Discussion
Johnson Noise in resistor R is given by :
Answer: A
Johnson noise is \(\bar{v}_{\text{rms}} = (4KTR\Delta f)^{1/2}\).
Thermal (Johnson-Nyquist) noise arises from the random thermal motion of charge carriers in any resistor. Nyquist showed that its mean square voltage over a bandwidth \(\Delta f\) is \(4kTR\Delta f\), independent of frequency (white noise) and present even with no current flowing.
For example, a 1 k\(\Omega\) resistor at 300 K over 10 kHz gives about 0.4 \(\mu\)V rms. \((2qI\Delta f)^{1/2}\) is shot noise current, which depends on a DC current and multiplied by R gives a shot noise voltage. The forms \(A/f\) and \(A/f^{2}\) describe flicker (1/f) and other frequency-dependent noise.
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