Current and Ohm's Law-filament diameter

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The discussion focuses on calculating the diameter of a tungsten filament in a 100 W lightbulb using current and Ohm's Law. The user has the power, voltage, and resistivity of tungsten but is unsure how to incorporate current density (J) into their calculations. They plan to use the equations for power and current density to find the filament's radius or diameter. Suggestions are sought on how to proceed without knowing J, with a mention of possibly using conductivity (sigma) and resistivity (rho). The goal is to determine the filament's diameter in micrometers.
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current and Ohm's Law--filament diameter

Homework Statement



A standard 100 W (120 V ) lightbulb contains a 8.50 cm -long tungsten filament. The high-temperature resistivity of tungsten is 9.0*10^-7.

Homework Equations


Power=I\DeltaV=\Delta^2/R
J=I/A

The Attempt at a Solution



I know power, \DeltaV, and R and am solving for either r or d.
I can use the first equation to solve for I. And then I want to use the second equation because it is the only equation that I've found that uses area (and thus r and d), but I don't know J. Any suggestions? Thanks!
 
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(solving for diameter of filament, in micrometers)
 


Maybe I use sigma and rho?
 

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