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Resistance vs. Temperature, etc.

  1. Feb 8, 2006 #1
    Hi, I have two homework questions that I'm stuck on. I've worked my way through both of them, but and coming up w/ the wrong answers. Here they are:

    1) A copper wire has a resistance of 0.501 ohms at 20.0 degrees C, and an iron wire has a resistance of 0.486 ohms at the same temperature. At what temperature are their resistances equal?

    First, I found the resistivities of each of the materials and filled in the following equation for each, then setting them eqaul: R = R(1 + alpha(T-T(ini.))

    I then set the equality equal to zero: 0 = (R(copper) - R(iron)) + ([R(copper)*alpha(copper)] - [R(iron)*alpha(iron)]) * (T - T(ini.))

    I then solved for T: T = T(ini.) + ( R(copper) - R(iron) ) \ ( [R(copper)*alpha(copper)] - [R(iron)*alpha(iron)])

    After plugging in all the values, I'm coming up w/ -11.2 degree C though this is the wrong answer

    2) In baking a cake, an electric oven uses an average of 19 A of electricity at 230 V for 45 minutes. A personal computer uses only 1.5 A at 115 V. With the same amount of electrical energy used in baking the cake, how long could you surf the internet on the computer?

    Starting out, I found the power of the oven: P = IV

    I then plugged to the power and other known values into the equation: P = (Q \ t)V to find the energy.

    Then, I found the power of the computer: again, P = IV

    Lastly, I plugged in the known values (P, Q, V) into: P = (Q \ t)V

    I'm coming up w/ 570 minutes, which is the wrong answer.

    If anyone can help me out and let me know what I'm doing wrong, I'd greatly appreciate it ... thanks in adavance.

  2. jcsd
  3. Feb 8, 2006 #2


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    2) The amount of electrical energy used in both processes are the same which can be calculated from
    [tex]I_1V_1\Delta t_1=I_2V_2\Delta t_2[/tex]
    the time shoud be in seconds for S.I. units, but factor 60 appears both sides, so you can drop it and work in minutes. I got 19 hours.
  4. Feb 8, 2006 #3
    Thanks a lot for your help andrevhd. Anyone have any ideas for the first problem?
  5. Feb 8, 2006 #4


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    1)Try it this way with symbols first
    so we are going to have all copper quantities on the lhs and iron on the rhs
    [tex]R_c(1+{\alpha}_c\Delta T)=R_i(1+{\alpha}_i\Delta T)[/tex]
    next the ratio
    changing the above to
    [tex]a+a{\alpha}_c\Delta T=1+{\alpha}_i\Delta T[/tex]
  6. Feb 8, 2006 #5
    So am I solving for T in the following equation then: [tex]a+a{\alpha}_c\Delta T=1+{\alpha}_i\Delta T[/tex]

    I tried doing that, but apparently my algebra sucks and I didn't rearrange the equation correctly. Sometimes I think math is my biggest problem w/ this class.
  7. Feb 9, 2006 #6


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    [tex]\Delta T=T-T_{ini}[/tex]
    so you want
    [tex]\Delta T[/tex]
    on the lhs of the equation, hopefully all the quantities on the rhs are known at that stage.
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