4/28/15 - Introduction to Capacitance

We start off the class session with something a little familiar: Kirchoff's Laws.

We're given a circuit with some resistors and voltage supplies, and we're asked to find the current in all branches of the circuit. Since we know the resistance and voltage at all points, we're able to find currents at certain points and back sub to solve for all points.

Here we make a capacitor by definition, two plates of conductive material separated by a length of dielectric. We use my Linear Algebra book, the lab workbook, and two sheets of aluminum foil to create the capacitor.

We vary the amount of sheets of paper between the two sheets of foil, and that varies the capacitance of our capacitor. We record the data and plot a rough graph of the data.

Here is the graphed data points in LoggerPro, as the relationship shows, the capacitance is related to an inverse graph.

Given a general formula for capacitance, we are given a problem to find a 1 Fared capacitor with just paper and a sheet of metal. We found that it would take over 3 miles on flat ground if we were to use a single sheet of paper and lay it down flat to obtain a 1 Fared capacitor.

Here we measure a more standard capatior used in circuitrry with a multi-meter.

We now measure two in parallel.

Here we have our recorded values along with an explanation of why the values are what they are.

We found that capacitors in parallel have an additive capacitance, while capacitors in series have an additive inverse capacitance.

Now given a problem and asked to find the total capacitance of the circuit from point A to point B, we used our previous understanding of adding capacitors in parallel and series to find the total capacitance.

This picture is from the another group as indicated by the doggie in the corner. We had errors in our calculations and was unable to fix the values in time.

Now given a different circuit, we are given values of the capacitance and asked to find the voltage supply. Since we are given the voltage at one point, we are able to find all unknowns with the formula C = Q / V.

We first solve for the second capacitor in series and find an equation for the voltage. We then found the total voltage of the supply.

Manipulation the formula C = Q / V, we can find the charge at any of the points. When asked for the point with the most charge, our answer of C3 made sense mathematically and logically.

We concluded with the calculation of  the total work done to charge the capacitors.

Since we found a total capacitance, we used that and the total voltage to find the work done in a simple formula. We then cross checked it with out initial values and summed them up for the same answer.