Madeline Horn edited untitled.tex  over 8 years ago

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\textit{Pre Write Up}   In order to find the Boltzmann constant and the charge of the electron, we had to perform the Johnson Noise Experiment and the Shot Noise Experiment. We performed the Johnson Noise Experiment in order to find the Boltzman Constant: $1.38064852 × 10^{-23} \textrm{m}^2 \textrm{kg} \textrm{ m}^2 \textrm{ kg}  \textrm{ s}^{-2} \textrm{K}^{-1}$. \textrm{ K}^{-1}$.  We performed the Shot Noise Experiment in order to find the charge of an electron: 1.60217662 × 10-19 coulombs. \textit{Johnson Noise}  To perform the Johnson Noise Experiment, we used the Noise Fundamentals devices and two digital multi-meters. Our settings for the Noise Fundamentals devices were as follows: 10K ohm resistor, we used a Gain of 1000 for all values, we used a room temperature of 295 degrees Kelvin, and we varied the high and low pass filters' frequency for each data set in order to vary the bandwidth. We varied our high pass filter one as follows: we started with 10 Hz, 30 Hz, 100 Hz, 300 Hz, 1000 Hz, and 3000 Hz. We varied our low pass filter as follows: we started with 0.33K Hz, 1K Hz, 3.3K Hz, 10K Hz, 33K Hz, and 100K Hz. We recorded all the values from the multi-meter for each combination of filters. For example, when we had a low pass of 0.33K Hz, a high pass of 10 Hz, our measured value was $5.13$ mV. In the end, we took 36 sets of data points.  To analyze this data, we made a plot of resistance (ohms) versus $V^2$ so that we could analyze the slope. The equation used to understand why we did this is: $V^2 = 4 K T R \Delta f$, where K 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 bandwidth that we varied by changing the values on the low and high pass filters. After plotting $V^2$ versus Bandwidth ($\Delta f$), we were able to find the slope. Because of how we plotted the data, the slope is therefore: $4*K*R*T$ $4 K R T$  and we know the values of R and T because we kept them constant. After solving for K, we found the Boltzmann Constant for our data to be $1.908 * 10^-23 m^2 kg s^-2 K^-1$. 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$.  This is close to the actual Boltzmann Constant, but we still need to subtract error in order to see if we got a better value. \textit{Shot Noise}