Capacitors and Capcitance

The day began with a recap on capacitors and capacitance. We began by doing some work on the lab manual predicting how capacitors would behave and constructing a graph representing how the brightness of a bulb would change over time if a charged capacitor was input into a closed circuit as a power source. We predicted that the brightness would decrease at an exponential rate until the capacitor ran out of power. We also found that the voltage would remain the same throughout the close circuit and as a result the charge would also remain the same, which goes back to the basics of current and voltage learned at the beginning. We also recapped on the behavior of capacitors in series and in parallel. We said that when capacitors were in series, the voltage increases because as the capacitance decreases, the charge remains the same and the voltage gets larger and it would work the opposite for capacitors in parallel. Finally, we measured some of the voltage of batteries in order to see whether our predictions made sense since capacitors also work as batteries.

Below is a picture of the set up we had in order to test for the voltage of the closed circuit.

In order to further understand the behavior of capacitors, Mason decided to let us use Logger Pro and graph the behavior of the capacitors as time increases when a capacitor was charging and when it was losing power. The graph below shows the graph of when the capacitor was decreasing in electric potential, or discharging. 

Below is a data table of the points that were used to make the graph above.

Below is a picture of how the set up was made when we were measuring for the electric potential of the capacitor when charging or when discharging.

The graph of the capacitor charging is shown below. As time increases, the electric potential grows exponentially meaning that potential energy is being stored within the capacitor until it reaches the maximum charge it can hold.

The data table of the data points for the graph above are shown below.

After looking at the behavior of the graphs, we can finally use Logger Pro and construct the best fit for the graphs and thus it led to the theory of exponential decay which showed how the voltage decreases over a period of time. All the derivations are shown below.

Then we decided to work with the theory of exponential decay and solve a problem which asked to find many unknown variables within that equation. We also graphed the relationship between voltage, brightness and current with respect to time with respect to the exponential decay.

Overall, we learned more about capacitors but the main focus of the class was showing how capacitors gained or lost charge and relating it to exponential decay and charge buildup