Resistivity of tungsten filament

In summary, using the given length and resistance, the diameter of the tungsten filament in a small lightbulb can be found using the formula for resistivity and the area of a circle. After solving for the radius and converting to millimeters, the diameter was determined to be 1.7e-7 mm. However, the answer was not correct due to forgetting to convert from meters to millimeters.
  • #1
rinarez7
27
0
]1. A 1.3 cm length of tungsten filament in a small lightbulb has a resistance of 0.032 ohms. Find its diameter.
Given: Length= 1.3 cm= .013m
R= 0.032 ohms
resistivity= 5.6e-8 ohms*meter



2.
A= pi (r^2)
R= resistivity (Length/ Area)



The Attempt at a Solution


R= resistivity ( Length/ pi* (r^2) )
.032 ohms= (5.6e-8 ohms*meter) * (.o13m/ (pi* (r^2)) )
.032 (pi) (r^2) = 7.28e-10
.100530965 (r^2) = 7.28e-10
r= 8.509e-5
diameter= 2r= 1.701e-4m

It asks for the answer in mm, so I divided my answer by 1000= 1.7 e-7 mm, but it's not correct = (
What am I missing?
Thanks in advance!
 
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  • #2
1m=1000mm...
 
  • #3
wow do I feel silly! = / thanks
 
  • #4
rinarez7 said:
wow do I feel silly! = / thanks

Those things happen to everybody from time to time! :biggrin: And you're welcome!
 

1. What is the resistivity of a tungsten filament?

The resistivity of a tungsten filament is approximately 5.6 x 10^-8 ohm-meters.

2. How does the resistivity of a tungsten filament affect its performance?

The resistivity of a tungsten filament directly affects its performance, as it determines the amount of resistance the filament has to the flow of electricity. A higher resistivity means a higher resistance, which can lead to a longer lifespan for the filament.

3. What factors can affect the resistivity of a tungsten filament?

The main factors that can affect the resistivity of a tungsten filament are temperature, impurities in the filament, and the length and diameter of the filament. Higher temperatures can increase the resistivity, while impurities and larger dimensions can decrease it.

4. How is the resistivity of a tungsten filament measured?

The resistivity of a tungsten filament is typically measured using a four-point probe method, which involves passing a known current through the filament and measuring the voltage drop across four points on the filament. This allows for an accurate calculation of the resistivity.

5. Can the resistivity of a tungsten filament be altered?

Yes, the resistivity of a tungsten filament can be altered by changing the temperature or dimensions of the filament. It can also be affected by the presence of impurities or by the use of different alloys of tungsten. However, the resistivity of tungsten is generally quite stable and does not vary significantly under normal conditions.

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