For full credit, make your work clear to the grader. Show formulas used, essenti

Question

For full credit, make your work clear to the grader. Show formulas used, essential steps, and results with correct units and significant figures. Partial credit is available if your work is clear. Points shown in parenthesis Aluminum wiring rated at 30.0 A maximum current is to be installed in a home. For safety it produce no more heat than 15 watts per meter of length. a) What resistance should a 1.00 meter length of the wire have, to safely carry 30.0 A? b) How thick (diameter) does the wire have to be?

Explanation / Answer

1. (A) It should not produce heat more then 15 watt.

so using Pmax = 15 Watt

and P = I^2 R

15 = 30^2 R

R = 0.0167 Ohm Or 16.7 x 10^-3 ohm

(b) R = rho L / A

16.7 x 10^-3 = (2.65 x 10^-8 ohm m ) (1 m ) / A

A = 1.59 x 10^-6 m^2

and A = pi D^2 / 4 = 1.59 x 10^-6

D = 1.42 x 10^-3 m Or 1.42 mm

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