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 1.745 mm.
How much power does the air conditioner draw?
P=______W
If the total length of wire is 10m , how much power is dissipated in the wiring?
PR=______W
If no. 12 wire, with a diameter of 2.053mm , was used instead, how much power would be dissipated?
PR=________W
Assuming that the air conditioner is run 12h 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 .
________Cent/month

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 = (8.725 X 10-4)2 = 2.392 X 10-6 m2

R = (1.7 X 10-8)(10)/(2.392 X 10-6) = .071

Power lost = I2R = (14)2(.071) = 13.92 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 = 13.92 - 10.07 = 3.85 W

3.85 W = 3.85 X 10-3 kW

Running the air conditioner for 12 hours per day for 30 days is 360 hours

Multiplying that by the net power loss, you get 1.386 kWhr

Since the cost is 12 cents per kWhr, multiply and get 17 cents in savings

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.