Question

Consider a power plant located 53 km away from a residential area, which uses 0-gauge (A = 42.40 mm²) copper wire to transmit power at a current of I = 7.00 A. How much more power (in W) is dissipated in a copper wire than would be in a superconducting wire?

Answer 1

As there is zero resistance in superconducting wire, so there is no energy loss due to resistance in the form of heat.

There will be a power loss in the form oh heat in copper wire,say P

We have P=i²R where i=current and R=resistance

We will firstly find resistance

R=rho x length/area

Rho=resistivity =1.7*10^-8

Length =53km=53*10³m

Area=3.14*(42.40*10-³)²/4

Area=1411*10^-6m²

So resistance =1.7*10^-8*53*10³/1411*10^-6

Resistance =0.0638*10=0.368ohm

Now power=7²*0.638=49*0.638=31 watt. This much extra amount of power is dissipated in copper wire.