this is for holding javascript data
Madeline Horn edited In_order_to_find_the__.tex
over 8 years ago
Commit id: 7c9a8b1feeee394363f594368a9069e1d931ac6b
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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 $k_B$. 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.