Calculating Annual Cost of Running Coffee Makers

[STEMucator]

Calculating yearly cost of running coffee makers

Homework Statement

Find the total cost for operating two 15Ω coffee makers connected to a 120V power supply for two hours a day each for one year.

Homework Equations

$R = 15Ω$
$V = 120V$
$∆t=(2h)(365)= 730h$ Two hours each 365 days a year.
$r_¢=6.4¢/kWh$
$I = V/R = 8A$

There is some basic physics involved, it's the answer I'm concerned with arithmetically.

The Attempt at a Solution

I find the power of one coffee maker using :

$P = IV = (8A)(120V) = 0.96kW$

There are two coffee makers, so the total power is :

$P_{Total} = (2)(0.96kW) = 1.92kW$

The energy would then be :

$E = P_{Total}∆t = (1.92 kW)(730h) = 1401.6 kWh$

Therefore the total cost is :

$C = Er_¢ = (1401.6 kWh)(6.4¢/kWh) = 8970.24¢ = 89.70$

Is this correct? The answer is listed as $370.02 so I'm not so sure.

 

[BruceW]

that's odd. Your method and answer look correct to me.

 

[SteamKing]

Must be inflation.

 

[STEMucator]

that's odd. Your method and answer look correct to me.

Yeah it didn't make any sense for two small coffee makers to be costing so much to run.

Must be inflation.

Lol! I wouldn't want to live if inflation was that high.

 

[Office_Shredder]

The smart money is to connect them in parallel to decrease the resistance.

Other than that I have nothing to add

 

[BruceW]

(I think) the problem was assuming that there is 120V across each of the resistors. If it meant 120V across both resistors in series, then he would get half of his current answer. (which unfortunately still doesn't get the textbook's answer).

 

[lendav_rott]

I can't get my head around it. There is no way a 120V coffee machine takes so much power that you'd have to pay 175 bucks per machine a year.

I'm going to go with it being the textbook's fault not your fault.

By that same logic - if I were to calculate how much my computer costs to keep running if it's on 24/7 I would be long broke.

 

[STEMucator]

(I think) the problem was assuming that there is 120V across each of the resistors. If it meant 120V across both resistors in series, then he would get half of his current answer. (which unfortunately still doesn't get the textbook's answer).

I believe the two coffee makers are on separate circuits; so I don't think concepts about $R_{eq}$ can be applied here.

 

[forsyth]

I believe the two coffee makers are on separate circuits; so I don't think concepts about $R_{eq}$ can be applied here.

Agreed, how weird would it be to have one coffee maker that hooks into the back of another one for electricity xD

If they were on a parallel circuit, presumably they'd still have 120V and 15 Ω no?