Current and Ohm's Law-filament diameter

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SUMMARY

The discussion focuses on calculating the diameter of a tungsten filament in a standard 100 W lightbulb using Ohm's Law and related equations. The filament is 8.50 cm long, and the high-temperature resistivity of tungsten is given as 9.0 x 10-7 ohm-meters. The user aims to find the filament's diameter in micrometers by first determining the current using the power equation and then applying the current density equation. The discussion highlights the need for understanding current density (J) and resistivity (ρ) in this context.

PREREQUISITES
  • Understanding of Ohm's Law and electrical power equations
  • Familiarity with the concept of resistivity and its units
  • Knowledge of current density (J) and its relationship to area
  • Basic skills in algebra for solving equations
NEXT STEPS
  • Learn how to calculate current using the formula P = IΔV
  • Study the relationship between current density (J) and filament diameter
  • Explore the concept of resistivity and its application in electrical engineering
  • Investigate the conversion of diameter measurements from meters to micrometers
USEFUL FOR

Students in physics or electrical engineering, educators teaching electrical concepts, and anyone interested in the practical applications of Ohm's Law in calculating filament properties.

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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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