A copper wire has a resistance of 27 ? at 11? C. An aluminum wire has three time

Question

A copper wire has a resistance of 27 ? at 11? C. An aluminum wire has three times the length and two times the radius of the copper wire. The resistivity of copper is 0.6 times that of aluminum. Both Al and Cu have temperature coefficients of resistivity of 0.004? C?1.

(a) What is the resistance of the aluminum wire at 11? C? __?

(b) The graph shows a V-I plot for the copper wire. What is the resistance of the wire when operating steadily at a current of 10 A? ____?

(c) What must the temperature of the copper wire have been when operating at 10 A? Ignore changes in the wire's dimensions. ___? C

Explanation / Answer

a)resistance of the aluminum wire at 11° C = 27 x 3x0.6/4 = 12.15 ohm b) R = 300/10 = 30 ohm c)R =R0(1+a(T-11)) = T-11 = 16.85/0.004 T = 4223.5 ohm

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