Diameter of wire from voltage, length, resistivity

In summary, the 100 W (120 V) lightbulb has a 8.50 cm-long tungsten filament with a high-temperature resistivity of 9.0*10^-7 ohm*m. To find the diameter of the filament, you can use the formula A = pi * r^2 to solve for r and then multiply by 2 to get the diameter. Alternatively, using the formulas p = resistivity, E = V/L, I = AV/pL, and R = pL/A, you can calculate the current and resistance of the bulb. The formula P = VI can also be used to relate power to voltage and current.
  • #1
Linus Pauling
190
0
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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  • #2
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?
 

1) What is the relationship between the diameter of a wire and its voltage?

The diameter of a wire and its voltage have an inverse relationship. This means that as the voltage increases, the diameter of the wire decreases, and vice versa. This is because a higher voltage requires less resistance, and a smaller diameter wire has less resistance than a larger diameter wire.

2) How does the length of a wire affect its diameter?

The length of a wire does not directly affect its diameter. The diameter of a wire is determined by its material and manufacturing process. However, the length of a wire can indirectly impact its diameter by increasing its resistance, which can then affect the voltage and current flow.

3) What is the role of resistivity in determining the diameter of a wire?

Resistivity is a measure of a material's ability to resist the flow of electricity. The higher the resistivity of a material, the larger the diameter of the wire needs to be in order to maintain a certain voltage and current. Therefore, resistivity plays a crucial role in determining the diameter of a wire.

4) How can I calculate the diameter of a wire based on voltage, length, and resistivity?

The formula for calculating the diameter of a wire is: diameter = (2 x resistivity x length)/voltage. This equation takes into account the inverse relationship between voltage and diameter, and the direct relationship between resistivity and diameter. You can plug in the known values to solve for the diameter of the wire.

5) Can the diameter of a wire be changed to adjust its voltage?

Yes, the diameter of a wire can be changed to adjust its voltage. However, this should only be done with caution and proper knowledge of the wire's capabilities. Changing the diameter can affect the wire's resistance, which can impact the overall circuit and potentially cause damage or failure. It is important to consult a professional or thoroughly research before making any changes to a wire's diameter.

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