 | The electrical resistance corresponding to operating at the fundamental unit of conductance is 0.5*h/e^2, or 13000 ohms. Practical room temperature voltage shouldn't go below 0.25 V (or 10*kT) for a single switch. This means a single quantized conductor (like a nanowire) hooked up across this voltage would dissipate at least V^2/R=4.8 micro-Watt. A billion of these conducting currents (in parallel) would add up to 4.8 kW!
Obviously by increasing the wire cross-sectional area, this resistance will go down. And also obviously, by putting many of these quantized conductors in series across the same voltage difference, the power consumption would go down (higher resistance, less current).
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