Quantitative Measurements on an RC System
For the following experiment we were asked to create an RC circuit with a resistor, power supply, and capacitor in series (this had to be done otherwise the charge time was too rapid to see). We hooked up the capacitor to logger pro using a voltage measuring lead. However, before this we made a few predictions. Primarily that the relationship between Potential (Voltage) and time would be inversely related as seen below. After logging all of our data we had the following graph.
By looking solely at the Discharge portion (pink line) we came up with a few conclusions. The first conclusion we came up with was that B in the natural exponential equation should be fairly close to 0. We also concluded that the A value should be our close to our original 4.5 Voltage (from the power supply). Our final conclusion was that C was our charge time which should have been the same for both Discharge and Charge. Our ideas are summarized below.
After finding our experimental value for the charge time, C=0.003620 sec., we theoretically found what the charge time of circuit should have been. In order to do this we first used a multimeter to determine the resistance of our resistor, R=2.15 kΩ. We next used the relationship we discovered: t=1/RC where R=Resistance and C=Capacitance to solve for our theoretical value of charge time. What we found is that theoretically the charge time should have been .00465 sec. That means there was a 22% error. This large error could be due to the fact that in our theoretical value we took the capacitors value straight off the labeling and it may have in fact been lower or higher.
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