deletions | additions       diff --git a/To_analyze_this_data_we__.tex b/To_analyze_this_data_we__.tex  index b8ed07a..9f08942 100644  --- a/To_analyze_this_data_we__.tex  +++ b/To_analyze_this_data_we__.tex 
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To analyze this data, we made a plot of resistance (ohms) versus $V^2$ so that we could analyze the slope. The equation used to understand why we did this is: $V^2 = 4 K T R \Delta f$, where K 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 bandwidth that we varied by changing the values on the low and high pass filters. In order to find the bandwidth, we had to use values that came from the Noise Fundamentals Test Data (Table 2) and gave us the real measured  values from the filters. You can see the values we used in Table 2, and as you can see, the real measured  values are different from the given nominal  values. After using the real measured  values from the Noise Fundamentals test data, we had to calculate the Equivolent Noise Bandwidth in order to find \Delta f. To do this, we used an equation: $\textrm{ENBW} = f_c (Pi \cdot Q / 2)$. The Q values came from the Noise Fundamental test data and are shown in Table 2. By using this equation, we found the Equivolent Noise Bandwith or \Delta f. After plotting $V^2$ versus Bandwidth ($\Delta f$), we were able to find the slope. Because of how we plotted the data, the slope is therefore: $4 K R T$ and we know the values of R and T because we kept them constant. After solving for K, we found the Boltzmann Constant for our data to be $1.908 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$. This is close to the actual Boltzmann Constant ($1.38064852 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$), but we still need to subtract the instrument noise from the total noise in order to see if we got a better value.