Review Conceptual Example Z as an aid in solving this problem. A portable electr

Question

Review Conceptual Example Z as an aid in solving this problem. A portable electric heater uses 16.9 A of current. The manufacturer recommends that an extension cord attached to the heater receive no more than 2.36 W of power per meter of length, what is the smallest radius of copper (resistivity 1.72 x 10-8 -m) wire that can be used in the extension cord? (Note: An extension cord contains two wires.) of power per meteroflength, what uI UnitsIt No unlts The number of significant digits is set to 3

Explanation / Answer

We can use P = I²R to find the resistance (R) of the wire:

R = 2.36 W/16.9^2 A² = 0.00826

But this is for the path out and the return path so we divide this in half:

R = 0.00413

Now we use the equation for resistance given, resistivity (), Length (L), and cross-sectional area (A) equation:

R = L/A

= 1.72 x 10^-8 •m, L = 1 m, and A = r² for a circular conductor.

0.00413 = (1.72 x 10^-8 •m)(1 m)/r²

Solving for the radius:

r = [(1.72 x 10^-8 •m)(1 m)/{(0.00413 )}]

r = 0.00115 m

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