deletions | additions       diff --git a/subsection_Johnson_Noise_Johnson_noise__.tex b/subsection_Johnson_Noise_Johnson_noise__.tex  index ee8fa0a..002521e 100644  --- a/subsection_Johnson_Noise_Johnson_noise__.tex  +++ b/subsection_Johnson_Noise_Johnson_noise__.tex 
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V_{\textrm{mean square ac voltage }} = = (4 R \Delta f) k_B T   \end{equation}  \begin{quote}  \begin{equation*}  \end{quote}  \begin{quote}  = (4 R \Delta f) k_B T   \end{quote}  \begin{quote}  \end{equation*}  \end{quote}  \begin{quote}  or   \end{quote}  \begin{quote}  \begin{equation*}  \end{quote}  \begin{quote}  {V_{ac}}^2 = = (4 R \Delta f) k_B T   \end{quote}  \begin{quote}  \end{equation*}  \end{quote}  or,