An air conditioner draws 15A at 220-V ac. The connecting cord is copper wire wit

Question

An air conditioner draws 15A at 220-V ac. The connecting cord is copper wire with a diameter of 1.538mm.

a. How much power does the air conditioner draw?
P= _________ W

b.If the total length of wire is 17m , how much power is dissipated in the wiring?
PR=__________W

c.If no. 12 wire, with a diameter of 2.053 , was used instead, how much power would be dissipated?
PR=__________W

d. Assuming that the air conditioner is run 11h per day, how much money per month (30 days) would be saved by using no. 12 wire? Assume that the cost of electricity is 12 cents per kWh.

=_________ cents/month

Explanation / Answer

Part A)

P = IV = (15)(220) = 3300 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 = (7.69 X 10-4)2 = 1.858 X 10-6 m2

R = (1.7 X 10-8)(17)/(1.858 X 10-6) = .156

Power lost = I2R = (15)2(.155) = 35 W

Part C)

New wire provides new area. New area = (1.0265 X 10-3)2 = 3.31 X 10-6 m2

New R = (1.7 X 10-8)(20)/(3.31 X 10-6) = .103

Power lost = I2R = (15)2(.103) = 23.1 W

Part D)

When you change the wire, you lose less power. The amount less loss = 35 - 23.1 = 11.9 W

11.9 W = .0119 kW

Running the air conditioner for 11 hours per day for 30 days is 330 hours

Multiplying that by the net power loss, you get 3.927 kWhr

Since the cost is 12 cents per kWhr, multiply and get 47 cents in savings

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