Physics Help Please!! Power, kWh, Joule, Watt-Best answer will be picked ASAP?

Question

Can someone help, my 7th grade cousin has this assignment and it is regarding a workup on the powerbill and we are using my powerbill?

On my powerbill the total kWh used this month is 222,
Days: 27, Avg KWh per Day is 8, & Avg Cost per Day is $0.87.
I needed some help doing some analysis.

To the nearest tenth of a cent, how much does 1 kWh cost?
-is that 0.087 cent?

I was trying to figure out in joules how energy i consume? Is there a formula and how do I do that?
-From my own research the answer I got was 799,200,000 J

Next, I wanted to find the average power consumption in Watts? (I am not sure what formula to use or how to go about this?

Also, the power company has noted that I am provided with 120 V? Based on the power consumption, what is the average current running in my house?

And in general, I was wondering how much would it cost me to leave all the lights on in the house for one day. I have 70 bulbs in my house that are all 75 watts?

Thanks!

Answer 1

We're given:

Total kWh this month = 222
AVG kWh per day = 8
AVG cost/day = $0.87
Total number of days is 27

(1) To the nearest tenth of a cent, how much does 1 kWh cost?

Total cost = 27 x $0.87 = $23.49

Cost per kWh = $23.49/222= $0.1058 or 10.6 cent per KWh if we round it to nearest tenth of a cent

Using the AVG kWh per day to calculate is not accurate because it is an average. We need to use the total kWh used and the total cost.

(2) Total joules consumed = 222 kWh x (3.6x10^6 J/kWh)

= 799,200,000 joules Yes, you got it right!

(3) Again here we need to use the total energy used, which is 222 kWh and the total number of hours:

222 kWh / (27 days) (24 hours/day) = 342.59 watts

(4) P = VI, so I = P/V = 342.59/120 = 2.85 Amps is the AVG current

(5) 70 light bulbs x 75 watts/bulb = 5250 watts or 5.25 kW

Running all the lights for 24 hours:

5.25 kW x 24 hours = 126 kWh

Now we used the answer found in (1): AVG cost per kWh = 10.6 cent

126 kWh x 10.6 cent/kWh = $13.36 is how much it'll cost you.

Answer 2

You used 222 kWh over 27 days with an average kWh usage of 8 kWh per day. Your cost per day is $0.87

If you use 8 kWh per day, and your cost is $0.87 per day, then the cost per kWh is: $0.87 / day ÷ 8 kWh / day = $0.10875 per kWh. 10.875¢ per kWh.

Energy can be expressed in the following units:
kWh, Joules, Calorie, Newton-meter

1 kWh = 3,600,000 Joules. The reason for the large conversion factor is because you’ve got kilowatts, (1000 watts) and hours (3600 seconds)

222 kWh x 3,600,000 Joules / kWh = 799,200,000 Joules

Your average power consumption is your average usage over 27 days. You need to convert this to hours. 27 days x 24 hours / day = 648 hours.

Your average power consumption is 222 kWh / 648 h = 0.342 kW or 342 watts.

You could have also computed this as 8 kWh / 24 h = 0.333 kW. The slight difference is due to the utility rounding the daily usage values.

I will use 342 watts for the remaining calculations:

Note: There is a concept called power factor that applies to AC power consumption, however this is beyond the scope of 7th grade science class. We will assume unity power factor for the remaining calculations.

Voltage x Current = Power
volts x amps = watts

We know watts and volts, so we use algebra to solve for amps.
amps = watts / volts
342 watts / 120 volts = 2.85 amps

70 light bulbs x 75 watts / bulb = 5250 watts or 5.25 kW
Burning for 24 hours: 5.25 kW x 24 hours = 126 kWh.

At your energy cost of $0.10875 per kWh:
126 kWh x $0.10875 = $13.70 per day

Answer 3

Hmmm, I've answered this before.

a) Divide the energy used in a day (given) by the cost per day (also given). That will give you the energy cost.

b) To convert kW-hours to joules, convert kW to W (multiply by 1000) and hours to seconds (multiply by 3600)

c) 8 kW-hours / day. Convert the days to hours (divide by 24) and cancel the hours. That's your average power.

d) Current*Voltage = Power. You just found power. Voltage is given. Solve for Current.

e) 70 bulbs * 75 watts/bulb * 24 hours = kilowatt hours you'd burn in a day. Divide that by your answer to (a) and you'll get your cost per day.

Good luck!