Saving $$ on Power Usage: Rewire Household Appliance

[fogvajarash]

Homework Statement

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?

Homework Equations

P = IV

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.

 

[NascentOxygen]

I think you must be expected to assume that the same percentage of money is wasted as you calculate here for power wasted.

 

[lendav_rott]

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$.