Diameter of wire from voltage, length, resistivity

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To determine the diameter of the tungsten filament in a 100 W lightbulb operating at 120 V, the resistivity of tungsten and the filament's length are key factors. The filament's resistance can be calculated using the formula R = V^2/P, which yields a resistance value. Once resistance is known, the current can be calculated using I = V/R. The cross-sectional area A can then be derived from the formula A = pL/R, and the diameter can be found using A = πr². This process effectively utilizes the relationships between voltage, power, and resistivity to solve for the filament's diameter.
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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