Question

00-gauge copper wire has a diameter of 9.00 mm. Calculate the power loss in 1.25 kilometer of such wire when it carries a current 90 A?

Answer 1

We have the equation of power loss due to resistance,

P = I² R

I is the current and R is the resistance.

Given that I =90 A

The resistance of the copper wire

R = L/A

A = area of cross section = π r²

r = diameter/2=9/2 = 4.5 mm = 4.5*10-³m

So A = π(4.5*10-³)² = 6.36*10-⁵m²

L= length of the wire = 1.25 km = 1250 m

= resistivity of copper = 1.72*10^-8 ohm metre

So resistance R = 1.72*10^-8*1250/(6.36*10^-5)

R = 0.338 ohm

So the power loss P = I² R

P = 90² *0.338

Power loss = 2737.8 Joules/sec

Or power loss in 1.25 km = 2738. Watts

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