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 1.770mm

How much power does the air conditioner draw?

If the total length of wire is 11m , how much power is dissipated in the wiring?

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

Assuming that the air conditioner is run 14h 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.

Explanation / Answer

a) 15 x 220 = 3300 watts

b) Resistance of a wire in ?
R = ?L/A
? is resistivity of the material in ?-m
L is length in meters
A is cross-sectional area in m
A = ?r, r is radius of wire in m
resistivity Cu 17.2e-9 ?-m

r = 1.770/2 = 0.885 mm = 0.000885 m
L = 2 x 11 (there are 2 wire in the cable)
A = ?(0.000885) = 2.45e-6 m
R = (17.2e-9)(22) / (2.45e-6)
R = 0.154 ohms

Voltage drop is 15 x 0.154 = 2.316 volts
power loss = 15 x 2.053 = 30.79 watts

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