# thermal noise and reason of '4' coeffecient

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in this relation for thermal noise (or resistor noise or jahnson,...):
N=4RkTRB
I want the reason of that 4 as coeffecient.where does that 4 come from? or why?
consider a V source as the source of noise and a series resistor.(may help)

#### A.Anand Srinivasan

Pnoise=(Vnoise)²/2R here the 2 is due to average power concept....

noise here the RMS value is used for Vnoise which leads to 1/(√2)² and hence leading to another 2 in the denominator...

we know that Pnoise=kTΔf .... Vnoise²=4kRTΔf.... here a Vnoise would be denoted by a e with a bar above it to mean that the rms value is being used....