= Thermal electrical noise
{title2=$v_{n,\rm rms}=\sqrt{4k_{\rm B}TRB}$}
= Johnson-Nyquist noise
{c}
{synonym}
= Johnson noise
{c}
{synonym}
<Thermal electrical noise> is the fluctuating <electric potential difference> or <electric current> produced by <thermal fluctuations> in a dissipative <electrical circuit>, even without an applied voltage. A <resistor> at <thermal equilibrium> is both a source of <noise> and a sink for electrical <energy>. Its <electrical resistance> describes the dissipation, and its absolute <temperature> sets the scale of the fluctuations. This connects a practical limit on <signal-to-noise ratio> to <statistical mechanics>: a warm, unbiased <resistor> is not electrically silent.
<John Bertrand Johnson> measured the effect using a vacuum-tube <amplifier> and thermocouple; his 1928 paper reported agreement with the <Boltzmann constant>. <Harry Nyquist>'s companion paper calculated the effect from <thermodynamics> and <statistical mechanics>.<Thermal Agitation of Electricity in Conductors by John Bertrand Johnson>[Johnson, Thermal Agitation of Electricity in Conductors, Physical Review 32, 97–109 (1928), abstract: amplifier and thermocouple measurement]{ref}<Thermal Agitation of Electric Charge in Conductors by Harry Nyquist>[Nyquist, Thermal Agitation of Electric Charge in Conductors, Physical Review 32, 110–113 (1928), abstract: thermodynamic and statistical calculation]{ref}
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