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Power usage in wires

  1. Feb 7, 2014 #1
    1. The problem statement, all variables and given/known data
    A household appliance consumes 1800W of power from a 120V wall plug. Calculate the power consumed due to a wire of length L = 22.0m and diameter D1 = 1.628mm (with resistivity p = 1.680 x 10-8Ωm). If a house spends $1400 per year in electricity bills, how much money can be saved per year by rewiring the house with a new wire of diameter D2 = 2.053mm?

    2. Relevant equations
    P = IV

    3. The attempt at a solution
    I have found the power dissipated by the wire, which should be P = 25.1W using the formula P = I2R (for the second wire) and P = 39.9W (for the first wire). However, I do not know how to relate this with the money spent. How should I approach this problem? I'm not sure on how to proceed. Thanks in advance.
     
  2. jcsd
  3. Feb 7, 2014 #2

    NascentOxygen

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    Staff: Mentor

    I think you must be expected to assume that the same percentage of money is wasted as you calculate here for power wasted.
     
  4. Feb 7, 2014 #3
    I haven't checked the dissipations, I'll roll with what you have.

    Some amount out of the 1400$ is spent on the lost power. The total bill is n(A + 0.0399)kWh*rate. "A" is just the sum of the power consumption of other appliances, which don't concern us and "n" represents whatever amount of time power was being consumed.
    If n(A + 0.0399)kWh * Rate = 1400$, how would you find the bill if you replaced the wire?

    You win some certain amount of power by replacing the wire (39.9 - 25.1 = 14.8W) this 0.0148* n * kWh * Rate is the amount of dollars you don't have to spend, hence you can subtract it from the 1400$.
     
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