Madeline Horn edited The_Q_values_came_from__.tex  over 8 years ago

Commit id: 051c52bebdd589075ac201b74ebfd6a4d8c95aea

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The Q values came from the Noise Fundamental test data and are shown in Table \ref{table:True_Bandwidth1}. By using this Equation \ref{eq:ENBW}, we found the Equivolent Noise Bandwith or $\Delta f$. After plotting $V^2/4TR$ versus Bandwidth ($\Delta f$) for both $10K \Omega$ and $1K \Omega$, we were able to find the slope. The slope of Figure 1 \ref{fig:JohnsonSetUp}, which  is $k_B$, the Boltlmann Constant. Both K values were obtained from the slope of Figure 1 and both values were $1.46 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1} \pm2.5 \cdot 10^{-21} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$ and $1.46 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1} \pm2.6 \cdot 10^{-21} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$. Where the first value listed was the $1K \Omega$ resistor and the second value was the $10K \Omega$ resistor.