Resistance and Resistivity of tungsten wire

In summary, a tungsten wire with a radius of .075mm and heated from 20.0 to 1320 degrees C has a temperature coefficient of resistivity of 4.5x10^-3 (C)^-1. When 120V is applied, a current of 1.5A is produced. Using the equation R= p x L/A, the length of the wire is calculated to be 3.685m. However, this may seem long for a tungsten wire, so further analysis is needed to determine the wire's true length.
  • #1
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please check my work someone.

A tungsten wire has a radius of .075mm and is heated from 20.0 to 1320 degrees C. The temperature coefficient of resistivity is 4.5x10^-3 (C)^-1. When 120V is applied across the ends of the hot wire, a current os 1.5A is produced. How long is the wire? Neglect anf effects due to thermal expansion.

OKay we all know 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 says 5.6x10^-8 is the resistivity for a tungsten wire.

So we solve the equation for L, L= R(A)/p

R= V/I soo 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+(coefficiant 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

is that correct?? anyone??
 
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  • #2
A= Pi x radius^2 so 3.14x(.075mm)^2= 17.67x10^-9 m^2

T= 1320-20=1300 C

P= (Resistivity)[1+(coefficiant of resistivity)(T)]
p= (56x10^-9)[1+(4.5x10^-3)(1300)] = 383.6x10^-9

L=80(17.67x10^-9)/(383.6x10^-9)=3.685m long

This seems intuitively long to me, so if the resistivity figure is ohm-cm then this seems OK at 3.685cm.

On the other hand, 1320 C is not even a glowing red, is it? So this is not a 180W light bulb, so 3.685m may be OK.

I wonder what it would take to get it up to 3000 - 4000 C like an ordinary light bulb? I guess I will save that for another rainy day. https://www.physicsforums.com/Nexus/editor/smilie.png
 
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  • #3


I would say that your calculations and approach seem to be correct. However, I would recommend double checking your units to ensure consistency and accuracy. Additionally, it is always a good practice to include any assumptions or limitations in your calculations, such as neglecting thermal expansion in this case. Overall, it seems like you have a good understanding of the concepts and have applied them correctly. Well done!
 

Related to Resistance and Resistivity of tungsten wire

What is the resistance of tungsten wire?

The resistance of tungsten wire varies depending on the length, diameter, and temperature of the wire. However, on average, the resistance of tungsten wire is about 5.65x10^-8 ohm-meters at room temperature.

What is the resistivity of tungsten wire?

The resistivity of tungsten wire is a measure of its ability to resist the flow of electric current. It is typically around 5.65x10^-8 ohm-meters at room temperature, making tungsten wire a highly conductive material.

How does the diameter of tungsten wire affect its resistance?

The resistance of tungsten wire is inversely proportional to its diameter. This means that as the diameter of the wire increases, its resistance decreases. This is because a larger diameter allows for more space for electrons to flow through, resulting in less resistance.

What is the temperature coefficient of resistivity for tungsten wire?

The temperature coefficient of resistivity for tungsten wire is approximately 0.0045 ohm/ohm/°C. This means that for every degree Celsius increase in temperature, the resistivity of tungsten wire increases by 0.0045 ohm/ohm.

How does the length of tungsten wire affect its resistance?

The resistance of tungsten wire is directly proportional to its length. This means that as the length of the wire increases, its resistance also increases. This is because a longer wire provides more obstacles for electrons to flow through, resulting in higher resistance.

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