a.) Find the individual monthly (30-day) electric costs (to the nearest dollar)

Question

a.) Find the individual monthly (30-day) electric costs (to the nearest dollar) for each of the following household appliances if the utility rate is $0.12/kWh: central air conditioning that runs 30% of the time; a blender that is used 0.50 h/month; a dishwasher that is used 8.0 h/month; a microwave that is used 15 min/day; the motor of a frost-free refrigerator that runs 15% of the time; a stove (burners plus oven) that is used a total of 10 h/month; and a color television that is operated a total of 10 h/ month.

b.) Determine the percentage that each appliance contributes to the total monthly electric cost.

c.) What is the resistance of each appliance and current in each appliance when they are operating?

Using this table

Appliance Power Current

Central Air conditioning 1500 W 12.5 A

Blender 800 W 6.7A

Dishwasher 1200 W 10.0 A

Microwave 900 W 5.2 A

Refrigerator 500 W 4.2 A

Stove (top burners) 6000 W 50.0 A

Stove (oven) 4500 W 37.5 A

Television, color 100 W 0.83 A

Explanation / Answer

30 days is 720 hrs

For the air conditioner, the hrs are (720)(.3) = 216 hrs

Multiply kW times hrs used times cost per kwh to get cost

(1.5)(216)(.12) = $38.88

For the blender

(.8)(.5)(.12) = $0.048 which is 4.8 cents (almost a nickel)

For the dishwasher

(1.2)(8)(.12) = $1.15

For the microwave (15 minutes per day times 30 days = 7.5 hrs)

(.9)(7.5)(.12) = $0.81

For the Refrigerator (720)(.15) = 108 hrs

(.5)(108)(.12) = $6.48

For the stove

(6)(10)(.12) + (4.5)(10)(.12) = $12.60

For the TV

(.1)(10)(.12) = $0.12

Total cost = $60.088

Percent of AC = 64.7%

Percent of Blender = 0.08%

Percent of Dishwasher = 1.91%

Percent of Microwave = 1.35%

Percent of Refrigerator = 10.8%

Percent of Stove = 21.0%

Percent of TV = 0.20%

The currents are listed in your table.

The resistances are found using V = IR

For the AC, R = 9.6 Ohms

For the Blender, R = 17.9 Ohms

For the Dishwasher, R = 12 Ohms

For the Microwave, R = 23.1 Ohms

For the Refrigerator, R = 28.6 Ohms

For the Stove Burners, R = 2.4 Ohms

For the Stove Oven, R = 3.2 Ohms

For the TV, R = 144.6 Ohms

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