Current and Ohm's Law-filament diameter

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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[tex]\Delta[/tex]V=[tex]\Delta[/tex]^2/R
J=I/A

The Attempt at a Solution



I know power, [tex]\Delta[/tex]V, 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?