Editing Johnson–Nyquist noise (section)

=== RMS noise voltage ===
[[File:JohnsonNoiseEquivalentCircuits.svg|thumb|Figure 4. These circuits are equivalent:<br><br>'''(A)''' A resistor at nonzero temperature with internal thermal noise;<br><br>'''(B)''' Its [[Thévenin equivalent]] circuit: a noiseless resistor [[Series and parallel circuits|in series]] with a noise [[voltage source]];<br><br>'''(C)''' Its [[Norton equivalent]] circuit: a noiseless resistance [[Series and parallel circuits|in parallel]] with a noise [[current source]].|303x303px]]The square root of the mean square voltage yields the [[root mean square]] (RMS) voltage observed over the bandwidth <math>\Delta f </math>:

: <math>V_\text{rms} = \sqrt{\overline {V_n^2}} = \sqrt{ 4 k_\text{B} T R \, \Delta f } \, .</math>

A resistor with thermal noise can be represented by its [[Thévenin equivalent]] circuit (Figure 4B) consisting of a noiseless resistor in series with a gaussian noise [[voltage source]] with the above RMS voltage.

Around room temperature, 3&nbsp;kΩ provides almost one microvolt of RMS noise over 20&nbsp;kHz (the [[human hearing range]]) and 60&nbsp;Ω·Hz for <math>R \, \Delta f</math> corresponds to almost one nanovolt of RMS noise.