deletions | additions       diff --git a/subsection_Method_for_Johnson_Noise__.tex b/subsection_Method_for_Johnson_Noise__.tex  index 7757da7..32fb87e 100644  --- a/subsection_Method_for_Johnson_Noise__.tex  +++ b/subsection_Method_for_Johnson_Noise__.tex 
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We chose to do this because if our apparatus and measurements are correct, all of the different $R_{in}$ should generate the same value for the Johnson Noise, $k_B$. We chose the three different resistances because the $10 \textrm{ k}\Omega$ and $1 \textrm{ k}\Omega$ were used to calculate the $k_B$ while the $1 \Omega$ measurement was used as an error source that needed to be subtracted. As with all electronics, there is some innate error associated with the device, in order to subtract this, we took data with the $1 \Omega$ resistor. We want to find a ratio in which both the numerator and denominator get bigger as you increase $R_in$ (the resistor that is the source of the voltage fluctuations), so the slope $k_B$ remains the same.   Nyquist found theoretically that the ratio $<(V_J_from_R)^2> / R = 4 k T \Delta f$, so you expect that ratio found in Equation \ref{eq:Equatoin},  to be the same produce $k_B$  even if you change $R$, just as long as you don't change $T$ or $\Delta f$. That means the slope $m = 4 kT \Delta f in <(V_J_from_R)^2> = m R$ should also remain constant. As seen in equation \ref{eq:NyquistPredictionForJohnsonNoise2}, we will be measuring the $<(V_J + V_{\textrm{other noise}})^2>$.