Pre-Lab 7 Assignment: Capacitors and RC Circuits

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Capacitors and RC Circuits v 0.3forms for decay or growth describe many physical and natural phenomena, such as radioactivedecay, the concentration of a reactant in a chemical reaction and the growth ofbacterial colonies.Mathematical reasoning based on the application of the definitions of resistance, currentand capacitance can be used to show that the following equation represents the potentialdifference across the capacitor, V, as a function of time:V(t) = V 0 e −t/RCIn this equation, V 0 is the initial potential difference across the capacitor. (Note that V 0is not necessarily the voltage of the battery.)Step 4: Utilize the fit routine in the software to examine whether an exponential decay accuratelyrepresents the behavior of the voltage across the capacitor as a function of time.Make sure you select and fit only that portion of the voltage graph where the voltage isdecaying (decreasing) - up to the point where the voltage just reaches its minimum value.Question 3.8 Record the equation as determined by the fit routine you used. How welldid the exponential function fit your data? Is the decay of voltage across the capacitor anexponential decay?Question 3.9 Find the value of RC from the exponent in the function that fit the data. Comparethis value to the one you calculated from the values of resistance and capacitance. Do theyagree? (Note that the resistance and capacitance values are each only known to an accuracy(tolerance) of about 10%.)When t = RC in the equation above, V = V 0 e −1 = 0.37V 0 . Thus RC is equal to the timeconstant.Question 3.10 How does the time constant you determined in step 3 compare with the value ofthe time constant you obtained by using the fit procedure in the later part of the above activity?If you have time after the above activities, do the following extension.Activity 3.3: Extension: Decay with Other Resistances and CapacitancesPrediction 3.1 How will the discharging behavior of a capacitor change if the capacitance ismade smaller? How do you think it will affect the time constant?PHYS-204:Physics II Laboratory 15
Capacitors and RC Circuits v 0.3Test your prediction.Step 1: Replace the 1F capacitor with the 3300µF capacitor. Note: Since this is a polarizedcapacitor, make sure you connect the positive end of the capacitor as shown in Fig. 6.Step 2: Start with the switch in position 2. Begin taking the data. When the graph linesappear on the screen, move the switch to position 1. Then move the switch to position 2.Step 3: Since this capacitor is considerably smaller than the one you first used, the decay issignificantly faster. Change the time scale on your graph so that you can clearly see thedecay of the voltage and current.Step 4: Select the portion of your graph that shows the decay after you moved the switch toposition 2. Record the equation as determined by the fit routine you used.Question E3.1 Use the constant in the exponent of the function given by the fit routineto determine the time constant for this circuit.Time constant:Did the time constant increase, decrease or stay the same? How does this compare withthe prediction you made prior to starting this activity?Question E3.2 Calculate the value of RC with the new capacitor. Is the time constantyou determined using the fit equal to the calculated value of RC?Prediction 3.2 How will the discharge of a capacitor change if the resistance it is connectedto doubled? How will this affect the time constant?Step 5: Increase the resistance to 20 ohms by adding a second 10 ohm resistor. (Use yourknowledge from resistors in series and parallel to figure out the appropriate configurationfor your two resistors i.e., in series or in parallel)Step 6: Collect data and graph the values for current and voltage while the capacitor is beingcharged and discharged. Use the fit routine to determine the mathematical form of thedischarging part of the graph, and write the formula with the values of the constantsgiven by the fit routine belowQuestion E3.3 Use the constant in the exponent of the function given by the fit routine todetermine the time constant. Did the time constant increase, decrease or stay the same? Howdoes the value obtained through the fit compare with your prediction?Time constant:PHYS-204:Physics II Laboratory 16
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Pre-Lab 7 Assignment: Capacitors and RC Circuits

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