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0.5V across 1.5m tungsten wire w/crosssect. area 0.6 mm^2  Find wire currentby student_fun
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#1
Mar3109, 09:22 PM

P: 8

1. The problem statement, all variables and given/known data
0.5 volts is maintained across a 1.5 meter tungsten wire that has a crosssectional area of 0.6 mm^{2}. What is the current in the wire? 2. Relevant equations Resistivity of tungsten: 5.6E8 ohm meters. Current Density: [tex]J = \sigma \cdot \frac{V}{l}, J = \frac{I}{A}[/tex] Definition of resistivity: [tex]\rho = \frac{1}{\sigma}[/tex] Variable meanings in equations used: I: current in amps, A: crosssectional area of wire in m^{2}, [tex]\sigma[/tex]: material conductivity, V: volts, l: length of extruded crosssectional area (in this case, a wire) in meters, [tex]\rho[/tex]: resistivity in ohm meters 3. The attempt at a solution Using the relations and data available it seems to make sense to find the current in the wire by relating the known tungsten resistivity to the two definitions of current density in which most variables are known except for the I (current) that I'm after. Doing this yields: [tex]\frac{I}{A} = \sigma\frac{V}{l}[/tex] [tex]\sigma = \frac{1}{\rho}[/tex] [tex]\frac{I}{A} = \frac{1}{\rho} \cdot \frac{V}{l}[/tex] [tex]I = A\left[\frac{1}{\rho} \cdot \frac{V}{l}\right][/tex] Then I plug and chug: [tex]I = 0.6\left[\frac{1}{5.6E8} \cdot \frac{0.5}{1.5}\right] = 3571428.571[/tex] Amps However this answer is not valid. Can anyone see something I am doing that is outright wrong? Invalid logic somewhere? Any hints to get me on the right track would be greatly appreciated. Thank you for your time. 


#2
Mar3109, 09:35 PM

P: 147

Your answer has the right procedure but the area is in mm^2 you need to convert it to m^2. So you are off by a factor of 10^6 meaning 3.57 amps.
Below is an easier way to go about the problem and attain the same answer. resistance = (resistivity*length)/cross sectional area in m^2 Current = voltage/ resistance 


#3
Mar3109, 09:39 PM

P: 8

Nevermind, lol, solved my own problem. Found out that I didn't convert millimeters squared to meters squared. Got it right now :)



#4
Mar3109, 09:42 PM

P: 8

0.5V across 1.5m tungsten wire w/crosssect. area 0.6 mm^2  Find wire current
Thanks for the reply fball558 :) It's nice to get other views while your pourin over pages and pages of physics :)



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