deletions | additions       diff --git a/subsection_Method_for_Johnson_Noise__.tex b/subsection_Method_for_Johnson_Noise__.tex  index 39c600d..7757da7 100644  --- a/subsection_Method_for_Johnson_Noise__.tex  +++ b/subsection_Method_for_Johnson_Noise__.tex 
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\textbf{Experimental Setup and Measurement - refer to theory on PLAN}  To In order to  get the best measurement of Johnson Noise, desired data,  we wanted decided to vary $\Delta f$ in order  to vary the $R_{in}$ from bandwidth. To do this, we kept the resistance ($R$) constant, but did three different trials where each trial had a different $R$ value. The values for $R$ are as follows:  $10 \textrm{ k}\Omega$, $1 \textrm{ k}\Omega$ k}\Omega$,  and $1 \Omega$. This is important because if our apparatus and measurements are correct, all of the different $R_{in}$ should generate the same value for You can perform  the Johnson Noise, $k_B$. 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, Noise experiment by varying resistance for a given bandwidth ($\Delta F$), but  we took data with the $1 \Omega$ resistor. chose to vary $\Delta f$ and keep resistance constant.  In order We chose  to get do this because if our apparatus and measurements are correct, all of  the desired data, we decided to vary $\Delta f$ in order to vary different $R_{in}$ should generate  the bandwidth. To do this, we kept same value for the Johnson Noise, $k_B$. We chose  theresistance ($R$) constant, but did  three different trials where each trial had a different $R$ value. The values for $R$ are as follows: resistances because the  $10 \textrm{ k}\Omega$, k}\Omega$ and  $1 \textrm{ k}\Omega$, and k}\Omega$ were used to calculate the $k_B$ while the  $1 \Omega$. \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. We want 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 $<(V_J_from_R)^2> / R = 4 k T \Delta f$, so you expect that ratio to be the same even if you change $R$, just as long as you don't change $T$ or $\Delta f$. That means the slope $m = 4 kT \Delta f in <(V_J_from_R)^2> = m R$ should also remain constant.  As seen in equation \ref{eq:NyquistPredictionForJohnsonNoise2}, we will be measuring the $<(V_J + V_{\textrm{other noise}})^2>$.