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

by student_fun
Tags: volts current wire
 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 cross-sectional area of 0.6 mm2. What is the current in the wire? 2. Relevant equations Resistivity of tungsten: 5.6E-8 ohm meters. Current Density: $$J = \sigma \cdot \frac{V}{l}, J = \frac{I}{A}$$ Definition of resistivity: $$\rho = \frac{1}{\sigma}$$ Variable meanings in equations used: I: current in amps, A: cross-sectional area of wire in m2, $$\sigma$$: material conductivity, V: volts, l: length of extruded cross-sectional area (in this case, a wire) in meters, $$\rho$$: 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: $$\frac{I}{A} = \sigma\frac{V}{l}$$ $$\sigma = \frac{1}{\rho}$$ $$\frac{I}{A} = \frac{1}{\rho} \cdot \frac{V}{l}$$ $$I = A\left[\frac{1}{\rho} \cdot \frac{V}{l}\right]$$ Then I plug and chug: $$I = 0.6\left[\frac{1}{5.6E-8} \cdot \frac{0.5}{1.5}\right] = 3571428.571$$ 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.