deletions | additions       diff --git a/section_Experiment_on_Johnson_Noise__.tex b/section_Experiment_on_Johnson_Noise__.tex  index 0a2d9e8..1abf80e 100644  --- a/section_Experiment_on_Johnson_Noise__.tex  +++ b/section_Experiment_on_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. The goal is 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 found in Equation \ref{eq:Equatoin}, \ref{eq:Equatoin}  to produce produces  $k_B$even  if you change $R$, $R$  just as long as you don't change $T$ or $\Delta f$. That means the slope should also remain constant. Because we want to keep the $R$ the same, we decided to vary $\Delta f$, so we needed to have a set-up where there was both a low pass and a high pass. This way, we could vary $\Delta f$ with 36 different settings. We also used two amplifiers in order to amplify the desired signal. Those values were: $X600$ for the first gain and $X1000$ for the second gain. We also squared the signal (an amplifier of AxA) in order to measure the voltage as: $<(V_J + V_{\textrm{other noise}})^2>$.