Capacitance Lab: Exploring Charging, Discharging, and Effects

Melissa Haddadi / Jerimiah Martin Lab 3 : Capacitance Introduction: In this lab, we learned the concept behind the capacitors being charged/discharged. We examined the relationship between capacitance and distance of plate separation and how the separation of the plates affected the capacitance of parallel plate capacitor. Procedure: Part1: We had to build a circuit with a C = 10 µF capacitor and R = 100 k Ω resistor. We attached the red positive lead of the voltage probe to the side of the capacitor connected to the resistor, and connected the black lead to the other side of the capacitor. Then we started collecting data, first, on discharging when the 100 k Ω resistor is in the circuit, then on charging. We also repeated the experiment with a lower value resistor 47 k Ω resistor. Part2: WE set up the equipment with the parallel plate capacitor connected to the electrometer via the locking BNC connector then wired leads to the 30V output and ground of the voltage source. We chargeed the capacitor a single time and then recorded the electrometer reading as we vary the separation distance Data:

47 k Ω resistor

Precautions and Sources of Error: incorrect layout, wire placing Questions: Question 1. How do the shapes of the charging and discharging graphs compare? The charging graph increases exponentially during the charging process, and the discharging graph decays exponentially. So t hey are the reciprocal of each other. Question 2. Compare the fit function parameter B to the time constant RC in Equations 2 and 3. How are they related? they share a time constant because of same resistance and capacitance values.

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Question 3. How close were the actual (measured) time constants to what you expected given the nominal values of resistance and capacitance (calculate percent difference)? Question 4. Look at your graphs for 47k vs. those for 100k. Qualitatively speaking, what effect did decreasing the resistance have on capacitor discharging/ charging times? The time constant RC decreased subsequently. Question 5. For the 100k data, did your charging and discharging have about the same time constant? Should they have the same time constant? No, the charging and discharging phases had different time constants and they should not have the same time constant because time constant is larger during the discharging process. Question 6. How would the graphs of your discharge data look if, instead of plotting the potential vs. time, you plotted the natural logarithm of the potential vs. time? Sketch a prediction. Now plot it by selecting your ‘discharging 100k’ data and hiding the other runs. Highlight the discharging part of the run and then click on the y-axis label and select ln(V). What is the significance of the slope of the plot of ln(V) vs. time for a capacitor discharge circuit? Hint: take the natural log of both sides of Equation 2 the natural logarithm of potential vs time graph will have a negative slope with a positive value for the y intercept. It increases while time decrease and RC is the time constant. Question 7. What percentage of the initial potential remains after one time constant has passed? After two time constants? Three? = e^ (-1) = 36.80% = e^ (-2) = 13.50% = e^ (-3) = 4.99%

Question 8. Our plan is to place a fixed amount of charge on the plates and then measure the voltage on the plates as we vary their separation; how does measuring the voltage across the plates give us information about the capacitance ? Measuring the voltage across the plates will examine capacitance since it is related to charge and voltage. Question 9. What does the graph of voltage vs. plate separation look like? How does the potential vary with separation? The graph of voltage vs. plate separation is a diagonal linear line. the potential variation with separation is proportional and even. Question 10. Based on the results of the investigation of a parallel-plate capacitor, how does its capacitance vary with the separation distance d ? the capacitance increases when the separation distance d in increased Discussion: During the experiment there was a source of error that prevented us from completing the lab successfully. The setup of the circuit was incorrect so that prevented us from getting accurate graphs so we had to use our classmates results for this lab.

Lab3

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