An air conditioner draws 14 A at 220-V ac. The connecting cord is copper wire wi

Question

An air conditioner draws 14 A at 220-V ac. The connecting cord is copper wire with a diameter of 1.758 mm. a) how much power does the air conditioner draw? b.) If the total length of wire is 10m, how much power is dissipated in the wiring? c.) If no. 12 wire, with a diameter of 2.053 mm, was used instead, how much power would be dissipated? d.) assuming that air conditioner is run 15 h per day, how much money per month (30 days) would be saving by using no. 12 wire? Assume that the cost of electricity is 12 cents per kWh.

Explanation / Answer

Part A)

P = IV = (14)(220) = 3080 W

Part B)

We need the resistance of the wire, where R = L/A

The resistivity of copper is 1.7 X 10-8 m

The area is r2 = (8.79 X 10-4)2 = 2.427 X 10-6 m2

R = (1.7 X 10-8)(10)/(2.427 X 10-6) = .07

Power lost = I2R = (14)2(.07) = 13.72 W

Part C)

New wire provides new area. New area = (1.0265 X 10-3) = 3.31 X 10-6 m2

New R = (1.7 X 10-8)(10)/(3.31 X 10-6) = .0514

Power lost = I2R = (14)2(.0514) = 10.07 W

Part D)

When you change the wire, you lose less power. The amount less loss = 13.72 - 10.07 = 3.65 W

3.65 W = 3.65 X 10-3 kW

Running the air conditioner for 15 hours per day for 30 days is 450 hours

Multiplying that by the net power loss, you get 1.6425 kWhr

Since the cost is 12 cents per kWhr, multiply and get 20 cents in savings

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