The Neuron - RC Circuit LAB PDF

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RC Circuit LAB...

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The Neuron - RC Circuit LAB 1. Take a screenshot of the neuron simulation with the Potential Chart of Membrane Potential vs. time. Paste the screenshot into your report.

2. Describe how a RC circuit is a model of a neuron? What parts of the RC circuit correspond to parts of the neuron? The neuron is comparable to to a RC circuit because energy is stored in the neuron through the motion of sodium Na and potassium K ions. When the neuron is stimulated, it’s like the red wire being plugged into the PASCO 550. When the membrane potential decreases after being stimulated, it’s representative of the red wire being pulled out of the PASCO 550 a few seconds later. The time it takes for the voltage of the neuron to return to its original value is known as a time constant. +

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3. What will you measure to determine the time constant of a RC circuit? The time constant value measures how long it takes for voltage to return to its original value. You calculate this using the capacitance (F) of the capacitor and resistance ( ) of the resistor. This explains the equation

4. Describe the voltage across the capacitor before and after the red wire to the PASCO 550 is connected then disconnected. Does the voltage remain constant or does it change with time? Is it increasing or decreasing? Is it changing in a linear or nonlinear way?

The voltage is zero before the red wire is connected to the PASCO 550. When connected, the voltage increases, spikes to ~5V and stays constant for the time that it is kept plugged in. When the red wire is removed from the PASCO 550, the voltage decreases over time at a nonlinear (exponential) rate.

5. What kind of mathematical formula (model) describes the voltage across the capacitor? An exponential formula (model) describes the voltage across the capacitor.

6. In Capstone click the menu “Display.” Choose “Copy Display” and paste into report.

7. In Capstone click the menu ”File.” Choose “Export Data.” Select the “Save as type” CSV. Give the file a name you recognized like your NetID_RC_discharge.csv. Upload the file to your Google Drive. *See excel sheet*

8. Make a plot of

vs. in Google Sheets.

As you look at your plot of vs. you want to represent your data in a linearized way. The time constant is one of the two parameters (slope and intercept ) that can be determined from a linear fit.

9. If your plot of vs. is an exponential, how will you transform the data of and to linearize your data? To linearize the data, I will transform the data of and by taking the natural log. I can then use the linearized equation y = mx + c. This will translate to ln(V (t)) = ln(V ) + (-t/T) where the slope (m) is ln(V ) and the intercept (b) is (t/T). c

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10. Calculated the linearized data. *see excel sheet*

11. Make a plot of your linearized data.

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12. Perform a linear fit to your linearized variables using LINEST(). Select a range of 10 values of your linearized data. *see excel sheet*

13. What are the values of slope and intercept Slope: -0.04213731151 Uncertainty of Slope: 0.1609018409 Intercept: -1.425179774 Uncertainty of Intercept: 0.951908128

with their respective uncertainties?

14. What is the relationship of the slope or intercept to the the time constant ? The relationship of the slope (m) is that it is the inverse of the time constant.

15. On a new page in your spreadsheet enter your value of the slope and its uncertainty from your linear fit. Use the function NORMINV() and RAND() to calculate a random value of slope . Repeat the calculation 500 times.

*see excel sheet*

16. For each of 500 values of the slope *see excel sheet*

calculate a value of

17. The resistor in the RC circuit is NORMINV() and RAND() to calculate a random value of times. *see excel sheet*

.

. Use the function . Repeat the calculation 500

18. Calculate the capacitance for each of the 500 values of and . What is the average and standard deviation of ? *values subject to change on excel sheet due to NORMINV() and RAND()* Average of C: -0.0001327 Standard deviation of C: 0.00006625

19. Perform a T-test to compare your experimental value of to the expected value calculated in question. Is your experimental value consistent with the expected value? Use this link and look up the p-value for either the one-tail or two-tail T-distribution. https://www.statisticshowto.datasciencecentral.com/tables/t-distribution-table/

not

Given value from TA: 150 µF (Circuit 3) SEM = 0.000022 T-value = 12.801 My T-value is 12.801, therefore it could not be converted to a P value because it’s too large. Thus, it is insignificant and the experimental capacitance (C) is statistically close enough to the known value to be significant....