# Calculating yearly cost

1. Aug 27, 2013

### Zondrina

Calculating yearly cost of running coffee makers

1. The problem statement, all variables and given/known data

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.

2. Relevant 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.

3. 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.

Last edited: Aug 28, 2013
2. Aug 28, 2013

### BruceW

3. Aug 28, 2013

### SteamKing

Staff Emeritus
Must be inflation.

4. Aug 28, 2013

### Zondrina

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

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

5. Aug 29, 2013

### Office_Shredder

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

Other than that I have nothing to add

6. Aug 30, 2013

### 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).

7. Aug 30, 2013

### 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 gonna 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.

Last edited: Aug 30, 2013
8. Aug 30, 2013

### Zondrina

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

9. Sep 29, 2013

### forsyth

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?