6. A 30.0 m long extension cord is made from two #19 gauge copper wire with a di

Question

6. A 30.0 m long extension cord is made from two #19 gauge copper wire with a diameter of 0.912 mm. (One carries current to the appliance while the other carries it from it. a) What is the resistance of each wire when at 20cc if the resistivity of copper at that is 1.67 105 Q b.) If the copper wire is to be replaced with an aluminum wire (resistivity of aluminum is 2.65 x 10 Q. m) of the same length, what is the minimum diameter the aluminum wire must have so that the new wire has as resistance no greater than the old?

Explanation / Answer

a)Resistance is given by

R = rho L/A

R = 1.67 x 10^-8 x 30/ 3.14 x (0.912 x 10^-3/2)^2 = 0.767 Ohm

Hence, R = 0.767 Ohm

b)R' = rho L/A

0.767 = 2.65 x 10^-8 x 30/[3.14 x R^2]

R = sqrt [2.65 x 10^-8 x 30/(3.14 x 0.767)]

R = 0.00057 m

D = 2R = 2 x 0.00057 = 0.00114 m = 1.14 mm

Hence, D = 1.14 m

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