A section of superconducting wire carries a current of 115 A and requires 1.00 L

Question

A section of superconducting wire carries a current of 115 A and requires 1.00 L of liquid nitrogen per hour to keep it below its critical temperature. For it to be economically advantageous to use a superconducting wire, the cost of cooling the wire must be less than the cost of energy lost to heat in the wire. Assume that the cost of liquid nitrogen is $0.30 per liter, and that electric energy costs $0.10 per kWh. What is the resistance of a normal wire that costs as much in wasted electric energy as the cost of liquid nitrogen for the superconductor?

Explanation / Answer

Here,

cost of cooling the superconducting wire = 1 * 0.30

cost of cooling the superconducting wire = 0.30 $

Now, let's assume the Power used in the wire is P W ,

Now,

P = 1000 * 0.30/.10

P = 3000 W

Now , as P = I^2 * R

3000 = 115^2 * R

R = 0.227 Ohm

the resistance of a normal wire is 0.227 Ohm

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