Question

In: Physics

Estimate the total power that your household draws from DTE, in one month. Then, if possible,...

Estimate the total power that your household draws from DTE, in one month. Then, if possible, compare the total power (in kWh) to the actual power that you were billed, last month. To successfully "compare" the numbers, you should determine the percent difference between your estimated power and the actual power that your household payed for last month.

You should show how you estimated your total power and your percent difference calculation.

Note:

DTE bills you in kWh. This stands for "kilo-Watt hours." To determine the number of kWh that you pay for, you simply take the power of an object and multiply by the time that the object is used (in hours). You may have to look up what DTE actually charges its residential customers per kWh.

Example:

For a 100 W lightbulb, that is used for six hours in a day, the bill would be for 600 Wh. This can be converted to 0.6 kWh. If you used the bulb for six hours a day, for the 31 days in March, the total monthly power draw from DTE would be 18.6 kWh.

Solutions

Expert Solution

Ans. Let us suppose, we want to calculate total power consumed in March '20 i.e for 31 days.

Total power that household draws from DTE in March '20 :

To calculate the following, we have to know the power rating of household appliances and no. of hours per day those were used.

Let us draw a table and list out the household appliances, it's power rating and no. of hours per day those were used.

Appliances Power rating No. of hours used per day
2 ceiling fans 70 W 10
3 light bulbs 60 W 8
Laptop 100 W 6

For 2 ceiling fans, each of 70 W, monthly energy consumption for March '20 = Power X Total time

Wh

kWh

kWh

For 3 light bulbs, each of 60 W, monthly energy consumption for March '20 = Power X Total time

Wh

kWh

kWh

For a laptop of 100 W, monthly energy consumption for March '20 = Power X Total time

Wh

kWh

kWh

So, total estimated power drawn from DTE in March '20 kWh

kWh (Ans.)

Now, let us suppose that DTE charges $ 0.12 per unit (kWh) and the actual payable amount which was billed for March '20 is $ 13.

Actual power that household payed for March '20   kWh

kWh

Percentage difference between the actual power and the estimated power :

Percentage difference = | (Actual power - Estimated power) / (Average of actual power and estimated power) | X 100 %

(Ans.)

N.B. ::  This problem basically belongs to "Work, Energy and Power" topic in Physics. To understand this problem, you need to know all the basic concept and formulae of work, energy and power.

If you are able to carry out in this way, you will be able to solve these kind of problems easily.


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