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Madeline Horn edited The_Q_values_came_from__.tex
over 8 years ago
Commit id: a3cc3279a3a5dc8190c787deb33d841fcf36dbd2
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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 \ref{fig:JohnsonSetUp}, which is $k_B$, the Boltlmann Constant.
Both K values were obtained from the slope of Figure
1 \ref{fig:JohnsonSetUp} 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.
\textbf{THIS PREVIOUS SENTENCE IS VERY DIFFICULT TO FOLLOW. TRY PUTTING IN TABLE FORM. ALSO, CHECK THE VALUES YOU HAVE USED FOR YOUR UNCERTAINTIES. YOU ARE SAYING THE UNCERTAINTY IS 100 TIMES LARGER THAN THE VALUE (!?) IS THAT WHAT YOU MEAN TO SAY? }