Finding the Length of a wire

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The Stefan-Boltzmann law states that the total power radiated from a blackbody is proportional to the fourth power of its absolute temperature and the surface area of the object. Therefore, by rearranging the equation, we can find the length of the wire by using the given power output and temperature. In summary, using the Stefan-Boltzmann law, we can find the length of the wire of a 3000 Kelvin incandescent light bulb that produces 60W of power with a diameter of 0.00005m.
  • #1
UnknownSoldier02
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Homework Statement
Finding the length of a wire of incandescent light bulb.
Relevant Equations
N/A
How to find the length of a wire of a 3000 Kelvin incandescent light bulb that produces L = 60W of power. The diameter of the wire is 0.00005m.

I'm quite confused, as the resistivity of the bulb isn't given so I'm not sure what equation to use as resistivity = resistance × area / length does not seem to work because I'm missing 2 variables.
 
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  • #2
UnknownSoldier02 said:
Homework Statement: Finding the length of a wire of incandescent light bulb.
Homework Equations: N/A

How to find the length of a wire of a 3000 Kelvin incandescent light bulb that produces L = 60W of power. The diameter of the wire is 0.00005m.

I'm quite confused, as the resistivity of the bulb isn't given so I'm not sure what equation to use as resistivity = resistance × area / length does not seem to work because I'm missing 2 variables.
Think of the wire as a blackbody radiator.
 
  • #3
tnich said:
Think of the wire as a blackbody radiator.
Would it be related to the Stefan-Boltzmann equation in some way?
 
  • #4
UnknownSoldier02 said:
Would it be related to the Stefan-Boltzmann equation in some way?
Yes.
 

1. How do you measure the length of a wire accurately?

To measure the length of a wire accurately, you will need a ruler or measuring tape. Begin by straightening out the wire and placing it on a flat surface. Then, line up the end of the wire with the starting point on the ruler or measuring tape. Carefully extend the wire along the ruler, making sure it stays straight. Once you reach the end of the wire, read the measurement on the ruler or measuring tape to determine the length of the wire in the desired unit of measurement.

2. Can I use any measuring tool to find the length of a wire?

While a ruler or measuring tape is the most common and accurate tool for measuring the length of a wire, there are other tools that can be used. For example, a caliper can be used to measure the diameter of the wire, which can then be used in a formula to calculate the length. However, the accuracy of this method may vary depending on the thickness of the wire and the precision of the caliper.

3. What should I do if the wire is curved or coiled?

If the wire is curved or coiled, it may be more difficult to get an accurate measurement using a ruler or measuring tape. In this case, it may be helpful to straighten out the wire as much as possible and measure the length in sections, then add these measurements together to get the total length. Alternatively, you could use a flexible measuring tool like a string to follow the curve of the wire and then measure the length of the string.

4. Is there a formula for finding the length of a wire?

Yes, there is a formula for finding the length of a wire if you know the diameter and cross-sectional area of the wire. The formula is length = (cross-sectional area x density x 4)/(pi x diameter). However, this formula may not be accurate for all types of wires and may require additional adjustments depending on the material and shape of the wire.

5. What are some common units of measurement used for wire length?

The most common units of measurement used for wire length are meters, feet, and inches. However, depending on the size and type of wire, other units such as millimeters or centimeters may be used. It is important to be consistent with the unit of measurement used when working with wires to ensure accurate and precise measurements.

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