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Resistance of a light bulb changing with temperature

  1. Mar 30, 2007 #1
    1. The problem statement, all variables and given/known data

    The resistance of the tungsten filament in a light bulb changes with temperature according to equation (1), below.
    I am supposed to calculate the temperature of the light bulb at voltage 0.8280 volts and a current of 0.0853 amps. The bulb is connected to a 1.5915 volt battery. The bulb's resistance is 2.28 ohms.


    2. Relevant equations

    R = Ro(1+a(T-To))......................................(1)

    T = (-1a^-1)+(a^-1)(Ro^-1)(R)+T................(2)

    Where Ro is the resistance at the initial temperature To, and R is the resistance at the final temperature, T. a is the coefficient of resistivity.

    3. The attempt at a solution

    The coefficient of resistivity for tungsten is 0.0045 degrees Celsius ^-1.
    I assumed To to be 20 degrees Celsius.
    I assumed Ro to be 2.28 ohms, the resistance of the bulb alone.
    I want to find T, but I didn't have R yet, so I calculated it with:

    R = voltage across bulb (V) / current through bulb (A)
    = 0.8280 V / 0.0853 A
    = 9.71 ohms

    I put my values for Ro, R, To, and a into equation (1). I got T = 20, the same as To, so I checked two different online equation solvers. They told me I had made a mistake in the calculation, and that T was actually 744 degrees Celsius. I checked this on equation (2) and got the same answer. I knew this couldn't be right, so I switched my values for R and Ro. The solver and equation (2) both had T = -147 degrees. This does not seem right.

    My question is, where did I go wrong? I am sure that To and a are correct. I suspect I have the wrong R value. How can I find the correct value for R? Is Ro correct? Any help will be greatly appreciated. This is due on April 2, and it has me stumped.
     
    Last edited: Mar 30, 2007
  2. jcsd
  3. Mar 30, 2007 #2

    berkeman

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    Staff: Mentor

    Equation #2 doesn't look correct to me. a by itself isn't useful -- seems like it needs to be more in the form of 1+a, like you have in the first equation. Plus the units don't seem to match up for each term in that equation. Each term should have units of degrees C (or degrees Kelvin?), but on the RHS the first two terms look to have units of 1/degrees C.

    And just to check (I don't know offhand) -- you're supposed to use degrees C or absolute temperature in Kelvin?
     
  4. Mar 30, 2007 #3

    marcusl

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    Your equation (1) gives the correct answer, 744 degrees. What did you do to get a different answer?

    I have no clue what eq. (2) is...
     
  5. Mar 30, 2007 #4
    Berkeman, a was given to me in the assignment, and that is how I am sure it is correct. I actually checked the units for equation (2), because I wasn't sure, and I got degrees Celsius... but I just tried again and I'm not sure! I'm going to try the calculation again, thank-you for pointing that out....
    marcusl, I am just no good at algebra! The equation is correct, it is R that I am not sure about. Equation (2) is just a re-arrangement of equation (1).
     
    Last edited: Mar 30, 2007
  6. Mar 30, 2007 #5
    I tried equation (2) again, this time paying more attention to the units. The answer comes out as 744 degrees Celsius, so it's not the wrong equation, but again, my R value.

    I found something in my notes saying Ro is correct, so it is R for sure.

    I need T in units of degrees Celsius.
     
    Last edited: Mar 30, 2007
  7. Mar 31, 2007 #6
    R must be wrong, because all the other variables are correct, but the temperature can't be 744 degrees! I just want to know what value I should use for R.
     
  8. Mar 31, 2007 #7

    marcusl

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    What's wrong with 744 degrees? Should it be higher?
     
  9. Mar 31, 2007 #8
    I think the temperature wouldn't rise that much from 20 degrees. 744 degrees is really hot, shouldn't it be more like 25 degrees or something?
     
  10. Mar 31, 2007 #9
    I'm supposed to make a graph of temperature vs. voltage. I actually have a number of voltages at which I'm supposed to calculate the temperature.
    Thank-you for helping, I was afraid my thread would be forgotten.
     
  11. Mar 31, 2007 #10

    marcusl

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    The color emitted by a "black body" depends on temperature. 744C would glow a dull red like an electric range element. A 100W light bulb operates at around 2400K or 2100C, so the filament is made of tungsten which won't melt until around 3700K.
     
  12. Mar 31, 2007 #11
    This was one of those really small lab light bulbs, I don't know the wattage...
    Do you think I haven't made a mistake?
     
  13. Apr 1, 2007 #12
    Thanks for the help!
     
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