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

cost of 1 L of liquid nitrogen = $0.30

cost of electrical energy =$0.10 per kW h

so 3kWh of electrical energy can be used with the cost of nitrogen per hour

so electrical power P = 3kW

P =i2R

R = P/i2

i = 115 A

plugging in the values we get

R = 0.23 ohms

the resistance required is 0.23 ohms

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