Question

Copper wire of diameter 0.229 cm is used to connect a set of appliances at 120 V, which draw 1750 W of power total. The resistivity of copper is 1.68×10−8Ω⋅m.

1. What power is wasted in 28.0 m of this wire?

Express your answer to three significant figures and include the appropriate units.

2. What is your answer if wire of diameter 0.417 cm is used?

Express your answer to three significant figures and include the appropriate units.

Answer 1

power drawn by set of appliances P = V*I

V = potential difference = 120 V

I = current in the wire

I = P/V = 1750/120 = 14.6 A

a)

resistance of copper wire R = rho*L/A

A = area of cross section = pi*r^2

r = radius of wire = 0.229/2 = 0.1145 cm = 0.1145*10^-2 m

Resistance R = 1.68*10^-8*28/(pi*(0.1145*10^-2)^2) = 0.114 ohm

power wasted in wire = I^2*R = 14.6^2*0.114 = 24.3 W

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2)

resistance of copper wire R = rho*L/A

A = area of cross section = pi*r^2

r = radius of wire = 0.417/2 = 0.2085 cm = 0.2085*10^-2 m

Resistance R = 1.68*10^-8*28/(pi*(0.2085*10^-2)^2) = 0.0344 ohm

power wasted in wire = I^2*R = 14.6^2*0.0344 = 7.33 W