Pre-Lab 7 Assignment: Capacitors and RC Circuits

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