The first experiment of class dealt with generating a graph of voltage across the capacitor vs. time so we could then attempt to generate an equation for the time it takes for a capacitor to reach full charge. Logger pro was used to measure voltage over a span of time.
After a graph for the voltage vs. time for a charging capacitor was generated, it could be easily seen that the voltage followed a pattern of exponential growth. A line was fit to the curve and an exponential equation was generated.
We then made a new graph for the voltage vs. time of a capacitor while it was discharging. We observed a similar pattern to that of the charging graph.
After generating equations for the two graphs, we then sought out to try and make sense of the constants that were given by the generated equations. We determined that the constant A was simply the initial voltage that was recorded at the start of the data collection. Constant B was simply a very low value that could be interpreted as zero and having no influence on the final voltage. In order to solver the constant C, we had to find a way in which the time unit canceled out since the total equation was supposed to be only in units of voltage. Through some tricky algebra, we discovered that the value for C was 1/RC.
We learned that the value of RC is referred to as the RC time constant and is denoted by the Greek letter Tau. We then began to explore the properties of the time constant.
Soon, we predicted the graph of current vs. time while a capacitor was charging and then learned that current in an RC circuit could also be written as a function of the time constant Tau.
With knowledge of the time constant, we then preformed a series of problems that dealt with finding how long it would take for an capacitor to charge or discharge to a specific value.
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