Diameter of wire from voltage, length, resistivity

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SUMMARY

The discussion focuses on calculating the diameter of a tungsten filament in a 100 W (120 V) lightbulb, which is 8.50 cm long. The resistivity of tungsten is given as 9.0 x 10-7 ohm*m. To find the diameter, one must first calculate the current using the formula P = IV, and then determine the resistance using R = V/I. Finally, the area A can be derived from the resistance formula R = pL/A, allowing for the calculation of the diameter using A = πr2.

PREREQUISITES
  • Understanding of electrical power formulas (P = IV)
  • Familiarity with resistivity and its implications in electrical circuits
  • Knowledge of geometric formulas for area (A = πr2)
  • Basic algebra for manipulating equations
NEXT STEPS
  • Learn how to calculate electrical current using P = IV
  • Study the relationship between resistance, resistivity, length, and cross-sectional area
  • Explore the geometric implications of circular cross-sections in electrical components
  • Investigate the properties of tungsten and its applications in lighting technology
USEFUL FOR

Electrical engineers, physics students, and anyone involved in the design or analysis of electrical components, particularly in lighting applications.

Linus Pauling
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1. 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} ohm*m. What is the diameter of the filament?



2. p= resistivity, E = V/L, I = AV/pL, R = pL/A...



3. I know that I'm going to solve for A = pi*r2, find r and multiply by 2 to get the diameter, but I just don't see how to do it with what I'm given. For example, I could do pi*r2 = IpL/V but I don't know I, or A = pL/R but I don't know R...
 
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The information that the bulb operates at 100W and 120V allows you to calculate the current through it and its resistance. Do you know a formula relating power to voltage and current?
 

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