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Lucy Liang edited Error_analysis_Johnson_Noise_The__.tex
over 8 years ago
Commit id: 5b7cc0d7caed246199b22ddb6ceed0cd5a8a1fad
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The discrepancy between our result ($1.46 \times 10^-23 \text{m2 kg s-2 K-1}$) and the accepted Boltzmann constant ($1.38 \times 10^-23 \text{m2 kg s-2 K-1}$)is approximately 5.8\% . Both sets of data we obtained (with a $1\textrm{k}\Omega$ resister and a $10\textrm{k}\Omega$) gave a consistent value for the Boltzmann constant which is a matter of accuracy rather than precision, so this error is most likely a systematic error.
Assuming that our thermometer is accurate (for room temperature), the temperature within the instrument, where the resister is, may be higher. As we can see in Eq.~ \ref{eq:boltzmann}, with a higher
$\textrm{T}$, $\textrm{T(K)}$, we would have a lower $\textrm{K}_\textrm{B}$ value which is opposite to what our value is, so this is unlikely what is causing the error.
R? The measured values(\textbf{add table of measured vs. actual in appendix}) for Rin is about 0.3 percent different from the claimed value. Rin is also not the main source of error.