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Lucy Liang edited Error_analysis_Johnson_Noise_The__.tex
over 8 years ago
Commit id: 413cadd845c1de53e4e6246644c91c45a3f3cbfd
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Error analysis(Johnson Noise)
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
$1\textrm{K\Omega}$ $1\textrm{K}\Omega$ resister and a
$10\textrm{K\Omega}$) $10\textrm{K}\Omega$) 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 $\textrm{T}$, 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.