0.5V across 1.5m tungsten wire w/cross-sect. area 0.6 mm^2 - Find wire current

In summary, the conversation discusses the process of finding the current in a tungsten wire given its resistivity, cross-sectional area, and voltage across it. The correct equation is used, but the answer is initially incorrect due to not converting the area from millimeters squared to meters squared. The correct answer is 3.57 amps.
  • #1
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Homework Statement


0.5 volts is maintained across a 1.5 meter tungsten wire that has a cross-sectional area of 0.6 mm2. What is the current in the wire?


Homework Equations


Resistivity of tungsten: 5.6E-8 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: cross-sectional area of wire in m2, [tex]\sigma[/tex]: material conductivity, V: volts, l: length of extruded cross-sectional area (in this case, a wire) in meters, [tex]\rho[/tex]: resistivity in ohm meters

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}{5.6E-8} \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.
 
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  • #2
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
Nevermind, lol, solved my own problem. Found out that I didn't convert millimeters squared to meters squared. Got it right now :)
 
  • #4
Thanks for the reply fball558 :) It's nice to get other views while your pourin over pages and pages of physics :)
 

1. What is the formula for calculating current in a wire?

The formula for calculating current in a wire is I = V/R, where I is the current in amperes (A), V is the voltage in volts (V), and R is the resistance in ohms (Ω).

2. How do you determine the resistance of a wire?

The resistance of a wire can be determined using the formula R = ρL/A, where R is the resistance in ohms (Ω), ρ is the resistivity of the material in ohm-meters (Ω*m), L is the length of the wire in meters (m), and A is the cross-sectional area of the wire in square meters (m^2).

3. What is the resistivity of tungsten?

The resistivity of tungsten is 5.6 x 10^-8 ohm-meters (Ω*m) at room temperature.

4. How do you convert millimeters squared to square meters?

To convert millimeters squared (mm^2) to square meters (m^2), divide the number of millimeters squared by 1,000,000. In this case, the cross-sectional area of 0.6 mm^2 would be equivalent to 0.0000006 m^2.

5. What is the current in the 1.5m tungsten wire with a voltage of 0.5V?

The current in the 1.5m tungsten wire would be 0.83 amperes (A) using the formula I = V/R, where V = 0.5V and R = (5.6 x 10^-8 ohm-meters * 1.5m)/0.0000006 m^2 = 0.83Ω.

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