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In the chapter on thermal noise it says that the spectral distribution per Ohm of resistance is a certain shape (constant till a certain f and then ~ 1/f²).

This means that, in the frequency range below the cutoff value, the noise power in the bandwidth [tex]\Delta f [/tex] is equal to [tex]4k_B T \Delta f[/tex] per Ohm of resistance.

What is this expression? Is it physically the power dissipitating in the resistor, at least a certain part of it corresponding to a specific selection of frequencies in the Fourier transform? So if you'd integrate over all the frequencies, you'd have the power dissipitated by the current in a resistor? Isn't this usually I or V-dependent? Or

**is this is a different phenomenon**

*additional*to the Joule heating?The next sentence I find the most puzzling:

The root mean square (rms) noise voltage on a resistor R will then be equal to [tex]V_{rms} = \sqrt{4k_B T (\Delta f )R}[/tex]. It can give large disturbances in broadband measurements.

So the rms voltage is a measure for the noise on the regular intended voltage, correct? But how is this dependent on a frequency-interval? What does it mean to say that if my interval of frequencies is bigger, the noise on my voltage is larger? I don't understand what interval of frequencies we're talking about. I would think it would only make sense if we integrated it over

*all*the frequencies, then I would think the rms voltage would stand for the mean noise on the voltage, but what does it mean for a selected range of frequencies? What is a "broadband measurement"? Basically: what's the physical relevance of [tex]\Delta f[/tex]? For example, the next line is "At 300K on 1 megaOhm resistor and Delta f = 10 MHz [...]" I get what it means to say "300K" and "1 megaOhm resistor", but not what "Delta f = 10 MHz" means...