Johnson Noise
Electronic noise in circuits is often very difficult to combat when one attempts to make measurements to high precision. There are many sources of this electronic noise; here we focus on Johnson Noise.
Johnson Noise (at a given frequency) is dependent upon two variables: the temperature of the system, and the resistivity in the circuit.
Microscopically, the electricity charge carriers (electrons) have some average drift velocity. This average drift velocity is the average of each particle's individual velocity. Each electron's velocity corresponds to some voltage per electron; even though there is an average current, there is some variability in the individual particles current, providing a variability in the output power (voltage squared).
Even without driving a circuit with any voltage, one will be able to observe this Johnson Noise, which happens to occur on a wide frequency spectrum.
We derive the expression for Johnson Noise,  , in two different ways on the next two pages.
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