ELECTRICAL WIRING

Electrical wiring is used all over the world to easily transport energy from place to place. A disadvantage of transporting energy by electrical wires is that the resistance in the wires turn electrical energy into heat (I²R loss). Because of these heat losses, the wiring can become quite hot. 

In this exercise, we are examining a copper (λ = 400 W/m°C) wire which we assume to be perfectly insulated all around, so there are no heat losses in the radial direction (take just 1 wire, not 4 stacked as is shown in the picture). Heat is produced uniformly throughout the whole wire, resulting in a total heat production in the cable of 20 W. To prevent the wire from becoming overly hot, it is cooled at both ends, which results in it having a constant temperature of 0 °C at the ends. The length of the wire is 200 meters and the diameter equals 25 centimeters.

Make a sketch of this situation! 

You can check your sketch by comparing it to the one we made. You can get a full screen image of the sketch by clicking on the picture below. It is important that you try it by yourself before looking at our version!