-8 is the resistivity for a tungsten wire.

So we solve the equation for L, L= R(A)/p R= V/I so 120v/1.5A= 80ohms R= 80ohms A= 4x3.14xradius^2 so 4x3.14x(.075mm)^2= .071mm^2 A= .071mm^2 or 7.1x10^-5m T= Tc + 273 20c+(273c)=293K and 1320c+(273c)=1593.15K 1593.15k-293k=1300.12 K P= (Resistivity)[1+(coefficient of resistivity)(1300.12K) p= (5.6x10^-8)[1+(4.5x10^-3)(1300.12)= 3.84x10^-7 p=3.83x10^-7 L=80A(7.1x10^-5m)/(3.83x10^-7ohmsxmeters)=14830m long

So we solve the equation for L, L= R(A)/p R= V/I so 120v/1.5A= 80ohms R= 80ohms A= 4x3.14xradius^2 so 4x3.14x(.075mm)^2= .071mm^2 A= .071mm^2 or 7.1x10^-5m T= Tc + 273 20c+(273c)=293K and 1320c+(273c)=1593.15K 1593.15k-293k=1300.12 K P= (Resistivity)[1+(coefficient of resistivity)(1300.12K) p= (5.6x10^-8)[1+(4.5x10^-3)(1300.12)= 3.84x10^-7 p=3.83x10^-7 L=80A(7.1x10^-5m)/(3.83x10^-7ohmsxmeters)=14830m long

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