deletions | additions       diff --git a/To_analyze_this_data_we__1.tex b/To_analyze_this_data_we__1.tex  index 9dead3f..70aa67e 100644  --- a/To_analyze_this_data_we__1.tex  +++ b/To_analyze_this_data_we__1.tex 
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To analyze this data, In order to find the $k_B$,  we made will be plotting the data as $V^2/4TR$ versus $\Delta f$ to find the slope which is proportional to $k_B$. Or, if you prefer, you can create  a plot of resistance (ohms) versus where the slope is equal to $k_B T \Delta f$ -(plotting  $V^2$ versus $4R$), than solve for $k_B$. Personally, we found it easier to plot the data  so thatwe could analyze  the slope. slope was proportional to $k_B$.  The equation used to understand why we did this is shown in Equation \ref{eq:Equatoin} ($V_{\textrm{mean square ac voltage }} = = (4 R \Delta f) k_B T$). where $k_B$ is the Boltzmann Constant we are looking for, $T$ is the temperature in Kelvin, $R$ is the resistance in ohms, and $\Delta f$ is the ``equivalent noise bandwidth'' (ENBW) that we varied by changing the values on the low and high pass filters.In order to find the $k_B$, we will be plotting the data as $V^2/4TR$ versus $\Delta f$ to find the slope which is proportional to $k_B$. Or, if you prefer, you can create a plot where the slope is equal to $k_B T \Delta f$ -(plotting $V^2$ versus $4R$), than solve for $k_B$. Personally, we found it easier to plot the data so that the slope was proportional to $k_B$.  In order to find the bandwidth, we had to use values that came from the Noise Fundamentals Test Data (\href{http://teachspin.com/instruments/noise/index.shtml}{Teachspin Manual}) (\ref{table:Johnson2}), which gave us the actual measured values from the different filters and amplifiers. You can see the values we used in \ref{table:Johnson2}, and as you can see, the measured values (from Noise Fundamentals Test Data) are different from the nominal values (values given on the apparatus). After using the measured values from the Noise Fundamentals test data, we had to calculate the Equivolent Noise Bandwidth (ENBW) in order to find $\Delta f$. To do this, we used an equation: