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In order to understand how a superconductor works, it may be helpful to examine how a regular conductor works first. Certain materials such as water and metal allow electrons to flow through them fairly easily, like water through a garden hose. Other materials, such as wood and plastic do not allow electrons to flow through, so they are considered non-conducting. Trying to run electricity through them would be like trying to run water through a brick.
Even among the materials considered conductive, there can be vast differences in how much electricity can actually pass through. In electrical terms, this is called resistance. Almost all normal conductors of electricity have some resistance because they have atoms of their own, which block or absorb the electrons as they pass through the wire, water or other material. A little resistance may be useful to keep the electrical flow under control, but it can also be inefficient and wasteful.
A superconductor takes the idea of resistance and turns it on its head. A superconductor is generally composed of synthetic materials or metals such as lead or niobiumtitanium which already have a low atomic count. When these materials are frozen to nearly absolute zero, what atoms they do have grind to a near-halt. Without all of this atomic activity, electricity can flow through the material with practically no resistance. In practical terms, a computer processor or electric train track equipped with a superconductor would use very little electricity to perform its functions.
The most obvious problem with a superconductor is the temperature. There are few practical ways to supercool large supplies of superconductive material to the required transition point. Once a superconductor begins to warm up, the original atomic energy is restored and the material creates resistance again. The trick for creating a practical superconductor lies in finding a material which becomes superconductive at room temperature. So far, researchers have not discovered any metal or composite material which loses all of its electrical resistance at high temperatures.
To illustrate this problem, imagine a standard copper wire as a river of water. A group of electrons are in a boat trying to arrive at their destination upstream. The power of the water flowing downstream creates resistance, which makes the boat have to work even harder to get through the entire river. By the time the boat reaches its destination, many of the electron passengers are too weak to continue. This is what happens with a regular conductor -- the natural resistance causes a loss of power.
Now imagine if the river were completely frozen, and the electrons were in a sled. Since there would be no water flowing downstream, there would be no resistance. The sled would simply pass over the ice and deposit almost all of the electron passengers safely upstream. The electrons didn't change, but the river was altered by temperature to put up no resistance. Finding a way to freeze the river at a normal temperature is the ultimate goal of superconductor research.